Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Entanglement as a signature of quantum chaos.

PubMed

Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

2004-01-01

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum-Classical Dynamics.

PubMed

Crespo-Otero, Rachel; Barbatti, Mario

2018-05-16

Nonadiabatic mixed quantum-classical (NA-MQC) dynamics methods form a class of computational theoretical approaches in quantum chemistry tailored to investigate the time evolution of nonadiabatic phenomena in molecules and supramolecular assemblies. NA-MQC is characterized by a partition of the molecular system into two subsystems: one to be treated quantum mechanically (usually but not restricted to electrons) and another to be dealt with classically (nuclei). The two subsystems are connected through nonadiabatic couplings terms to enforce self-consistency. A local approximation underlies the classical subsystem, implying that direct dynamics can be simulated, without needing precomputed potential energy surfaces. The NA-MQC split allows reducing computational costs, enabling the treatment of realistic molecular systems in diverse fields. Starting from the three most well-established methods-mean-field Ehrenfest, trajectory surface hopping, and multiple spawning-this review focuses on the NA-MQC dynamics methods and programs developed in the last 10 years. It stresses the relations between approaches and their domains of application. The electronic structure methods most commonly used together with NA-MQC dynamics are reviewed as well. The accuracy and precision of NA-MQC simulations are critically discussed, and general guidelines to choose an adequate method for each application are delivered.

Quantum localization for a kicked rotor with accelerator mode islands.

PubMed

Iomin, A; Fishman, S; Zaslavsky, G M

2002-03-01

Dynamical localization of classical superdiffusion for the quantum kicked rotor is studied in the semiclassical limit. Both classical and quantum dynamics of the system become more complicated under the conditions of mixed phase space with accelerator mode islands. Recently, long time quantum flights due to the accelerator mode islands have been found. By exploration of their dynamics, it is shown here that the classical-quantum duality of the flights leads to their localization. The classical mechanism of superdiffusion is due to accelerator mode dynamics, while quantum tunneling suppresses the superdiffusion and leads to localization of the wave function. Coupling of the regular type dynamics inside the accelerator mode island structures to dynamics in the chaotic sea proves increasing the localization length. A numerical procedure and an analytical method are developed to obtain an estimate of the localization length which, as it is shown, has exponentially large scaling with the dimensionless Planck's constant (tilde)h<1 in the semiclassical limit. Conditions for the validity of the developed method are specified.

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Sang-Bong

1993-09-01

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaoticmore » nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.« less

Quantum-to-classical crossover near quantum critical point

DOE PAGES

Vasin, M.; Ryzhov, V.; Vinokur, V. M.

2015-12-21

A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while non-dissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transitionmore » from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d+zΛ(T), where z is the dynamical exponent, and temperature-depending parameter Λ(T)ε[0, 1] decreases with the temperature such that Λ(T=0) = 1 and Λ(T →∞) = 0. Lastly, our findings lead to a unified picture of quantum critical phenomena including both dissipation- and dissipationless quantum dynamic effects and offer a quantitative description of the quantum-to-classical crossover.« less

Application of Dirac's Generalized Hamiltonian Dynamics to Atomic and Molecular Systems

NASA Astrophysics Data System (ADS)

Uzer, Turgay

2002-10-01

Incorporating electronic degrees of freedom into classical treatments of atoms and molecules is a challenging problem from both the practical and fundamental points of view. Because it goes to the heart of classical-quantal correspondence, there are now a number of prescriptions which differ by the extent of quantal information that they include. We reach back to Dirac for inspiration, who, half a century ago, designed a so-called Generalized Hamiltonian Dynamics (GHD) with applications to field theory in mind. Physically, the GHD is a purely classical formalism for systems with constraints; it incorporates the constraints into the Hamiltonian. We apply the GHD to atomic and molecular physics by choosing integrals of motion as the constraints. We show that this purely classical formalism allows the derivation of energies of non-radiating states.

Density-functional theory simulation of large quantum dots

NASA Astrophysics Data System (ADS)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

NASA Astrophysics Data System (ADS)

Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

1990-12-01

Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

Classical dynamics on curved Snyder space

NASA Astrophysics Data System (ADS)

Ivetić, B.; Meljanac, S.; Mignemi, S.

2014-05-01

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parameterizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Including Memory Friction in Single- and Two-State Quantum Dynamics Simulations.

PubMed

Brown, Paul A; Messina, Michael

2016-03-03

We present a simple computational algorithm that allows for the inclusion of memory friction in a quantum dynamics simulation of a small, quantum, primary system coupled to many atoms in the surroundings. We show how including a memory friction operator, F̂, in the primary quantum system's Hamiltonian operator builds memory friction into the dynamics of the primary quantum system. We show that, in the harmonic, semi-classical limit, this friction operator causes the classical phase-space centers of a wavepacket to evolve exactly as if it were a classical particle experiencing memory friction. We also show that this friction operator can be used to include memory friction in the quantum dynamics of an anharmonic primary system. We then generalize the algorithm so that it can be used to treat a primary quantum system that is evolving, non-adiabatically on two coupled potential energy surfaces, i.e., a model that can be used to model H atom transfer, for example. We demonstrate this approach's computational ease and flexibility by showing numerical results for both harmonic and anharmonic primary quantum systems in the single surface case. Finally, we present numerical results for a model of non-adiabatic H atom transfer between a reactant and product state that includes memory friction on one or both of the non-adiabatic potential energy surfaces and uncover some interesting dynamical effects of non-memory friction on the H atom transfer process.

Thermalization dynamics in a quenched many-body state

NASA Astrophysics Data System (ADS)

Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus

2016-05-01

Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.

The dynamical mass of a classical Cepheid variable star in an eclipsing binary system.

PubMed

Pietrzyński, G; Thompson, I B; Gieren, W; Graczyk, D; Bono, G; Udalski, A; Soszyński, I; Minniti, D; Pilecki, B

2010-11-25

Stellar pulsation theory provides a means of determining the masses of pulsating classical Cepheid supergiants-it is the pulsation that causes their luminosity to vary. Such pulsational masses are found to be smaller than the masses derived from stellar evolution theory: this is the Cepheid mass discrepancy problem, for which a solution is missing. An independent, accurate dynamical mass determination for a classical Cepheid variable star (as opposed to type-II Cepheids, low-mass stars with a very different evolutionary history) in a binary system is needed in order to determine which is correct. The accuracy of previous efforts to establish a dynamical Cepheid mass from Galactic single-lined non-eclipsing binaries was typically about 15-30% (refs 6, 7), which is not good enough to resolve the mass discrepancy problem. In spite of many observational efforts, no firm detection of a classical Cepheid in an eclipsing double-lined binary has hitherto been reported. Here we report the discovery of a classical Cepheid in a well detached, double-lined eclipsing binary in the Large Magellanic Cloud. We determine the mass to a precision of 1% and show that it agrees with its pulsation mass, providing strong evidence that pulsation theory correctly and precisely predicts the masses of classical Cepheids.

Classical molecular dynamics simulation of electronically non-adiabatic processes.

PubMed

Miller, William H; Cotton, Stephen J

2016-12-22

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

Quench dynamics of a dissipative Rydberg gas in the classical and quantum regimes

NASA Astrophysics Data System (ADS)

Gribben, Dominic; Lesanovsky, Igor; Gutiérrez, Ricardo

2018-01-01

Understanding the nonequilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time postquench quantum dynamics. In classical many-body systems, the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first-order phase transition. Here, we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum nonequilibrium effects. We are able to gain an analytical understanding of the time evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a nonequilibrium phase transition and provides an approximate analytical solution deep in the quantum domain.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

PubMed

Marsalek, Ondrej; Markland, Thomas E

2016-02-07

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Relativistic quantum Darwinism in Dirac fermion and graphene systems

NASA Astrophysics Data System (ADS)

Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

2012-02-01

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

Surface-hopping dynamics and decoherence with quantum equilibrium structure.

PubMed

Grunwald, Robbie; Kim, Hyojoon; Kapral, Raymond

2008-04-28

In open quantum systems, decoherence occurs through interaction of a quantum subsystem with its environment. The computation of expectation values requires a knowledge of the quantum dynamics of operators and sampling from initial states of the density matrix describing the subsystem and bath. We consider situations where the quantum evolution can be approximated by quantum-classical Liouville dynamics and examine the circumstances under which the evolution can be reduced to surface-hopping dynamics, where the evolution consists of trajectory segments exclusively evolving on single adiabatic surfaces, with probabilistic hops between these surfaces. The justification for the reduction depends on the validity of a Markovian approximation on a bath averaged memory kernel that accounts for quantum coherence in the system. We show that such a reduction is often possible when initial sampling is from either the quantum or classical bath initial distributions. If the average is taken only over the quantum dispersion that broadens the classical distribution, then such a reduction is not always possible.

Terminal Model Of Newtonian Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

Dynamic condensation of non-classically damped structures using the method of Maclaurin expansion of the frequency response function in Laplace domain

NASA Astrophysics Data System (ADS)

Esmaeilzad, Armin; Khanlari, Karen

2018-07-01

As the number of degrees of freedom (DOFs) in structural dynamic problems becomes larger, the analyzing complexity and CPU usage of computers increase drastically. Condensation (or reduction) method is an efficient technique to reduce the size of the full model or the dimension of the structural matrices by eliminating the unimportant DOFs. After the first presentation of condensation method by Guyan in 1965 for undamped structures, which ignores the dynamic effects of the mass term, various forms of dynamic condensation methods were presented to overcome this issue. Moreover, researchers have tried to expand the dynamic condensation method to non-classically damped structures. Dynamic reduction of such systems is far more complicated than undamped systems. The proposed non-iterative method in this paper is introduced as 'Maclaurin Expansion of the frequency response function in Laplace Domain' (MELD) applied for dynamic reduction of non-classically damped structures. The present approach is implemented in four numerical examples of 2D bending-shear-axial frames with various numbers of stories and spans and also a floating raft isolation system. The results of natural frequencies and dynamic responses of models are compared with each other before and after the dynamic reduction. It is shown that the result accuracy has acceptable convergence in both cases. In addition, it is indicated that the result of the proposed method is more accurate than the results of some other existing condensation methods.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.

ERIC Educational Resources Information Center

Gannon, Gerald E.; Martelli, Mario U.

2001-01-01

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Epidemic Dynamics in Open Quantum Spin Systems

NASA Astrophysics Data System (ADS)

Pérez-Espigares, Carlos; Marcuzzi, Matteo; Gutiérrez, Ricardo; Lesanovsky, Igor

2017-10-01

We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.

Quantum algorithm for energy matching in hard optimization problems

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.

2018-06-01

We consider the ability of local quantum dynamics to solve the "energy-matching" problem: given an instance of a classical optimization problem and a low-energy state, find another macroscopically distinct low-energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here, we show that the introduction of quantum dynamics can provide a speedup over classical algorithms in a large class of hard optimization problems. Tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. Specifically, we study energy matching in the random p -spin model of spin-glass theory. Using perturbation theory and exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field "trapped" phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field "excited" phase, in which the field excites the system into high-energy states, effectively forgetting the initial energy; and (3) the intermediate "tunneling" phase, in which the system succeeds at energy matching. The rate at which distant states are found in the tunneling phase, although exponentially slow in system size, is exponentially faster than classical search algorithms.

Trivial dynamics in discrete-time systems: carrying simplex and translation arcs

NASA Astrophysics Data System (ADS)

Niu, Lei; Ruiz-Herrera, Alfonso

2018-06-01

In this paper we show that the dynamical behavior in (first octant) of the classical Kolmogorov systems of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points in with local attractors on the carrying simplex and local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in Int. Our results are applied to some classical models including the Leslie–Gower models, Atkinson-Allen systems and Ricker maps.

Classical simulation of quantum error correction in a Fibonacci anyon code

NASA Astrophysics Data System (ADS)

Burton, Simon; Brell, Courtney G.; Flammia, Steven T.

2017-02-01

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128 ×128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for Abelian and (nonuniversal) non-Abelian anyon models.

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

NASA Astrophysics Data System (ADS)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

The Adiabatic Invariance of the Action Variable in Classical Dynamics

ERIC Educational Resources Information Center

Wells, Clive G.; Siklos, Stephen T. C.

2007-01-01

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We present a new proof of the adiabatic invariance of this quantity and illustrate our arguments by means of…

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

NASA Astrophysics Data System (ADS)

López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marsalek, Ondrej; Markland, Thomas E., E-mail: tmarkland@stanford.edu

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding asmore » a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.« less

Application of quantum Darwinism to a structured environment

NASA Astrophysics Data System (ADS)

Pleasance, Graeme; Garraway, Barry M.

2017-12-01

Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual "pseudomode" components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countably many quasistable states has at least the computational power of a universal Turing machine. Such an analysis assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countablely many quasistable states has at least the computational power of a universal Turing machine. Such an analyses assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khrennikov, Andrei

2010-08-15

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Classical Limit and Quantum Logic

NASA Astrophysics Data System (ADS)

Losada, Marcelo; Fortin, Sebastian; Holik, Federico

2018-02-01

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Experimental studies of tuned particle damper: Design and characterization

NASA Astrophysics Data System (ADS)

Zhang, Kai; Xi, Yanhui; Chen, Tianning; Ma, Zhihao

2018-01-01

To better suppress the structural vibration in the micro vibration and harsh environment, a new type of damper, tuned particle damper (TPD), was designed by combining the advantage of classical dynamic vibration absorber (DVA) and particle damper (PD). An equivalent theoretical model was established to describe the dynamic behavior of a cantilever system treated with TPD. By means of a series of sine sweep tests, the dynamic characteristic of TPD under different excitation intensity was explored and the damping performance of TPD was investigated by comparing with classical DVA and PD with the same mass ratio. Experimental results show that with the increasing of excitation intensity TPD shows two different dynamic characteristics successively, i.e., PD-like and DVA-like. TPD shows a wider suppression frequency band than classical DVA and better practicability than PD in the micro vibration environment. Moreover, to characterize the dynamic characteristic of TPD, a simple evaluation of the equivalent dynamic mass and equivalent dynamic damping of the cantilever system treated with TPD was performed by fitting the experimental data to the presented theoretical model. Finally, based on the rheology behaviors of damping particles reported by the previous research results, an approximate phase diagram which shows the motion states of damping particles in TPD was employed to analyze the dynamic characteristic of TPD and several motion states of damping particles in TPD were presented via a high-speed camera.

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

NASA Astrophysics Data System (ADS)

Kadowaki, Tadashi

2018-02-01

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alonso, J. L.; Instituto de Biocomputacion y Fisica de Sistemas Complejos; Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza

2012-08-07

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamicsmore » makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de; Homrighausen, Ingo; Kehrein, Stefan

We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurementsmore » in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.« less

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr's doctrine of classical concepts?

NASA Astrophysics Data System (ADS)

Camilleri, Kristian; Schlosshauer, Maximilian

2015-02-01

Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum-classical transition that were pursued by several of Bohr's followers and culminated in the development of decoherence theory.

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

NASA Astrophysics Data System (ADS)

Kreis, Karsten; Kremer, Kurt; Potestio, Raffaello; Tuckerman, Mark E.

2017-12-01

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

NASA Astrophysics Data System (ADS)

Chen, Hong-Bin; Gneiting, Clemens; Lo, Ping-Yuan; Chen, Yueh-Nan; Nori, Franco

2018-01-01

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.

Toward simulating complex systems with quantum effects

NASA Astrophysics Data System (ADS)

Kenion-Hanrath, Rachel Lynn

Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation parameters, and demonstrate the ability of this approach to optimize MQC-IVR simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stabilitymore » parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.« less

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

PubMed

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.

Driven topological systems in the classical limit

NASA Astrophysics Data System (ADS)

Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

2017-03-01

Periodically driven quantum systems can exhibit topologically nontrivial behavior, even when their quasienergy bands have zero Chern numbers. Much work has been conducted on noninteracting quantum-mechanical models where this kind of behavior is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The noninteracting model, proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013), 10.1103/PhysRevX.3.031005], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time-dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.

Approximate Quantum Dynamics using Ab Initio Classical Separable Potentials: Spectroscopic Applications.

PubMed

Hirshberg, Barak; Sagiv, Lior; Gerber, R Benny

2017-03-14

Algorithms for quantum molecular dynamics simulations that directly use ab initio methods have many potential applications. In this article, the ab initio classical separable potentials (AICSP) method is proposed as the basis for approximate algorithms of this type. The AICSP method assumes separability of the total time-dependent wave function of the nuclei and employs mean-field potentials that govern the dynamics of each degree of freedom. In the proposed approach, the mean-field potentials are determined by classical ab initio molecular dynamics simulations. The nuclear wave function can thus be propagated in time using the effective potentials generated "on the fly". As a test of the method for realistic systems, calculations of the stationary anharmonic frequencies of hydrogen stretching modes were carried out for several polyatomic systems, including three amino acids and the guanine-cytosine pair of nucleobases. Good agreement with experiments was found. The method scales very favorably with the number of vibrational modes and should be applicable for very large molecules, e.g., peptides. The method should also be applicable for properties such as vibrational line widths and line shapes. Work in these directions is underway.

Entanglement in Quantum-Classical Hybrid

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

Dynamic Network-Based Epistasis Analysis: Boolean Examples

PubMed Central

Azpeitia, Eugenio; Benítez, Mariana; Padilla-Longoria, Pablo; Espinosa-Soto, Carlos; Alvarez-Buylla, Elena R.

2011-01-01

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches. PMID:22645556

Modeling light-induced charge transfer dynamics across a metal-molecule-metal junction: Bridging classical electrodynamics and quantum dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar, E-mail: t-seideman@northwestern.edu

2014-12-14

We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify ourmore » approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.« less

One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping

NASA Astrophysics Data System (ADS)

Silva, L. D. Da; Dos Santos, J. L. L.; Ranciaro Neto, A.; Sales, M. O.; de Moura, F. A. B. F.

In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron-phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron-lattice interaction promote a sub-diffusive electronic dynamics.

Classicalization by phase space measurements

NASA Astrophysics Data System (ADS)

Bolaños, Marduk

2018-05-01

This article provides an illustration of the measurement approach to the quantum–classical transition suitable for beginning graduate students. As an example, we apply this framework to a quantum system with a general quadratic Hamiltonian, and obtain the exact solution of the dynamics for an arbitrary measurement strength using phase space methods.

Experimental Demonstration of Coherent Control in Quantum Chaotic Systems

NASA Astrophysics Data System (ADS)

Bitter, M.; Milner, V.

2017-01-01

We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.

Quantum-to-classical transition and entanglement sudden death in Gaussian states under local-heat-bath dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goyal, Sandeep K.; Ghosh, Sibasish

2010-10-15

Entanglement sudden death (ESD) in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterization of classicality in Gaussian states, the time to ESD is calculated by analyzing the covariance matrices of the system. The results for the two-mode system at T=0 and T>0 for the two types of bath states are generalized to n modes, and are shown to be similar in nature to the results for the general discrete n-qubit system.

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Generic emergence of classical features in quantum Darwinism.

PubMed

Brandão, Fernando G S L; Piani, Marco; Horodecki, Paweł

2015-08-12

Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.

Generic emergence of classical features in quantum Darwinism

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Piani, Marco; Horodecki, Paweł

2015-08-01

Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.

Periodic solutions of a spring-pendulum system.

NASA Technical Reports Server (NTRS)

Broucke, R.; Baxa, P. A.

1973-01-01

A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular, the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.

Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition

NASA Astrophysics Data System (ADS)

Bose, Chandan; Sarkar, Sunetra

2018-04-01

The present study investigates the complex vortex interactions in two-dimensional flow-field behind a symmetric NACA0012 airfoil undergoing a prescribed periodic pitching-plunging motion in low Reynolds number regime. The flow-field transitions from periodic to chaotic through a quasi-periodic route as the plunge amplitude is gradually increased. This study unravels the role of the complex interactions that take place among the main vortex structures in making the unsteady flow-field transition from periodicity to chaos. The leading-edge separation plays a key role in providing the very first trigger for aperiodicity. Subsequent mechanisms like shredding, merging, splitting, and collision of vortices in the near-field that propagate and sustain the disturbance have also been followed and presented. These fundamental mechanisms are seen to give rise to spontaneous and irregular formation of new vortex couples at arbitrary locations, which are the primary agencies for sustaining chaos in the flow-field. The interactions have been studied for each dynamical state to understand the course of transition in the flow-field. The qualitative changes observed in the flow-field are manifestation of changes in the underlying dynamical system. The overall dynamics are established in the present study by means of robust quantitative measures derived from classical and non-classical tools from the dynamical system theory. As the present analysis involves a high fidelity multi-unknown system, non-classical dynamical tools such as recurrence-based time series methods are seen to be very efficient. Moreover, their application is novel in the context of pitch-plunge flapping flight.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system.

PubMed

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Dynamic sensitivity analysis of biological systems

PubMed Central

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2008-01-01

Background A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. Results We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. Conclusion By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input. PMID:19091016

Multivariable Hermite polynomials and phase-space dynamics

NASA Technical Reports Server (NTRS)

Dattoli, G.; Torre, Amalia; Lorenzutta, S.; Maino, G.; Chiccoli, C.

1994-01-01

The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.

Computation and Dynamics: Classical and Quantum

NASA Astrophysics Data System (ADS)

Kisil, Vladimir V.

2010-05-01

We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed quantum-classical dynamics we look for a full cost of computations on quantum computers with classical terminals.

Correlated electron-nuclear dissociation dynamics: classical versus quantum motion

NASA Astrophysics Data System (ADS)

Schaupp, Thomas; Albert, Julian; Engel, Volker

2017-01-01

We investigate the coupled electron-nuclear dynamics in a model system which undergoes dissociation. In choosing different initial conditions, the cases of adiabatic and non-adiabatic dissociation are realized. We treat the coupled electronic and nuclear motion in the complete configuration space so that classically, no surface hopping procedures have to be incorporated in the case that more than a single adiabatic electronic state is populated during the fragmentation. Due to the anharmonic interaction potential, it is expected that classical mechanics substantially deviate from quantum mechanics. However, we provide examples where the densities and fragmentation yields obtained from the two treatments are in astonishingly strong agreement in the case that one starts in the electronic ground state initially. As expected, larger deviations are found if one starts in electronically excited states where trajectories are sampled from the more spatially extended electronic wave function. In that case, higher initial energies are accessed, and the motion proceeds in regions with increasing degree of anharmonicity. Contribution to the Topical Issue "Dynamics of Molecular Systems (MOLEC 2016)", edited by Alberto Garcia-Vela, Luis Banares and Maria Luisa Senent.

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Dynamic facial expressions of emotion transmit an evolving hierarchy of signals over time.

PubMed

Jack, Rachael E; Garrod, Oliver G B; Schyns, Philippe G

2014-01-20

Designed by biological and social evolutionary pressures, facial expressions of emotion comprise specific facial movements to support a near-optimal system of signaling and decoding. Although highly dynamical, little is known about the form and function of facial expression temporal dynamics. Do facial expressions transmit diagnostic signals simultaneously to optimize categorization of the six classic emotions, or sequentially to support a more complex communication system of successive categorizations over time? Our data support the latter. Using a combination of perceptual expectation modeling, information theory, and Bayesian classifiers, we show that dynamic facial expressions of emotion transmit an evolving hierarchy of "biologically basic to socially specific" information over time. Early in the signaling dynamics, facial expressions systematically transmit few, biologically rooted face signals supporting the categorization of fewer elementary categories (e.g., approach/avoidance). Later transmissions comprise more complex signals that support categorization of a larger number of socially specific categories (i.e., the six classic emotions). Here, we show that dynamic facial expressions of emotion provide a sophisticated signaling system, questioning the widely accepted notion that emotion communication is comprised of six basic (i.e., psychologically irreducible) categories, and instead suggesting four. Copyright © 2014 Elsevier Ltd. All rights reserved.

Application of the GRC Stirling Convertor System Dynamic Model

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.; Schreiber, Jeffrey G. (Technical Monitor)

2004-01-01

The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.

Non-Markovian Complexity in the Quantum-to-Classical Transition

PubMed Central

Xiong, Heng-Na; Lo, Ping-Yuan; Zhang, Wei-Min; Feng, Da Hsuan; Nori, Franco

2015-01-01

The quantum-to-classical transition is due to environment-induced decoherence, and it depicts how classical dynamics emerges from quantum systems. Previously, the quantum-to-classical transition has mainly been described with memory-less (Markovian) quantum processes. Here we study the complexity of the quantum-to-classical transition through general non-Markovian memory processes. That is, the influence of various reservoirs results in a given initial quantum state evolving into one of the following four scenarios: thermal state, thermal-like state, quantum steady state, or oscillating quantum nonstationary state. In the latter two scenarios, the system maintains partial or full quantum coherence due to the strong non-Markovian memory effect, so that in these cases, the quantum-to-classical transition never occurs. This unexpected new feature provides a new avenue for the development of future quantum technologies because the remaining quantum oscillations in steady states are decoherence-free. PMID:26303002

Shortcuts to adiabaticity using flow fields

NASA Astrophysics Data System (ADS)

Patra, Ayoti; Jarzynski, Christopher

2017-12-01

A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Computational quantum-classical boundary of noisy commuting quantum circuits

PubMed Central

Fujii, Keisuke; Tamate, Shuhei

2016-01-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039

Computational quantum-classical boundary of noisy commuting quantum circuits.

PubMed

Fujii, Keisuke; Tamate, Shuhei

2016-05-18

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Computational quantum-classical boundary of noisy commuting quantum circuits

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Tamate, Shuhei

2016-05-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

SIAM conference on applications of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

NASA Astrophysics Data System (ADS)

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems—a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solutions based upon mixed quantum-classical approximation. I. Proton transfer reaction in water

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu, E-mail: okazaki@apchem.nagoya-u.ac.jp

2014-08-28

In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfermore » process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.« less

Out-of-time-ordered measurements as a probe of quantum dynamics

NASA Astrophysics Data System (ADS)

Bordia, Pranjal; Alet, Fabien; Hosur, Pavan

2018-03-01

Probing the out-of-equilibrium dynamics of quantum matter has gained renewed interest owing to immense experimental progress in artificial quantum systems. Dynamical quantum measures such as the growth of entanglement entropy and out-of-time-ordered correlators (OTOCs) have been shown to provide great insight by exposing subtle quantum features invisible to traditional measures such as mass transport. However, measuring them in experiments requires either identical copies of the system, an ancilla qubit coupled to the whole system, or many measurements on a single copy, thereby making scalability extremely complex and hence, severely limiting their potential. Here, we introduce an alternative quantity, the out-of-time-ordered measurement (OTOM), which involves measuring a single observable on a single copy of the system, while retaining the distinctive features of the OTOCs. We show, theoretically, that OTOMs are closely related to OTOCs in a doubled system with the same quantum statistical properties as the original system. Using exact diagonalization, we numerically simulate classical mass transport, as well as quantum dynamics through computations of the OTOC, the OTOM, and the entanglement entropy in quantum spin chain models in various interesting regimes (including chaotic and many-body localized systems). Our results demonstrate that an OTOM can successfully reveal subtle aspects of quantum dynamics hidden to classical measures and, crucially, provide experimental access to them.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ying-Jie, E-mail: yingjiezhang@qfnu.edu.cn; Han, Wei; Xia, Yun-Jie, E-mail: yjxia@qfnu.edu.cn

We propose a scheme of controlling entanglement dynamics of a quantum system by applying the external classical driving field for two atoms separately located in a single-mode photon cavity. It is shown that, with a judicious choice of the classical-driving strength and the atom–photon detuning, the effective atom–photon interaction Hamiltonian can be switched from Jaynes–Cummings model to anti-Jaynes–Cummings model. By tuning the controllable atom–photon interaction induced by the classical field, we illustrate that the evolution trajectory of the Bell-like entanglement states can be manipulated from entanglement-sudden-death to no-entanglement-sudden-death, from no-entanglement-invariant to entanglement-invariant. Furthermore, the robustness of the initial Bell-like entanglementmore » can be improved by the classical driving field in the leaky cavities. This classical-driving-assisted architecture can be easily extensible to multi-atom quantum system for scalability.« less

Control of entanglement dynamics in a system of three coupled quantum oscillators.

PubMed

Gonzalez-Henao, J C; Pugliese, E; Euzzor, S; Meucci, R; Roversi, J A; Arecchi, F T

2017-08-30

Dynamical control of entanglement and its connection with the classical concept of instability is an intriguing matter which deserves accurate investigation for its important role in information processing, cryptography and quantum computing. Here we consider a tripartite quantum system made of three coupled quantum parametric oscillators in equilibrium with a common heat bath. The introduced parametrization consists of a pulse train with adjustable amplitude and duty cycle representing a more general case for the perturbation. From the experimental observation of the instability in the classical system we are able to predict the parameter values for which the entangled states exist. A different amount of entanglement and different onset times emerge when comparing two and three quantum oscillators. The system and the parametrization considered here open new perspectives for manipulating quantum features at high temperatures.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

PubMed

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-23

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera

NASA Astrophysics Data System (ADS)

Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

2018-03-01

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting—henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Dynamics of tripartite quantum entanglement and discord under a classical dephasing random telegraph noise

NASA Astrophysics Data System (ADS)

Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius

2017-02-01

We address the dynamics of quantum correlations, including entanglement and quantum discord of a three-qubit system interacting with a classical pure dephasing random telegraph noise (RTN) in three different physical environmental situations (independent, mixed and common environments). Two initial entangled states of the system are examined, namely the Greenberger-Horne-Zeilinger (GHZ)- and Werner (W)-type states. The classical noise is introduced as a stochastic process affecting the energy splitting of the qubits. With the help of suitable measures of tripartite entanglement (entanglement witnesses and lower bound of concurrence) and quantum discord (global quantum discord and quantum dissension), we show that the evolution of quantum correlations is not only affected by the type of the system-environment interaction but also by the input configuration of the qubits and the memory properties of the environmental noise. Indeed, depending on the memory properties of the environmental noise and the initial state considered, we find that independent, common and mixed environments can play opposite roles in preserving quantum correlations, and that the sudden death and revival phenomena or the survival of quantum correlations may occur. On the other hand, we also show that the W-type state has strong dynamics under this noise than the GHZ-type ones.

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

PubMed

Hele, Timothy J H; Willatt, Michael J; Muolo, Andrea; Althorpe, Stuart C

2015-04-07

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Oligopolies with contingent workforce and unemployment insurance systems

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2015-10-01

In the recent literature the introduction of modified cost functions has added reality into the classical oligopoly analysis. Furthermore, the market evolution requires much more flexibility to firms, and in several countries contingent workforce plays an important role in the production choices by the firms. Therefore, an analysis of dynamic adjustment costs is in order to understand oligopoly dynamics. In this paper, dynamic single-product oligopolies without product differentiation are first examined with the additional consideration of production adjustment costs. Linear inverse demand and cost functions are considered and it is assumed that the firms adjust their outputs partially toward best response. The set of the steady states is characterized by a system of linear inequalities and there are usually infinitely many steady states. The asymptotic behavior of the output trajectories is examined by using computer simulation. The numerical results indicate that the resulting dynamics is richer than in the case of the classical Cournot model. This model and results are then compared to oligopolies with unemployment insurance systems when the additional cost is considered if firms do not use their maximum capacities.

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium.

PubMed

Qian, Hong; Beard, Daniel A

2005-04-22

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.

Transferability of polarizable models for ion-water electrostatic interaction

NASA Astrophysics Data System (ADS)

Masia, Marco

2009-06-01

Studies of ion-water systems at condensed phase and at interfaces have pointed out that molecular and ionic polarization plays an important role for many phenomena ranging from hydrogen bond dynamics to water interfaces' structure. Classical and ab initio Molecular Dynamics simulations reveal that induced dipole moments at interfaces (e.g. air-water and water-protein) are usually high, hinting that polarizable models to be implemented in classical force fields should be very accurate in reproducing the electrostatic properties of the system. In this paper the electrostatic properties of three classical polarizable models for ion-water interaction are compared with ab initio results both at gas and condensed phase. For Li+- water and Cl--water dimers the reproducibility of total dipole moments obtained with high level quantum chemical calculations is studied; for the same ions in liquid water, Car-Parrinello Molecular Dynamics simulations are used to compute the time evolution of ionic and molecular dipole moments, which are compared with the classical models. The PD2-H2O model developed by the author and coworkers [Masia et al. J. Chem. Phys. 2004, 121, 7362] together with the gaussian intermolecular damping for ion-water interaction [Masia et al. J. Chem. Phys. 2005, 123, 164505] showed to be the fittest in reproducing the ab initio results from gas to condensed phase, allowing for force field transferability.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Dynamical properties of magnetized two-dimensional one-component plasma

NASA Astrophysics Data System (ADS)

Dubey, Girija S.; Gumbs, Godfrey; Fessatidis, Vassilios

2018-05-01

Molecular dynamics simulation are used to examine the effect of a uniform perpendicular magnetic field on a two-dimensional interacting electron system. In this simulation we include the effect of the magnetic field classically through the Lorentz force. Both the Coulomb and the magnetic forces are included directly in the electron dynamics to study their combined effect on the dynamical properties of the 2D system. Results are presented for the velocity autocorrelation function and the diffusion constants in the presence and absence of an external magnetic field. Our simulation results clearly show that the external magnetic field has an effect on the dynamical properties of the system.

Non-classical Correlations and Quantum Coherence in Mixed Environments

NASA Astrophysics Data System (ADS)

Hu, Zheng-Da; Wei, Mei-Song; Wang, Jicheng; Zhang, Yixin; He, Qi-Liang

2018-05-01

We investigate non-classical correlations (entanglement and quantum discord) and quantum coherence for an open two-qubit system each independently coupled to a bosonic environment and a spin environment, respectively. The modulating effects of spin environment and bosonic environment are respectively explored. A relation among the quantum coherence, quantum discord and classical correlation is found during the sudden transition phenomenon. We also compare the case of mixed environments with that of the same environments, showing that the dynamics is dramatically changed.

Boolean Networks in Inference and Dynamic Modeling of Biological Systems at the Molecular and Physiological Level

NASA Astrophysics Data System (ADS)

Thakar, Juilee; Albert, Réka

The following sections are included: * Introduction * Boolean Network Concepts and History * Extensions of the Classical Boolean Framework * Boolean Inference Methods and Examples in Biology * Dynamic Boolean Models: Examples in Plant Biology, Developmental Biology and Immunology * Conclusions * References

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

Dynamic Grover search: applications in recommendation systems and optimization problems

NASA Astrophysics Data System (ADS)

Chakrabarty, Indranil; Khan, Shahzor; Singh, Vanshdeep

2017-06-01

In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.

Identifying a Superfluid Reynolds Number via Dynamical Similarity.

PubMed

Reeves, M T; Billam, T P; Anderson, B P; Bradley, A S

2015-04-17

The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, Re(s), that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at Re(s)≈0.7, irrespective of obstacle width.

Environment and initial state engineered dynamics of quantum and classical correlations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Cheng-Zhi, E-mail: czczwang@outlook.com; Li, Chun-Xian; Guo, Yu

Based on an open exactly solvable system coupled to an environment with nontrivial spectral density, we connect the features of quantum and classical correlations with some features of the environment, initial states of the system, and the presence of initial system–environment correlations. Some interesting features not revealed before are observed by changing the structure of environment, the initial states of system, and the presence of initial system–environment correlations. The main results are as follows. (1) Quantum correlations exhibit temporary freezing and permanent freezing even at high temperature of the environment, for which the necessary and sufficient conditions are given bymore » three propositions. (2) Quantum correlations display a transition from temporary freezing to permanent freezing by changing the structure of environment. (3) Quantum correlations can be enhanced all the time, for which the condition is put forward. (4) The one-to-one dependency relationship between all kinds of dynamic behaviors of quantum correlations and the initial states of the system as well as environment structure is established. (5) In the presence of initial system–environment correlations, quantum correlations under local environment exhibit temporary multi-freezing phenomenon. While under global environment they oscillate, revive, and damp, an explanation for which is given. - Highlights: • Various interesting behaviors of quantum and classical correlations are observed in an open exactly solvable model. • The important effects of the bath structure on quantum and classical correlations are revealed. • The one-to-one correspondence between the type of dynamical behavior of quantum discord and the initial state is given. • Quantum correlations are given in the presence of initial qubits–bath correlations.« less

New results on the apsidal-motion test to stellar structure and evolution including the effects of dynamic tides

NASA Astrophysics Data System (ADS)

Claret, A.; Willems, B.

2002-06-01

We revised the current status of the apsidal-motion test to stellar structure and evolution. The observational sample was increased by about 50% in comparison to previous studies. Classical and relativistic systems were analyzed simultaneously and only systems with accurate absolute dimensions were considered. New interior models incorporating recent opacity tables, stellar rotation, mass loss, and moderate core overshooting were used as theoretical tools to compare the predicted with the observed shifts of the position of the periastron. The stellar models were computed for the precise observed masses and the adopted chemical compositions are consistent with the corresponding tables of opacities to avoid the inherent problems of interpolation in mass and in (X, Z). The derived chemical composition for each individual system was used to infer the primordial helium content as well as a law of enrichment. The values found are in good agreement with those obtained from various independent sources. For the first time, the effects of dynamic tides are taken into account systematically to determine the contribution of the tidal distortion to the predicted apsidal-motion rate. The deviations between the apsidal-motion rates resulting from the classical formula and those determined by taking into account the effects of dynamic tides are presented as a function of the level of synchronism. For systems close to synchronisation, dynamic tides cause deviations with respect to the classical apsidal-motion formula due to the effects of the compressibility of the stellar fluid. For systems with higher rotational angular velocities, additional deviations due to resonances arise when the forcing frequencies of the dynamic tides come into the range of the free oscillation modes of the component stars. The resulting comparison shows a good agreement between the observed and theoretical apsidal-motion rates. No systematic effects in the sense that models are less mass concentrated than real stars and no correlations with the evolutionary status of the systems were detected.

Ensembles and Experiments in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Neumaier, Arnold

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.; Santhanam, M. S.

2017-01-01

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Imaging with organic indicators and high-speed charge-coupled device cameras in neurons: some applications where these classic techniques have advantages.

PubMed

Ross, William N; Miyazaki, Kenichi; Popovic, Marko A; Zecevic, Dejan

2015-04-01

Dynamic calcium and voltage imaging is a major tool in modern cellular neuroscience. Since the beginning of their use over 40 years ago, there have been major improvements in indicators, microscopes, imaging systems, and computers. While cutting edge research has trended toward the use of genetically encoded calcium or voltage indicators, two-photon microscopes, and in vivo preparations, it is worth noting that some questions still may be best approached using more classical methodologies and preparations. In this review, we highlight a few examples in neurons where the combination of charge-coupled device (CCD) imaging and classical organic indicators has revealed information that has so far been more informative than results using the more modern systems. These experiments take advantage of the high frame rates, sensitivity, and spatial integration of the best CCD cameras. These cameras can respond to the faster kinetics of organic voltage and calcium indicators, which closely reflect the fast dynamics of the underlying cellular events.

Time Domain Stability Margin Assessment of the NASA Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time Domain Stability Margin Assessment of the NS Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems.

PubMed

Smith, Kyle K G; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J

2015-06-28

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

Time Domain Stability Margin Assessment Method

NASA Technical Reports Server (NTRS)

Clements, Keith

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time-Domain Stability Margin Assessment

NASA Technical Reports Server (NTRS)

Clements, Keith

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Non-Markovianity hinders Quantum Darwinism.

PubMed

Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

2016-01-20

We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.

Non-Markovianity hinders Quantum Darwinism

NASA Astrophysics Data System (ADS)

Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

2016-01-01

We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.

Non-Markovianity hinders Quantum Darwinism

PubMed Central

Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

2016-01-01

We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors. PMID:26786857

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

NASA Astrophysics Data System (ADS)

Demina, Maria V.

2018-05-01

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.

Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions

DOE PAGES

Rademaker, Louk; Vinokur, Valerii M.; Galda, Alexey

2017-03-16

Here, we study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions.

PubMed

Rademaker, Louk; Vinokur, Valerii M; Galda, Alexey

2017-03-16

We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

Quantum spin chains with multiple dynamics

NASA Astrophysics Data System (ADS)

Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William

2017-11-01

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤z <2.7 , which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.

CLASSICAL AREAS OF PHENOMENOLOGY: Correcting dynamic residual aberrations of conformal optical systems using AO technology

NASA Astrophysics Data System (ADS)

Li, Yan; Li, Lin; Huang, Yi-Fan; Du, Bao-Lin

2009-07-01

This paper analyses the dynamic residual aberrations of a conformal optical system and introduces adaptive optics (AO) correction technology to this system. The image sharpening AO system is chosen as the correction scheme. Communication between MATLAB and Code V is established via ActiveX technique in computer simulation. The SPGD algorithm is operated at seven zoom positions to calculate the optimized surface shape of the deformable mirror. After comparison of performance of the corrected system with the baseline system, AO technology is proved to be a good way of correcting the dynamic residual aberration in conformal optical design.

Methods of applied dynamics

NASA Technical Reports Server (NTRS)

Rheinfurth, M. H.; Wilson, H. B.

1991-01-01

The monograph was prepared to give the practicing engineer a clear understanding of dynamics with special consideration given to the dynamic analysis of aerospace systems. It is conceived to be both a desk-top reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject. Beginning with the basic concepts of kinematics and dynamics, the discussion proceeds to treat the dynamics of a system of particles. Both classical and modern formulations of the Lagrange equations, including constraints, are discussed and applied to the dynamic modeling of aerospace structures using the modal synthesis technique.

Experimental Observation of Classical Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Nerem, M. P.; Salmon, D.; Aubin, S.; Delos, J. B.

2018-03-01

A Hamiltonian system is said to have nontrivial monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit in angular momentum-energy space. This process has been predicted to have consequences which can be seen in dynamical systems, called dynamical monodromy. Using an apparatus consisting of a spherical pendulum subject to magnetic potentials and torques, we observe nontrivial monodromy by the associated topological change in the evolution of a loop of trajectories.

Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase.

PubMed

Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele

2014-11-14

Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

Roughness as classicality indicator of a quantum state

NASA Astrophysics Data System (ADS)

Lemos, Humberto C. F.; Almeida, Alexandre C. L.; Amaral, Barbara; Oliveira, Adélcio C.

2018-03-01

We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L2 (R2) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [ 0 , 1 ], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness approaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.

Appearance of gauge structure in simple dynamical systems

NASA Technical Reports Server (NTRS)

Wilczek, F.; Zee, A.

1984-01-01

By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.

Period doubling in period-one steady states

NASA Astrophysics Data System (ADS)

Wang, Reuben R. W.; Xing, Bo; Carlo, Gabriel G.; Poletti, Dario

2018-02-01

Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos," including period doubling, i.e., the system evolves with a period which is twice that of the driving. However, typically the attractor of a periodically driven quantum open system evolves with a period which exactly matches that of the driving. Here, we analyze a periodically driven many-body open quantum system whose classical correspondent presents period doubling. We show that by studying the dynamical correlations, it is possible to show the occurrence of period doubling in the quantum (period-one) steady state. We also discuss that such systems are natural candidates for clean and intrinsically robust Floquet time crystals.

Recurrence theorems: A unified account

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

Multistructure index in revealing complexity of regulatory mechanisms of human cardiovascular system at rest and orthostatic stress in healthy humans

NASA Astrophysics Data System (ADS)

Makowiec, Danuta; Graff, Beata; Struzik, Zbigniew R.

2017-02-01

Biological regulation is sufficiently complex to pose an enduring challenge for characterization of both its equilibrium and transient non-equilibrium dynamics. Two univariate but coupled observables, heart rate and systolic blood pressure, are commonly characterized in the benchmark example of the human cardiovascular regulatory system. Asymmetric distributions of accelerations and decelerations of heart rate, as well as rises and falls in systolic blood pressure, recorded in humans during a head-up tilt test provide insights into the dynamics of cardiovascular response to a rapid, controlled deregulation of the system's homeostasis. The baroreflex feedback loop is assumed to be the fundamental physiological mechanism for ensuring homeostatic blood supply to distant organs at rest and during orthostatic stress, captured in a classical beat-to-beat autoregressive model of baroreflex by de Boer et al. (1987). For model corroboration, a multistructure index statistic is proposed, seamlessly evaluating the size spectrum of magnitudes of neural reflexes such as baroreflex, responsible for maintaining the homeostatic dynamics. The multistructure index exposes a distinctly different dynamics of multiscale asymmetry between results obtained from real-life signals recorded from healthy subjects and those simulated using both the classical and perturbed versions of the model. Nonlinear effects observed suggest the pronounced presence of complex mechanisms resulting from baroreflex regulation when a human is at rest, which is aggravated in the system's response to orthostatic stress. Using our methodology of multistructure index, we therefore show a marked difference between model and real-life scenarios, which we attribute to multiscale asymmetry of non-linear origin in real-life signals, which we are not reproducible by the classical model.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

An Experimental and Theoretical Study of Nitrogen-Broadened Acetylene Lines

NASA Technical Reports Server (NTRS)

Thibault, Franck; Martinez, Raul Z.; Bermejo, Dionisio; Ivanov, Sergey V.; Buzykin, Oleg G.; Ma, Qiancheng

2014-01-01

We present experimental nitrogen-broadening coefficients derived from Voigt profiles of isotropic Raman Q-lines measured in the 2 band of acetylene (C2H2) at 150 K and 298 K, and compare them to theoretical values obtained through calculations that were carried out specifically for this work. Namely, full classical calculations based on Gordon's approach, two kinds of semi-classical calculations based on Robert Bonamy method as well as full quantum dynamical calculations were performed. All the computations employed exactly the same ab initio potential energy surface for the C2H2N2 system which is, to our knowledge, the most realistic, accurate and up-to-date one. The resulting calculated collisional half-widths are in good agreement with the experimental ones only for the full classical and quantum dynamical methods. In addition, we have performed similar calculations for IR absorption lines and compared the results to bibliographic values. Results obtained with the full classical method are again in good agreement with the available room temperature experimental data. The quantum dynamical close-coupling calculations are too time consuming to provide a complete set of values and therefore have been performed only for the R(0) line of C2H2. The broadening coefficient obtained for this line at 173 K and 297 K also compares quite well with the available experimental data. The traditional Robert Bonamy semi-classical formalism, however, strongly overestimates the values of half-width for both Qand R-lines. The refined semi-classical Robert Bonamy method, first proposed for the calculations of pressure broadening coefficients of isotropic Raman lines, is also used for IR lines. By using this improved model that takes into account effects from line coupling, the calculated semi-classical widths are significantly reduced and closer to the measured ones.

Atom transistor from the point of view of nonequilibrium dynamics

NASA Astrophysics Data System (ADS)

Zhang, Z.; Dunjko, V.; Olshanii, M.

2015-12-01

We analyze the atom field-effect transistor scheme (Stickney et al 2007 Phys. Rev. A 75 013608) using the standard tools of quantum and classical nonequlilibrium dynamics. We first study the correspondence between the quantum and the mean-field descriptions of this system by computing, both ab initio and by using their mean-field analogs, the deviations from the Eigenstate Thermalization Hypothesis, quantum fluctuations, and the density of states. We find that, as far as the quantities that interest us, the mean-field model can serve as a semi-classical emulator of the quantum system. Then, using the mean-field model, we interpret the point of maximal output signal in our transistor as the onset of ergodicity—the point where the system becomes, in principle, able to attain the thermal values of the former integrals of motion, albeit not being fully thermalized yet.

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

NASA Astrophysics Data System (ADS)

Graefe, E. M.; Korsch, H. J.; Rush, A.

2016-07-01

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.

Efficient Quantum Pseudorandomness.

PubMed

Brandão, Fernando G S L; Harrow, Aram W; Horodecki, Michał

2016-04-29

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

NASA Astrophysics Data System (ADS)

Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.

2017-07-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.

Using qubits to reveal quantum signatures of an oscillator

NASA Astrophysics Data System (ADS)

Agarwal, Shantanu

In this thesis, we seek to study the qubit-oscillator system with the aim to identify and quantify inherent quantum features of the oscillator. We show that the quantum signatures of the oscillator get imprinted on the dynamics of the joint system. The two key features which we explore are the quantized energy spectrum of the oscillator and the non-classicality of the oscillator's wave function. To investigate the consequences of the oscillator's discrete energy spectrum, we consider the qubit to be coupled to the oscillator through the Rabi Hamiltonian. Recent developments in fabrication technology have opened up the possibility to explore parameter regimes which were conventionally inaccessible. Motivated by these advancements, we investigate in this thesis a parameter space where the qubit frequency is much smaller than the oscillator frequency and the Rabi frequency is allowed to be an appreciable fraction of the bare frequency of the oscillator. We use the adiabatic approximation to understand the dynamics in this quasi-degenerate qubit regime. By deriving a dressed master equation, we systematically investigate the effects of the environment on the system dynamics. We develop a spectroscopic technique, using which one can probe the steady state response of the driven and damped system. The spectroscopic signal clearly reveals the quantized nature of the oscillator's energy spectrum. We extend the adiabatic approximation, earlier developed only for the single qubit case, to a scenario where multiple qubits interact with the oscillator. Using the extended adiabatic approximation, we study the collapse and revival of multi-qubit observables. We develop analytic expressions for the revival signals which are in good agreement with the numerically evaluated results. Within the quantum restriction imposed by Heisenberg's uncertainty principle, the uncertainty in the position and momentum of an oscillator is minimum and shared equally when the oscillator is prepared in a coherent state. For this reason, coherent states and states which can be thought of as a statistical mixture of coherent states are categorized as classical; whereas states which are not valid coherent state mixtures are classified as non-classical. In this thesis, we propose a new non-classicality witness operation which does not require a tomography of the oscillator's state. We show that by coupling a qubit longitudinally to the oscillator, one can infer about the non-classical nature of the initial state of the oscillator. Using a qubit observable, we derive a non-classicality witness inequality, a violation of which definitively indicates the non-classical nature of an oscillator's state.

Convergence acceleration of molecular dynamics methods for shocked materials using velocity scaling

NASA Astrophysics Data System (ADS)

Taylor, DeCarlos E.

2017-03-01

In this work, a convergence acceleration method applicable to extended system molecular dynamics techniques for shock simulations of materials is presented. The method uses velocity scaling to reduce the instantaneous value of the Rankine-Hugoniot conservation of energy constraint used in extended system molecular dynamics methods to more rapidly drive the system towards a converged Hugoniot state. When used in conjunction with the constant stress Hugoniostat method, the velocity scaled trajectories show faster convergence to the final Hugoniot state with little difference observed in the converged Hugoniot energy, pressure, volume and temperature. A derivation of the scale factor is presented and the performance of the technique is demonstrated using the boron carbide armour ceramic as a test material. It is shown that simulation of boron carbide Hugoniot states, from 5 to 20 GPa, using both a classical Tersoff potential and an ab initio density functional, are more rapidly convergent when the velocity scaling algorithm is applied. The accelerated convergence afforded by the current algorithm enables more rapid determination of Hugoniot states thus reducing the computational demand of such studies when using expensive ab initio or classical potentials.

The complexity of proving chaoticity and the Church-Turing thesis

NASA Astrophysics Data System (ADS)

Calude, Cristian S.; Calude, Elena; Svozil, Karl

2010-09-01

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Exact treatment of the Jaynes-Cummings model under the action of an external classical field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdalla, M. Sebawe, E-mail: m.sebaweh@physics.org; Khalil, E.M.; Mathematics Department, College of Science, Taibah University, Al-MaDinah

2011-09-15

We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strongmore » value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: > The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. > A new approach is applied through a certain canonical transformation. > The classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states.« less

First principles molecular dynamics of molten NaCl

NASA Astrophysics Data System (ADS)

Galamba, N.; Costa Cabral, B. J.

2007-03-01

First principles Hellmann-Feynman molecular dynamics (HFMD) results for molten NaCl at a single state point are reported. The effect of induction forces on the structure and dynamics of the system is studied by comparison of the partial radial distribution functions and the velocity and force autocorrelation functions with those calculated from classical MD based on rigid-ion and shell-model potentials. The first principles results reproduce the main structural features of the molten salt observed experimentally, whereas they are incorrectly described by both rigid-ion and shell-model potentials. Moreover, HFMD Green-Kubo self-diffusion coefficients are in closer agreement with experimental data than those predicted by classical MD. A comprehensive discussion of MD results for molten NaCl based on different ab initio parametrized polarizable interionic potentials is also given.

Electrical control of spin dynamics in finite one-dimensional systems

NASA Astrophysics Data System (ADS)

Pertsova, A.; Stamenova, M.; Sanvito, S.

2011-10-01

We investigate the possibility of the electrical control of spin transfer in monoatomic chains incorporating spin impurities. Our theoretical framework is the mixed quantum-classical (Ehrenfest) description of the spin dynamics, in the spirit of the s-d model, where the itinerant electrons are described by a tight-binding model while localized spins are treated classically. Our main focus is on the dynamical exchange interaction between two well-separated spins. This can be quantified by the transfer of excitations in the form of transverse spin oscillations. We systematically study the effect of an electrostatic gate bias Vg on the interconnecting channel and we map out the long-range dynamical spin transfer as a function of Vg. We identify regions of Vg giving rise to significant amplification of the spin transmission at low frequencies and relate this to the electronic structure of the channel.

The classical and quantum dynamics of molecular spins on graphene.

PubMed

Cervetti, Christian; Rettori, Angelo; Pini, Maria Gloria; Cornia, Andrea; Repollés, Ana; Luis, Fernando; Dressel, Martin; Rauschenbach, Stephan; Kern, Klaus; Burghard, Marko; Bogani, Lapo

2016-02-01

Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.

The classical and quantum dynamics of molecular spins on graphene

NASA Astrophysics Data System (ADS)

Cervetti, Christian; Rettori, Angelo; Pini, Maria Gloria; Cornia, Andrea; Repollés, Ana; Luis, Fernando; Dressel, Martin; Rauschenbach, Stephan; Kern, Klaus; Burghard, Marko; Bogani, Lapo

2016-02-01

Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain’s threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.

Moyal dynamics and trajectories

NASA Astrophysics Data System (ADS)

Braunss, G.

2010-01-01

We give first an approximation of the operator δh: f → δhf := h*planckf - f*planckh in terms of planck2n, n >= 0, where h\\equiv h(p,q), (p,q)\\in {\\mathbb R}^{2 n} , is a Hamilton function and *planck denotes the star product. The operator, which is the generator of time translations in a *planck-algebra, can be considered as a canonical extension of the Liouville operator Lh: f → Lhf := {h, f}Poisson. Using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the Hamilton-Jacobi method for classical dynamics to Moyal dynamics. The examples we have chosen are Hamiltonians with a one-dimensional quartic potential and two-dimensional radially symmetric nonrelativistic and relativistic Coulomb potentials, and the Hamiltonian for a Schwarzschild metric. We further state a conjecture concerning an extension of the Bohr-Sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories.

Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

NASA Astrophysics Data System (ADS)

Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen

2015-07-01

We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

Emerging technology for advancing the treatment of epilepsy using a dynamic control framework.

PubMed

Stanslaski, Scott; Giftakis, John; Stypulkowski, Paul; Carlson, Dave; Afshar, Pedram; Cong, Peng; Denison, Timothy

2011-01-01

We briefly describe a dynamic control system framework for neuromodulation for epilepsy, with an emphasis on its practical challenges and the preliminary validation of key prototype technologies in a chronic animal model. The current state of neuromodulation can be viewed as a classical dynamic control framework such that the nervous system is the classical "plant", the neural stimulator is the controller/actuator, clinical observation, patient diaries and/or measured bio-markers are the sensor, and clinical judgment applied to these sensor inputs forms the state estimator. Technology can potentially address two main factors contributing to the performance limitations of existing systems: "observability," the ability to observe the state of the system from output measurements, and "controllability," the ability to drive the system to a desired state. In addition to improving sensors and actuator performance, methods and tools to better understand disease state dynamics and state estimation are also critical for improving therapy outcomes. We describe our preliminary validation of key "observability" and "controllability" technology blocks using an implanted research tool in an epilepsy disease model. This model allows for testing the key emerging technologies in a representative neural network of therapeutic importance. In the future, we believe these technologies might enable both first principles understanding of neural network behavior for optimizing therapy design, and provide a practical pathway towards clinical translation.

Quantum stochastic walks on networks for decision-making.

PubMed

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-31

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

NASA Astrophysics Data System (ADS)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

PubMed Central

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-01-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making. PMID:27030372

Quantum and classical behavior in interacting bosonic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hertzberg, Mark P.

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular differencemore » in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.« less

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Characterizing and modeling the dynamics of online popularity.

PubMed

Ratkiewicz, Jacob; Fortunato, Santo; Flammini, Alessandro; Menczer, Filippo; Vespignani, Alessandro

2010-10-08

Online popularity has an enormous impact on opinions, culture, policy, and profits. We provide a quantitative, large scale, temporal analysis of the dynamics of online content popularity in two massive model systems: the Wikipedia and an entire country's Web space. We find that the dynamics of popularity are characterized by bursts, displaying characteristic features of critical systems such as fat-tailed distributions of magnitude and interevent time. We propose a minimal model combining the classic preferential popularity increase mechanism with the occurrence of random popularity shifts due to exogenous factors. The model recovers the critical features observed in the empirical analysis of the systems analyzed here, highlighting the key factors needed in the description of popularity dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Somnath, Suhas; Collins, Liam; Matheson, Michael A.

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify themore » findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip–sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. In conclusion, GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.« less

The quantum CP-violating kaon system reproduced in the electronic laboratory

NASA Astrophysics Data System (ADS)

Caruso, M.; Fanchiotti, H.; García Canal, C. A.; Mayosky, M.; Veiga, A.

2016-11-01

The equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analysed. Moreover, under CPT invariance, the relevant ɛ parameter that measures CP violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.

Evanescent radiation, quantum mechanics and the Casimir effect

NASA Technical Reports Server (NTRS)

Schatten, Kenneth H.

1989-01-01

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Software Applications on the Peregrine System | High-Performance Computing

Science.gov Websites

programming and optimization. Gaussian Chemistry Program for calculating molecular electronic structure and Materials Science Open-source classical molecular dynamics program designed for massively parallel systems framework Q-Chem Chemistry ab initio quantum chemistry package for predictin molecular structures

The Development of Rigorously Correct, Dynamical Pseudopotentials for Use in Mixed Quantum/Classical Molecular Dynamics Simulations in the Condensed Phase

NASA Astrophysics Data System (ADS)

Kahros, Argyris

Incorporating quantum mechanics into an atomistic simulation necessarily involves solving the Schrodinger equation. Unfortunately, the computational expense associated with solving this equation scales miserably with the number of included quantum degrees of freedom (DOF). The situation is so dire, in fact, that a molecular dynamics (MD) simulation cannot include more than a small number of quantum DOFs before it becomes computationally intractable. Thus, if one were to simulate a relatively large system, such as one containing several hundred atoms or molecules, it would be unreasonable to attempt to include the effects of all of the electrons associated with all of the components of the system. The mixed quantum/classical (MQC) approach provides a way to circumvent this issue. It involves treating the vast majority of the system classically, which incurs minimal computational expense, and reserves the consideration of quantum mechanical effects for only the few degrees of freedom more directly involved in the chemical phenomenon being studied. For example, if one were to study the bonding of a single diatomic molecule in the gas phase, one could employ a MQC approach by treating the nuclei of the molecule's two atoms classically---including the deeply bound, low-energy electrons that change relatively little---and solving the Schrodinger equation only for the high energy electron(s) directly involved in the bonding of the classical cores. In such a way, one could study the bonding of this molecule in a rigorous fashion while treating only the directly related degrees of freedom quantum mechanically. Pseudopotentials are then responsible for dictating the interactions between the quantum and classical degrees of freedom. As these potentials are the sole link between the quantum and classical DOFs, their proper development is of the utmost importance. This Thesis is concerned primarily with my work on the development of novel, rigorous and dynamical pseudopotentials for use in mixed quantum/ classical simulations in the condensed phase. The pseudopotentials discussed within are constructed in an ab initio fashion, without the introduction of any empiricism, and are able to exactly reproduce the results of higher level, fully quantum mechanical Hartree-Fock calculations. A recurring theme in the following pages is overcoming the so-called frozen core approximation (FCA). This essentially comes down to creating pseudopotentials that are able to respond in some way to the local molecular environment in a rigorous fashion. The various methods and discussions that are part of this document are presented in the context of two particular systems. The first is the sodium dimer cation molecule, which serves as a proof of concept for the development of coordinate-dependent pseudopotentials and is the subject of Chapters 2 and 3. Next, the hydrated electron---the excess electron in liquid water---is tackled in an effort to address the recent controversy concerning its true structure and is the subject of Chapters 4 and 5. In essence, the work in this Dissertation is concerned with finding new ways to overcome the problem of a lack of infinite computer processing power.

Dynamical Casimir effect in stochastic systems: Photon harvesting through noise

NASA Astrophysics Data System (ADS)

Román-Ancheyta, Ricardo; Ramos-Prieto, Irán; Perez-Leija, Armando; Busch, Kurt; León-Montiel, Roberto de J.

2017-09-01

We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold—which we referred to as a metal-insulator phase transition—between exponential growth and low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analog of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.

Quantum vs Classical Mechanics for a 'Simple' Dissociation Reaction. Should They Give the Same Results?

NASA Astrophysics Data System (ADS)

Holloway, Stephen

1997-03-01

When performing molecular dynamical simulations on light systems at low energies, there is always the risk of producing data that bear no similarity to experiment. Indeed, John Barker himself was particularly anxious about treating Ar scattering from surfaces using classical mechanics where it had been shown experimentally in his own lab that diffraction occurs. In such cases, the correct procedure is probably to play the trump card "... well of course, quantum effects will modify this so that....." and retire gracefully. For our particular interests, the tables are turned in that we are interested in gas-surface dynamical studies for highly quantized systems, but would be interested to know when it is possible to use classical mechanics in order that a greater dimensionality might be treated. For molecular dissociation and scattering, it has been oft quoted that the greater the number of degrees of freedom, the more appropriate is classical mechanics, primarily because of the mass averaging over the quantized dimensions. Is this true? We have been investigating the dissociation of hydrogen molecules at surfaces and in this talk I will present quantum results for dissociation and scattering, along with a novel method for their interpretation based upon adiabatic potential energy surfaces. Comparison with classical calculations will be made and conclusions drawn. a novel method for their interpretation based upon adiabatic potential energy surfaces

Limit Theorems for Dispersing Billiards with Cusps

NASA Astrophysics Data System (ADS)

Bálint, P.; Chernov, N.; Dolgopyat, D.

2011-12-01

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Efficient multidimensional free energy calculations for ab initio molecular dynamics using classical bias potentials

NASA Astrophysics Data System (ADS)

VandeVondele, Joost; Rothlisberger, Ursula

2000-09-01

We present a method for calculating multidimensional free energy surfaces within the limited time scale of a first-principles molecular dynamics scheme. The sampling efficiency is enhanced using selected terms of a classical force field as a bias potential. This simple procedure yields a very substantial increase in sampling accuracy while retaining the high quality of the underlying ab initio potential surface and can thus be used for a parameter free calculation of free energy surfaces. The success of the method is demonstrated by the applications to two gas phase molecules, ethane and peroxynitrous acid, as test case systems. A statistical analysis of the results shows that the entire free energy landscape is well converged within a 40 ps simulation at 500 K, even for a system with barriers as high as 15 kcal/mol.

A Functional Cartography of Cognitive Systems

PubMed Central

Mattar, Marcelo G.; Cole, Michael W.; Thompson-Schill, Sharon L.; Bassett, Danielle S.

2015-01-01

One of the most remarkable features of the human brain is its ability to adapt rapidly and efficiently to external task demands. Novel and non-routine tasks, for example, are implemented faster than structural connections can be formed. The neural underpinnings of these dynamics are far from understood. Here we develop and apply novel methods in network science to quantify how patterns of functional connectivity between brain regions reconfigure as human subjects perform 64 different tasks. By applying dynamic community detection algorithms, we identify groups of brain regions that form putative functional communities, and we uncover changes in these groups across the 64-task battery. We summarize these reconfiguration patterns by quantifying the probability that two brain regions engage in the same network community (or putative functional module) across tasks. These tools enable us to demonstrate that classically defined cognitive systems—including visual, sensorimotor, auditory, default mode, fronto-parietal, cingulo-opercular and salience systems—engage dynamically in cohesive network communities across tasks. We define the network role that a cognitive system plays in these dynamics along the following two dimensions: (i) stability vs. flexibility and (ii) connected vs. isolated. The role of each system is therefore summarized by how stably that system is recruited over the 64 tasks, and how consistently that system interacts with other systems. Using this cartography, classically defined cognitive systems can be categorized as ephemeral integrators, stable loners, and anything in between. Our results provide a new conceptual framework for understanding the dynamic integration and recruitment of cognitive systems in enabling behavioral adaptability across both task and rest conditions. This work has important implications for understanding cognitive network reconfiguration during different task sets and its relationship to cognitive effort, individual variation in cognitive performance, and fatigue. PMID:26629847

Imaging via complete cantilever dynamic detection: General dynamic mode imaging and spectroscopy in scanning probe microscopy

DOE PAGES

Somnath, Suhas; Collins, Liam; Matheson, Michael A.; ...

2016-09-08

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify themore » findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip–sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. In conclusion, GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.« less

Young's moduli of carbon materials investigated by various classical molecular dynamics schemes

NASA Astrophysics Data System (ADS)

Gayk, Florian; Ehrens, Julian; Heitmann, Tjark; Vorndamme, Patrick; Mrugalla, Andreas; Schnack, Jürgen

2018-05-01

For many applications classical carbon potentials together with classical molecular dynamics are employed to calculate structures and physical properties of such carbon-based materials where quantum mechanical methods fail either due to the excessive size, irregular structure or long-time dynamics. Although such potentials, as for instance implemented in LAMMPS, yield reasonably accurate bond lengths and angles for several carbon materials such as graphene, it is not clear how accurate they are in terms of mechanical properties such as for instance Young's moduli. We performed large-scale classical molecular dynamics investigations of three carbon-based materials using the various potentials implemented in LAMMPS as well as the EDIP potential of Marks. We show how the Young's moduli vary with classical potentials and compare to experimental results. Since classical descriptions of carbon are bound to be approximations it is not astonishing that different realizations yield differing results. One should therefore carefully check for which observables a certain potential is suited. Our aim is to contribute to such a clarification.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro

2013-07-01

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

Dynamical class of a two-dimensional plasmonic Dirac system.

PubMed

Silva, Érica de Mello

2015-10-01

A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

Multiple spatially localized dynamical states in friction-excited oscillator chains

NASA Astrophysics Data System (ADS)

Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M.; Ciavarella, M.

2018-03-01

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Skinner-Rusk unified formalism for higher-order systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2012-07-01

The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.

Time, Dynamics and Chaos: Integrating Poincare's 'Non-Integrable Systems'

DOE R&D Accomplishments Database

Prigogine, I.

1990-10-01

This report discusses the nature of time. The author attempts to resolve the conflict between the concept of time reversibility in classical and quantum mechanics with the macroscopic world's irreversibility of time. (LSP)

Classic-Ada(TM)

NASA Technical Reports Server (NTRS)

Valley, Lois

1989-01-01

The SPS product, Classic-Ada, is a software tool that supports object-oriented Ada programming with powerful inheritance and dynamic binding. Object Oriented Design (OOD) is an easy, natural development paradigm, but it is not supported by Ada. Following the DOD Ada mandate, SPS developed Classic-Ada to provide a tool which supports OOD and implements code in Ada. It consists of a design language, a code generator and a toolset. As a design language, Classic-Ada supports the object-oriented principles of information hiding, data abstraction, dynamic binding, and inheritance. It also supports natural reuse and incremental development through inheritance, code factoring, and Ada, Classic-Ada, dynamic binding and static binding in the same program. Only nine new constructs were added to Ada to provide object-oriented design capabilities. The Classic-Ada code generator translates user application code into fully compliant, ready-to-run, standard Ada. The Classic-Ada toolset is fully supported by SPS and consists of an object generator, a builder, a dictionary manager, and a reporter. Demonstrations of Classic-Ada and the Classic-Ada Browser were given at the workshop.

A high performance system for molecular dynamics simulation of biomolecules using a special-purpose computer.

PubMed

Komeiji, Y; Yokoyama, H; Uebayasi, M; Taiji, M; Fukushige, T; Sugimoto, D; Takata, R; Shimizu, A; Itsukashi, K

1996-01-01

GRAPE (GRavity PipE) processors are special purpose computers for simulation of classical particles. The performance of MD-GRAPE, one of the GRAPEs developed for molecular dynamics, was investigated. The effective speed of MD-GRAPE was equivalent to approximately 6 Gflops. The precision of MD-GRAPE was good judging from the acceptable fluctuation of the total energy. Then a software named PEACH (Program for Energetic Analysis of bioCHemical molecules) was developed for molecular dynamics of biomolecules in combination with MD-GRAPE. Molecular dynamics simulation was performed for several protein-solvent systems with different sizes. Simulation of the largest system investigated (27,000 atoms) took only 5 sec/step. Thus, the PEACH-GRAPE system is expected to be useful in accurate and reliable simulation of large biomolecules.

Classical command of quantum systems.

PubMed

Reichardt, Ben W; Unger, Falk; Vazirani, Umesh

2013-04-25

Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics.

Quantum critical dynamics of the boson system in the Ginzburg-Landau model

NASA Astrophysics Data System (ADS)

Vasin, M. G.

2014-12-01

The quantum critical dynamics of the quantum phase transitions is considered. In the framework of the unified theory, based on the Keldysh technique, we consider the crossover from the classical to the quantum description of the boson many-body system dynamics close to the second order quantum phase transition. It is shown that in this case the upper critical space dimension of this model is dc+=2, therefore the quantum critical dynamics approach is useful in case of d<2. In the one-dimension system the phase coherence time does diverge at the quantum critical point, gc, and has the form of τ∝-ln∣g-gc∣/∣g-gc∣, the correlation radius diverges as rc∝∣g-gc∣(ν=0.6).

GPU accelerated Discrete Element Method (DEM) molecular dynamics for conservative, faceted particle simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spellings, Matthew; Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109; Marson, Ryan L.

Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method ismore » a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.« less

A survey on hysteresis modeling, identification and control

NASA Astrophysics Data System (ADS)

Hassani, Vahid; Tjahjowidodo, Tegoeh; Do, Thanh Nho

2014-12-01

The various mathematical models for hysteresis such as Preisach, Krasnosel'skii-Pokrovskii (KP), Prandtl-Ishlinskii (PI), Maxwell-Slip, Bouc-Wen and Duhem are surveyed in terms of their applications in modeling, control and identification of dynamical systems. In the first step, the classical formalisms of the models are presented to the reader, and more broadly, the utilization of the classical models is considered for development of more comprehensive models and appropriate controllers for corresponding systems. In addition, the authors attempt to encourage the reader to follow the existing mathematical models of hysteresis to resolve the open problems.

Quantum chaos: An entropy approach

NASA Astrophysics Data System (ADS)

Sl/omczyński, Wojciech; Życzkowski, Karol

1994-11-01

A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II

Quantum Landauer erasure with a molecular nanomagnet

NASA Astrophysics Data System (ADS)

Gaudenzi, R.; Burzurí, E.; Maegawa, S.; van der Zant, H. S. J.; Luis, F.

2018-06-01

The erasure of a bit of information is an irreversible operation whose minimal entropy production of kB ln 2 is set by the Landauer limit1. This limit has been verified in a variety of classical systems, including particles in traps2,3 and nanomagnets4. Here, we extend it to the quantum realm by using a crystal of molecular nanomagnets as a quantum spin memory and showing that its erasure is still governed by the Landauer principle. In contrast to classical systems, maximal energy efficiency is achieved while preserving fast operation owing to its high-speed spin dynamics. The performance of our spin register in terms of energy-time cost is orders of magnitude better than existing memory devices to date. The result shows that thermodynamics sets a limit on the energy cost of certain quantum operations and illustrates a way to enhance classical computations by using a quantum system.

Making Conjectures in Dynamic Geometry: The Potential of a Particular Way of Dragging

ERIC Educational Resources Information Center

Mariotti, Maria Alessandra; Baccaglini-Frank, Anna

2011-01-01

When analyzing what has changed in the geometry scenario with the advent of dynamic geometry systems (DGS), one can notice a transition from the traditional graphic environment made of paper-and-pencil, and the classical construction tools like the ruler and compass, to a virtual graphic space, made of a computer screen, graphical tools that are…

Quantum dynamics of hydrogen atoms on graphene. II. Sticking.

PubMed

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H; Burghardt, Irene; Martinazzo, Rocco

2015-09-28

Following our recent system-bath modeling of the interaction between a hydrogen atom and a graphene surface [Bonfanti et al., J. Chem. Phys. 143, 124703 (2015)], we present the results of converged quantum scattering calculations on the activated sticking dynamics. The focus of this study is the collinear scattering on a surface at zero temperature, which is treated with high-dimensional wavepacket propagations with the multi-configuration time-dependent Hartree method. At low collision energies, barrier-crossing dominates the sticking and any projectile that overcomes the barrier gets trapped in the chemisorption well. However, at high collision energies, energy transfer to the surface is a limiting factor, and fast H atoms hardly dissipate their excess energy and stick on the surface. As a consequence, the sticking coefficient is maximum (∼0.65) at an energy which is about one and half larger than the barrier height. Comparison of the results with classical and quasi-classical calculations shows that quantum fluctuations of the lattice play a primary role in the dynamics. A simple impulsive model describing the collision of a classical projectile with a quantum surface is developed which reproduces the quantum results remarkably well for all but the lowest energies, thereby capturing the essential physics of the activated sticking dynamics investigated.

Quantum dynamics of hydrogen atoms on graphene. II. Sticking

NASA Astrophysics Data System (ADS)

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H.; Burghardt, Irene; Martinazzo, Rocco

2015-09-01

Following our recent system-bath modeling of the interaction between a hydrogen atom and a graphene surface [Bonfanti et al., J. Chem. Phys. 143, 124703 (2015)], we present the results of converged quantum scattering calculations on the activated sticking dynamics. The focus of this study is the collinear scattering on a surface at zero temperature, which is treated with high-dimensional wavepacket propagations with the multi-configuration time-dependent Hartree method. At low collision energies, barrier-crossing dominates the sticking and any projectile that overcomes the barrier gets trapped in the chemisorption well. However, at high collision energies, energy transfer to the surface is a limiting factor, and fast H atoms hardly dissipate their excess energy and stick on the surface. As a consequence, the sticking coefficient is maximum (˜0.65) at an energy which is about one and half larger than the barrier height. Comparison of the results with classical and quasi-classical calculations shows that quantum fluctuations of the lattice play a primary role in the dynamics. A simple impulsive model describing the collision of a classical projectile with a quantum surface is developed which reproduces the quantum results remarkably well for all but the lowest energies, thereby capturing the essential physics of the activated sticking dynamics investigated.

Fractal attractors in economic growth models with random pollution externalities

NASA Astrophysics Data System (ADS)

La Torre, Davide; Marsiglio, Simone; Privileggi, Fabio

2018-05-01

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.

Predictor-Based Model Reference Adaptive Control

NASA Technical Reports Server (NTRS)

Lavretsky, Eugene; Gadient, Ross; Gregory, Irene M.

2009-01-01

This paper is devoted to robust, Predictor-based Model Reference Adaptive Control (PMRAC) design. The proposed adaptive system is compared with the now-classical Model Reference Adaptive Control (MRAC) architecture. Simulation examples are presented. Numerical evidence indicates that the proposed PMRAC tracking architecture has better than MRAC transient characteristics. In this paper, we presented a state-predictor based direct adaptive tracking design methodology for multi-input dynamical systems, with partially known dynamics. Efficiency of the design was demonstrated using short period dynamics of an aircraft. Formal proof of the reported PMRAC benefits constitute future research and will be reported elsewhere.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

A time-series approach to dynamical systems from classical and quantum worlds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fossion, Ruben

2014-01-08

This contribution discusses some recent applications of time-series analysis in Random Matrix Theory (RMT), and applications of RMT in the statistial analysis of eigenspectra of correlation matrices of multivariate time series.

Detecting gravitational decoherence with clocks: Limits on temporal resolution from a classical-channel model of gravity

NASA Astrophysics Data System (ADS)

Khosla, Kiran E.; Altamirano, Natacha

2017-05-01

The notion of time is given a different footing in quantum mechanics and general relativity, treated as a parameter in the former and being an observer-dependent property in the latter. From an operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modeled as a two-level system. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. This model, known as the classical-channel gravity (CCG), postulates that gravity is mediated by a fundamentally classical force carrier and is therefore unable to entangle particles gravitationally. In particular, we focus on the decoherence rates and temporal resolution of arrays of N clocks, showing how the minimum dephasing rate scales with N , and the spatial configuration. Furthermore, we consider the gravitational redshift between a clock and a massive particle and show that a classical-channel model of gravity predicts a finite-dephasing rate from the nonlocal interaction. In our model we obtain a fundamental limitation in time accuracy that is intrinsic to each clock.

The Anderson localization problem, the Fermi-Pasta-Ulam paradox and the generalized diffusion approach

NASA Astrophysics Data System (ADS)

Kuzovkov, V. N.

2011-12-01

The goal of this paper is twofold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a modified dynamical system containing both stable and unstable (inverted) modes. Delocalized states in the AL are analogous to the stable quasi-periodic motion in FPU, whereas localized states are analogous to thermalization, respectively. The second aim is to use the classical Hamilton map for a simplified derivation of exact equations for the localization operator H(z). The latter was presented earlier (Kuzovkov et al 2002 J. Phys.: Condens. Matter 14 13777) treating the AL as a generalized diffusion in a dynamical system. We demonstrate that counter-intuitive results of our studies of the AL are similar to the FPU counter-intuitivity.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cotton, Stephen J.; Miller, William H., E-mail: millerwh@berkeley.edu

A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.

Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps

NASA Astrophysics Data System (ADS)

Mihalcea, Bogdan M.

2018-01-01

Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) or radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for both combined and RF nonlinear traps, that exhibit axial symmetry. We also build the classical Hamiltonian functions for the particular traps we considered, and find the classical equations of motion.

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations

NASA Astrophysics Data System (ADS)

Cotton, Stephen Joshua

An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible. To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H2 reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H 2 vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure. The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model---representing the occupations of the electronic states---in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence effects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase non-adiabatic dynamics, in both its symmetric and asymmetric forms---the latter of which many classical approaches fail to treat successfully. The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [S.J. Cotton, K. Igumenshchev, and W.H. Miller, J. Chem. Phys., 141, 084104 (2014)] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models---representing the successful treatment of another regime that classical approaches generally have difficulty in correctly describing. Relatedly, a model of photoinduced proton coupled electron transfer (PCET) was also addressed, and it was shown that the SQC/MM approach could reasonably model the explicit population dynamics of the photoexcited electron donor and acceptor states over the four parameter regimes considered. The potential utility of the SQC/MM technique lies in its stunning simplicity and the ease by which it may readily be incorporated into "ordinary" molecular dynamics (MD) simulations. In short, a typical MD simulation may be augmented to take non-adiabatic effects into account simply by introducing an auxiliary pair of classical "electronic" action-angle variables for each energetically viable Born-Oppenheimer surface, and time-evolving these auxiliary variables via Hamilton's equations (using the MM electronic Hamiltonian) in the same manner that the other classical variables---i.e., the coordinates of all the nuclei---are evolved forward in time. In a complex molecular system involving many hundreds or thousands of nuclear DOFs, the propagation of these extra "electronic" variables represents a modest increase in computational effort, and yet, the examples presented herein suggest that in many instances the SQC/MM approach will describe the true non-adiabatic quantum dynamics to a reasonable and useful degree of quantitative accuracy.

In vitro dynamic model simulating the digestive tract of 6-month-old infants.

PubMed

Passannanti, Francesca; Nigro, Federica; Gallo, Marianna; Tornatore, Fabio; Frasso, Annalisa; Saccone, Giulia; Budelli, Andrea; Barone, Maria V; Nigro, Roberto

2017-01-01

In vivo assays cannot always be conducted because of ethical reasons, technical constraints or costs, but a better understanding of the digestive process, especially in infants, could be of great help in preventing food-related pathologies and in developing new formulas with health benefits. In this context, in vitro dynamic systems to simulate human digestion and, in particular, infant digestion could become increasingly valuable. To simulate the digestive process through the use of a dynamic model of the infant gastroenteric apparatus to study the digestibility of starch-based infant foods. Using M.I.D.A (Model of an Infant Digestive Apparatus), the oral, gastric and intestinal digestibility of two starch-based products were measured: 1) rice starch mixed with distilled water and treated using two different sterilization methods (the classical method with a holding temperature of 121°C for 37 min and the HTST method with a holding temperature of 137°C for 70 sec) and 2) a rice cream with (premium product) or without (basic product) an aliquot of rice flour fermented by Lactobacillus paracasei CBA L74. After the digestion the foods were analyzed for the starch concentration, the amount of D-glucose released and the percentage of hydrolyzed starch. An in vitro dynamic system, which was referred to as M.I.D.A., was obtained. Using this system, the starch digestion occurred only during the oral and intestinal phase, as expected. The D-glucose released during the intestinal phase was different between the classical and HTST methods (0.795 grams for the HTST versus 0.512 for the classical product). The same analysis was performed for the basic and premium products. In this case, the premium product had a significant difference in terms of the starch hydrolysis percentage during the entire process. The M.I.D.A. system was able to digest simple starches and a more complex food in the correct compartments. In this study, better digestibility of the premium product was revealed.

Synchronisation of chaos and its applications

NASA Astrophysics Data System (ADS)

Eroglu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

2017-07-01

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

Experimental validation of docking and capture using space robotics testbeds

NASA Technical Reports Server (NTRS)

Spofford, John; Schmitz, Eric; Hoff, William

1991-01-01

This presentation describes the application of robotic and computer vision systems to validate docking and capture operations for space cargo transfer vehicles. Three applications are discussed: (1) air bearing systems in two dimensions that yield high quality free-flying, flexible, and contact dynamics; (2) validation of docking mechanisms with misalignment and target dynamics; and (3) computer vision technology for target location and real-time tracking. All the testbeds are supported by a network of engineering workstations for dynamic and controls analyses. Dynamic simulation of multibody rigid and elastic systems are performed with the TREETOPS code. MATRIXx/System-Build and PRO-MATLAB/Simulab are the tools for control design and analysis using classical and modern techniques such as H-infinity and LQG/LTR. SANDY is a general design tool to optimize numerically a multivariable robust compensator with a user-defined structure. Mathematica and Macsyma are used to derive symbolically dynamic and kinematic equations.

NEPTUNE'S WILD DAYS: CONSTRAINTS FROM THE ECCENTRICITY DISTRIBUTION OF THE CLASSICAL KUIPER BELT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dawson, Rebekah I.; Murray-Clay, Ruth, E-mail: rdawson@cfa.harvard.edu

2012-05-01

Neptune's dynamical history shaped the current orbits of Kuiper Belt objects (KBOs), leaving clues to the planet's orbital evolution. In the 'classical' region, a population of dynamically 'hot' high-inclination KBOs overlies a flat 'cold' population with distinct physical properties. Simulations of qualitatively different histories for Neptune, including smooth migration on a circular orbit or scattering by other planets to a high eccentricity, have not simultaneously produced both populations. We explore a general Kuiper Belt assembly model that forms hot classical KBOs interior to Neptune and delivers them to the classical region, where the cold population forms in situ. First, wemore » present evidence that the cold population is confined to eccentricities well below the limit dictated by long-term survival. Therefore, Neptune must deliver hot KBOs into the long-term survival region without excessively exciting the eccentricities of the cold population. Imposing this constraint, we explore the parameter space of Neptune's eccentricity and eccentricity damping, migration, and apsidal precession. We rule out much of parameter space, except where Neptune is scattered to a moderately eccentric orbit (e > 0.15) and subsequently migrates a distance {Delta}a{sub N} = 1-6 AU. Neptune's moderate eccentricity must either damp quickly or be accompanied by fast apsidal precession. We find that Neptune's high eccentricity alone does not generate a chaotic sea in the classical region. Chaos can result from Neptune's interactions with Uranus, exciting the cold KBOs and placing additional constraints. Finally, we discuss how to interpret our constraints in the context of the full, complex dynamical history of the solar system.« less

The effect of host relaxation and dynamics on guest molecule dynamics in H2/tetrahydrofuranhydrate.

PubMed

Peterson, Vanessa K; Shoko, Elvis; Kearley, Gordon J

2011-01-01

We use ab initio molecular dynamics simulations to obtain classically the effects of H2O cage motions on the potential-energy surface (PES) of encapsulated H2 in the H2/tetrahydrofuran-hydrate system. The significant differences between the PES for the H2 in rigid and flexible cages that we find will influence calculation of the quantum dynamics of the H2. Part of these differences arises from the relaxation of the H2O cage around the classical H2, with a second part arising from the coupling of both translational and rotational motions of H2 with the H20 cage. We find that isotopic substitution of 2H for 1H of the H2O cage affects the coupling, which has implications for experiments that require the use of 2H2O, including inelastic neutron scattering that uses 2H2O cages in order to focus on the H2 guest dynamics. Overall, this work emphasizes the importance of taking into account cage dynamics in any approach used to understand the dynamics of H2 guests in porous framework materials.

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

A Comparison of Kinetic Energy and Momentum in Special Relativity and Classical Mechanics

ERIC Educational Resources Information Center

Riggs, Peter J.

2016-01-01

Kinetic energy and momentum are indispensable dynamical quantities in both the special theory of relativity and in classical mechanics. Although momentum and kinetic energy are central to understanding dynamics, the differences between their relativistic and classical notions have not always received adequate treatment in undergraduate teaching.…

The classical and quantum dynamics of molecular spins on graphene

PubMed Central

Cervetti, Christian; Rettori, Angelo; Pini, Maria Gloria; Cornia, Andrea; Repollés, Ana; Luis, Fernando; Dressel, Martin; Rauschenbach, Stephan; Kern, Klaus; Burghard, Marko; Bogani, Lapo

2015-01-01

Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic1 and quantum computing2 devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics3,4, and electrical spin-manipulation4-11. However, the influence of the graphene environment on the spin systems has yet to be unraveled12. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets13 on graphene. While the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly-developed model. Coupling to Dirac electrons introduces a dominant quantum-relaxation channel that, by driving the spins over Villain’s threshold, gives rise to fully-coherent, resonant spin tunneling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin-manipulation in graphene nanodevices. PMID:26641019

Hidden Statistics Approach to Quantum Simulations

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

A new model-free index of dynamic cerebral blood flow autoregulation.

PubMed

Chacón, Max; Jara, José Luis; Panerai, Ronney B

2014-01-01

The classic dynamic autoregulatory index (ARI), proposed by Aaslid and Tiecks, is one of the most widely used methods to assess the efficiency of dynamic cerebral autoregulation. Although this index is often used in clinical research and is also included in some commercial equipment, it exhibits considerable intra-subject variability, and has the tendency to produce false positive results in clinical applications. An alternative index of dynamic cerebral autoregulation is proposed, which overcomes most of the limitations of the classic method and also has the advantage of being model-free. This new index uses two parameters that are obtained directly from the response signal of the cerebral blood flow velocity to a transient decrease in arterial blood pressure provoked by the sudden release of bilateral thigh cuffs, and a third parameter measuring the difference in slope of this response and the change in arterial blood pressure achieved. With the values of these parameters, a corresponding classic autoregulatory index value could be calculated by using a linear regression model built from theoretical curves generated with the Aaslid-Tiecks model. In 16 healthy subjects who underwent repeated thigh-cuff manoeuvres, the model-free approach exhibited significantly lower intra-subject variability, as measured by the unbiased coefficient of variation, than the classic autoregulatory index (p = 0.032) and the Rate of Return (p<0.001), another measure of cerebral autoregulation used for this type of systemic pressure stimulus, from 39.23%±41.91% and 55.31%±31.27%, respectively, to 15.98%±7.75%.

A New Model-Free Index of Dynamic Cerebral Blood Flow Autoregulation

PubMed Central

Chacón, Max; Jara, José Luis; Panerai, Ronney B.

2014-01-01

The classic dynamic autoregulatory index (ARI), proposed by Aaslid and Tiecks, is one of the most widely used methods to assess the efficiency of dynamic cerebral autoregulation. Although this index is often used in clinical research and is also included in some commercial equipment, it exhibits considerable intra-subject variability, and has the tendency to produce false positive results in clinical applications. An alternative index of dynamic cerebral autoregulation is proposed, which overcomes most of the limitations of the classic method and also has the advantage of being model-free. This new index uses two parameters that are obtained directly from the response signal of the cerebral blood flow velocity to a transient decrease in arterial blood pressure provoked by the sudden release of bilateral thigh cuffs, and a third parameter measuring the difference in slope of this response and the change in arterial blood pressure achieved. With the values of these parameters, a corresponding classic autoregulatory index value could be calculated by using a linear regression model built from theoretical curves generated with the Aaslid-Tiecks model. In 16 healthy subjects who underwent repeated thigh-cuff manoeuvres, the model-free approach exhibited significantly lower intra-subject variability, as measured by the unbiased coefficient of variation, than the classic autoregulatory index (p = 0.032) and the Rate of Return (p<0.001), another measure of cerebral autoregulation used for this type of systemic pressure stimulus, from 39.23%±41.91% and 55.31%±31.27%, respectively, to 15.98%±7.75%. PMID:25313519

Computer Simulations and Theoretical Studies of Complex Systems: from complex fluids to frustrated magnets

NASA Astrophysics Data System (ADS)

Choi, Eunsong

Computer simulations are an integral part of research in modern condensed matter physics; they serve as a direct bridge between theory and experiment by systemactically applying a microscopic model to a collection of particles that effectively imitate a macroscopic system. In this thesis, we study two very differnt condensed systems, namely complex fluids and frustrated magnets, primarily by simulating classical dynamics of each system. In the first part of the thesis, we focus on ionic liquids (ILs) and polymers--the two complementary classes of materials that can be combined to provide various unique properties. The properties of polymers/ILs systems, such as conductivity, viscosity, and miscibility, can be fine tuned by choosing an appropriate combination of cations, anions, and polymers. However, designing a system that meets a specific need requires a concrete understanding of physics and chemistry that dictates a complex interplay between polymers and ionic liquids. In this regard, molecular dynamics (MD) simulation is an efficient tool that provides a molecular level picture of such complex systems. We study the behavior of Poly (ethylene oxide) (PEO) and the imidazolium based ionic liquids, using MD simulations and statistical mechanics. We also discuss our efforts to develop reliable and efficient classical force-fields for PEO and the ionic liquids. The second part is devoted to studies on geometrically frustrated magnets. In particular, a microscopic model, which gives rise to an incommensurate spiral magnetic ordering observed in a pyrochlore antiferromagnet is investigated. The validation of the model is made via a comparison of the spin-wave spectra with the neutron scattering data. Since the standard Holstein-Primakoff method is difficult to employ in such a complex ground state structure with a large unit cell, we carry out classical spin dynamics simulations to compute spin-wave spectra directly from the Fourier transform of spin trajectories. We conclude the study by showing an excellent agreement between the simulation and the experiment.

Liquid li structure and dynamics: A comparison between OFDFT and second nearest-neighbor embedded-atom method

DOE PAGES

Chen, Mohan; Vella, Joseph R.; Panagiotopoulos, Athanassios Z.; ...

2015-04-08

The structure and dynamics of liquid lithium are studied using two simulation methods: orbital-free (OF) first-principles molecular dynamics (MD), which employs OF density functional theory (DFT), and classical MD utilizing a second nearest-neighbor embedded-atom method potential. The properties we studied include the dynamic structure factor, the self-diffusion coefficient, the dispersion relation, the viscosity, and the bond angle distribution function. Our simulation results were compared to available experimental data when possible. Each method has distinct advantages and disadvantages. For example, OFDFT gives better agreement with experimental dynamic structure factors, yet is more computationally demanding than classical simulations. Classical simulations can accessmore » a broader temperature range and longer time scales. The combination of first-principles and classical simulations is a powerful tool for studying properties of liquid lithium.« less

DFT-derived reactive potentials for the simulation of activated processes: the case of CdTe and CdTe:S.

PubMed

Hu, Xiao Liang; Ciaglia, Riccardo; Pietrucci, Fabio; Gallet, Grégoire A; Andreoni, Wanda

2014-06-19

We introduce a new ab initio derived reactive potential for the simulation of CdTe within density functional theory (DFT) and apply it to calculate both static and dynamical properties of a number of systems (bulk solid, defective structures, liquid, surfaces) at finite temperature. In particular, we also consider cases with low sulfur concentration (CdTe:S). The analysis of DFT and classical molecular dynamics (MD) simulations performed with the same protocol leads to stringent performance tests and to a detailed comparison of the two schemes. Metadynamics techniques are used to empower both Car-Parrinello and classical molecular dynamics for the simulation of activated processes. For the latter, we consider surface reconstruction and sulfur diffusion in the bulk. The same procedures are applied using previously proposed force fields for CdTe and CdTeS materials, thus allowing for a detailed comparison of the various schemes.

Quantum vertex model for reversible classical computing.

PubMed

Chamon, C; Mucciolo, E R; Ruckenstein, A E; Yang, Z-C

2017-05-12

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

Quantum vertex model for reversible classical computing

NASA Astrophysics Data System (ADS)

Chamon, C.; Mucciolo, E. R.; Ruckenstein, A. E.; Yang, Z.-C.

2017-05-01

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without `learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

Anharmonic quantum mechanical systems do not feature phase space trajectories

NASA Astrophysics Data System (ADS)

Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole

2018-07-01

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

Ares I Flight Control System Overview

NASA Technical Reports Server (NTRS)

Hall, Charles; Lee, Chong; Jackson, Mark; Whorton, Mark; West, mark; Brandon, Jay; Hall, Rob A.; Jang, Jimmy; Bedrossian, Naz; Compton, Jimmy;

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1994-01-01

During the first half of the year, the investigators concentrated their efforts on completing the design of control laws for the longitudinal axis of the HARV. During the second half of the year they concentrated on the synthesis of control laws for the lateral-directional axes. The longitudinal control law design efforts can be briefly summarized as follows. Longitudinal control laws were developed for the HARV using mu synthesis design techniques coupled with dynamic inversion. An inner loop dynamic inversion controller was used to simplify the system dynamics by eliminating the aerodynamic nonlinearities and inertial cross coupling. Models of the errors resulting from uncertainties in the principal longitudinal aerodynamic terms were developed and included in the model of the HARV with the inner loop dynamic inversion controller. This resulted in an inner loop transfer function model which was an integrator with the modeling errors characterized as uncertainties in gain and phase. Outer loop controllers were then designed using mu synthesis to provide robustness to these modeling errors and give desired response to pilot inputs. Both pitch rate and angle of attack command following systems were designed. The following tasks have been accomplished for the lateral-directional controllers: inner and outer loop dynamic inversion controllers have been designed; an error model based on a linearized perturbation model of the inner loop system was derived; controllers for the inner loop system have been designed, using classical techniques, that control roll rate and Dutch roll response; the inner loop dynamic inversion and classical controllers have been implemented on the six degree of freedom simulation; and lateral-directional control allocation scheme has been developed based on minimizing required control effort.

Quantization of Non-Lagrangian Systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.

Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Nakajima, Kohei

2017-08-01

The quantum computer has an amazing potential of fast information processing. However, the realization of a digital quantum computer is still a challenging problem requiring highly accurate controls and key application strategies. Here we propose a platform, quantum reservoir computing, to solve these issues successfully by exploiting the natural quantum dynamics of ensemble systems, which are ubiquitous in laboratories nowadays, for machine learning. This framework enables ensemble quantum systems to universally emulate nonlinear dynamical systems including classical chaos. A number of numerical experiments show that quantum systems consisting of 5-7 qubits possess computational capabilities comparable to conventional recurrent neural networks of 100-500 nodes. This discovery opens up a paradigm for information processing with artificial intelligence powered by quantum physics.

Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.

PubMed

Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E

2015-02-01

We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.

Classical and quantum dynamics in an inverse square potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx; Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx; Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx

2014-10-15

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence ofmore » bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.« less

Application of a New Ensemble Conserving Quantum Dynamics Simulation Algorithm to Liquid para-Hydrogen and ortho-Deuterium

DOE PAGES

Smith, Kyle K.G.; Poulsen, Jens Aage; Nyman, Gunnar; ...

2015-06-30

Here, we apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm -3) and (T = 23.0 K, n = 24.61 nm -3), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. Moreover, this showsmore » that FK-QCW provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is not formally limited to correlation functions involving linear operators.« less

Application of a New Ensemble Conserving Quantum Dynamics Simulation Algorithm to Liquid para-Hydrogen and ortho-Deuterium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Kyle K.G.; Poulsen, Jens Aage; Nyman, Gunnar

Here, we apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm -3) and (T = 23.0 K, n = 24.61 nm -3), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. Moreover, this showsmore » that FK-QCW provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is not formally limited to correlation functions involving linear operators.« less

Application of a new ensemble conserving quantum dynamics simulation algorithm to liquid para-hydrogen and ortho-deuterium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Kyle K. G., E-mail: kylesmith@utexas.edu; Poulsen, Jens Aage, E-mail: jens72@chem.gu.se; Nyman, Gunnar, E-mail: nyman@chem.gu.se

We apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm{sup −3}) and (T = 23.0 K, n = 24.61 nm{sup −3}), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. This shows that FK-QCWmore » provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is not formally limited to correlation functions involving linear operators.« less

Application of a new ensemble conserving quantum dynamics simulation algorithm to liquid para-hydrogen and ortho-deuterium.

PubMed

Smith, Kyle K G; Poulsen, Jens Aage; Nyman, Gunnar; Cunsolo, Alessandro; Rossky, Peter J

2015-06-28

We apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm(-3)) and (T = 23.0 K, n = 24.61 nm(-3)), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. This shows that FK-QCW provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is not formally limited to correlation functions involving linear operators.

Dynamics and Novel Mechanisms of SN2 Reactions on ab Initio Analytical Potential Energy Surfaces.

PubMed

Szabó, István; Czakó, Gábor

2017-11-30

We describe a novel theoretical approach to the bimolecular nucleophilic substitution (S N 2) reactions that is based on analytical potential energy surfaces (PESs) obtained by fitting a few tens of thousands high-level ab initio energy points. These PESs allow computing millions of quasi-classical trajectories thereby providing unprecedented statistical accuracy for S N 2 reactions, as well as performing high-dimensional quantum dynamics computations. We developed full-dimensional ab initio PESs for the F - + CH 3 Y [Y = F, Cl, I] systems, which describe the direct and indirect, complex-forming Walden-inversion, the frontside attack, and the new double-inversion pathways as well as the proton-transfer channels. Reaction dynamics simulations on the new PESs revealed (a) a novel double-inversion S N 2 mechanism, (b) frontside complex formation, (c) the dynamics of proton transfer, (d) vibrational and rotational mode specificity, (e) mode-specific product vibrational distributions, (f) agreement between classical and quantum dynamics, (g) good agreement with measured scattering angle and product internal energy distributions, and (h) significant leaving group effect in accord with experiments.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

PubMed Central

Malhado, João Pedro; Bearpark, Michael J.; Hynes, James T.

2014-01-01

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field. PMID:25485263

Precise measurement of coupling strength and high temperature quantum effect in a nonlinearly coupled qubit-oscillator system

NASA Astrophysics Data System (ADS)

Ge, Li; Zhao, Nan

2018-04-01

We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.

Hamiltonian dynamics for complex food webs

NASA Astrophysics Data System (ADS)

Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

2016-03-01

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Removing the barrier to the calculation of activation energies

DOE PAGES

Mesele, Oluwaseun O.; Thompson, Ward H.

2016-10-06

Approaches for directly calculating the activation energy for a chemical reaction from a simulation at a single temperature are explored with applications to both classical and quantum systems. The activation energy is obtained from a time correlation function that can be evaluated from the same molecular dynamics trajectories or quantum dynamics used to evaluate the rate constant itself and thus requires essentially no extra computational work.

U1108 performance model

NASA Technical Reports Server (NTRS)

Trachta, G.

1976-01-01

A model of Univac 1108 work flow has been developed to assist in performance evaluation studies and configuration planning. Workload profiles and system configurations are parameterized for ease of experimental modification. Outputs include capacity estimates and performance evaluation functions. The U1108 system is conceptualized as a service network; classical queueing theory is used to evaluate network dynamics.

Students' Understanding of Equilibrium and Stability: The Case of Dynamic Systems

ERIC Educational Resources Information Center

Canu, Michaël; de Hosson, Cécile; Duque, Mauricio

2016-01-01

Engineering students in control courses have been observed to lack an understanding of equilibrium and stability, both of which are crucial concepts in this discipline. The introduction of these concepts is generally based on the study of classical examples from Newtonian mechanics supplemented with a control system. Equilibrium and stability are…

Reversibility and stability of information processing systems

NASA Technical Reports Server (NTRS)

Zurek, W. H.

1984-01-01

Classical and quantum models of dynamically reversible computers are considered. Instabilities in the evolution of the classical 'billiard ball computer' are analyzed and shown to result in a one-bit increase of entropy per step of computation. 'Quantum spin computers', on the other hand, are not only microscopically, but also operationally reversible. Readoff of the output of quantum computation is shown not to interfere with this reversibility. Dissipation, while avoidable in principle, can be used in practice along with redundancy to prevent errors.

Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2017-08-01

We study the problem of separation of variables for classical integrable Hamiltonian systems governed by non-skew-symmetric non-dynamical so(3)\\otimes so(3) -valued elliptic r-matrices with spectral parameters. We consider several examples of such models, and perform separation of variables for classical anisotropic one- and two-spin Gaudin-type models in an external magnetic field, and for Jaynes-Cummings-Dicke-type models without the rotating wave approximation.

Observer properties for understanding dynamical displays: Capacities, limitations, and defaults

NASA Technical Reports Server (NTRS)

Proffitt, Dennis R.; Kaiser, Mary K.

1991-01-01

People's ability to extract relevant information while viewing ongoing events is discussed in terms of human capabilities, limitations, and defaults. A taxonomy of event complexity is developed which predicts which dynamical events people can and cannot construe. This taxonomy is related to the distinction drawn in classical mechanics between particle and extended body motions. People's commonsense understandings of simple mechanical systems are impacted little by formal training, but rather reflect heuristical simplifications that focus on a single dimension of perceived dynamical relevance.

New features in the structure of the classical Kuiper Belt

NASA Astrophysics Data System (ADS)

Gladman, Brett; Bannister, Michele T.; Alexandersen, Mike; Chen, Ying-Tung; Gwyn, Stephen; Kavelaars, J. J.; Petit, Jean-Marc; Volk, Kathryn; OSSOS Collaboration

2016-10-01

We report fascinating new dynamical structures emerging from a higher precision view of the classical Kuiper belt (the plentiful non-resonant orbits with semimajor axes in roughly the a=35-60 au range). The classical Kuiper Belt divides into multiple sub-populations: an 'inner' classical belt (a small group of non-resonant objects with a<39.4 au where the 3:2 resonance is located), an abundant 'main' classical belt (between the 3:2 and the 2:1 at a=47.4 au), and a difficult to study outer classical belt beyond the 2:1. We examine the dynamical structure, as precisely revealed in the detections from OSSOS (the Outer Solar System Origin's Survey); the data set is of superb quality in terms of orbital element and numbers of detections (Kavelaars et al, this meeting).The previous CFEPS survey showed that the main classical belt requires a complex dynamical substructure that goes beyond a simple 'hot versus cold' division based primarily on orbital inclination; the 'cold' inclination component requires two sub-components in the semimajor axis and perihelion distance q space (Petit et al 2011). CFEPS modelled this as a 'stirred' component present at all a=40-47 AU semimajor axes, with a dense superposed 'kernel' near a=44 AU at low eccentricity; the first OSSOS data release remained consistent with this (Bannister et al 2016). As with the main asteroid belt, as statistics and orbital quality improve we see additional significant substructure emerging in the classical belt's orbital distribution.OSSOS continues to add evidence that the cold stirred component extends smoothly beyond the 2:1 (Bannister et al 2016). Unexpectedly, the data also reveal the clear existence of a paucity of orbits just beyond the outer edge of the kernel; there are significantly fewer TNOs in the narrow semimajor axis band from a=44.5-45.0 AU. This may be related to the kernel population's creation, or it may be an independent feature created by planet migration as resonances moved in the primordial Kuiper Belt.

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium.

PubMed

Hone, Tyler D; Voth, Gregory A

2004-10-01

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids. (c) 2004 American Institute of Physics

Ab Initio Calculations of Transport in Titanium and Aluminum Mixtures

NASA Astrophysics Data System (ADS)

Walker, Nicholas; Novak, Brian; Tam, Ka Ming; Moldovan, Dorel; Jarrell, Mark

In classical molecular dynamics simulations, the self-diffusion and shear viscosity of titanium about the melting point have fallen within the ranges provided by experimental data. However, the experimental data is difficult to collect and has been rather scattered, making it of limited value for the validation of these calculations. By using ab initio molecular dynamics simulations within the density functional theory framework, the classical molecular dynamics data can be validated. The dynamical data from the ab initio molecular dynamics can also be used to calculate new potentials for use in classical molecular dynamics, allowing for more accurate classical dynamics simulations for the liquid phase. For metallic materials such as titanium and aluminum alloys, these calculations are very valuable due to an increasing demand for the knowledge of their thermophysical properties that drive the development of new materials. For example, alongside knowledge of the surface tension, viscosity is an important input for modeling the additive manufacturing process at the continuum level. We are developing calculations of the viscosity along with the self-diffusion for aluminum, titanium, and titanium-aluminum alloys with ab initio molecular dynamics. Supported by the National Science Foundation through cooperative agreement OIA-1541079 and the Louisiana Board of Regents.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches.

PubMed

Antipov, Sergey V; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2017-11-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H 2 , local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

PubMed Central

Antipov, Sergey V.; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2018-01-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research “Molecular Ultrafast Science and Technology,” are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase. PMID:29376107

A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

NASA Astrophysics Data System (ADS)

Ghosh, Shankar; Merin, A. P.; Bhattacharya, S.; Nitsure, Nitin

2018-04-01

We present a geometric framework to deal with mechanical systems which have unilateral constraints, and are subject to damping/friction, which cannot be treated within usual classical mechanics. In this new framework, the dynamical evolution of the system takes place on a multidimensional curvilinear polyhedron, and energetics near the corners of the polyhedron leads to qualitative behaviour such as stable entrapment and bifurcation. We illustrate this by an experiment in which dumbbells, placed inside a tilted hollow cylindrical drum that rotates slowly around its axis, climb uphill by forming dynamically stable pairs, seemingly against the pull of gravity.

Neural dynamic optimization for control systems. I. Background.

PubMed

Seong, C Y; Widrow, B

2001-01-01

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the background and motivations for the development of NDO, while the two other subsequent papers of this topic present the theory of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

Neural dynamic optimization for control systems.III. Applications.

PubMed

Seong, C Y; Widrow, B

2001-01-01

For pt.II. see ibid., p. 490-501. The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper demonstrates NDO with several applications including control of autonomous vehicles and of a robot-arm, while the two other companion papers of this topic describes the background for the development of NDO and present the theory of the method, respectively.

Neural dynamic optimization for control systems.II. Theory.

PubMed

Seong, C Y; Widrow, B

2001-01-01

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the theory of NDO, while the two other companion papers of this topic explain the background for the development of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

Communication: Note on detailed balance in symmetrical quasi-classical models for electronically non-adiabatic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

2015-04-07

It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employedmore » in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.« less

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Car and Parrinello meet Green and Kubo: simulating atomic heat transport from equilibrium ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Baroni, Stefano

Modern simulation methods based on electronic-structure theory have long been deemed unfit to compute heat transport coefficients within the Green-Kubo formalism. This is so because the quantum-mechanical energy density from which the heat flux is derived is inherently ill defined, thus allegedly hampering the use of the Green-Kubo formula. While this objection would actually apply to classical systems as well, I will demonstrate that the thermal conductivity is indeed independent of the specific microscopic expression for the energy density and current from which it is derived. This fact results from a kind of gauge invariance stemming from energy conservation and extensivity, which I will illustrate numerically for a classical Lennard-Jones fluid. I will then introduce an expression for the adiabatic energy flux, derived within density-functional theory, that allows simulating atomic heat transport using equilibrium ab initio molecular dynamics. The resulting methodology is demonstrated by comparing results from ab-initio and classical molecular-dynamics simulations of a model liquid-Argon system, for which accurate inter-atomic potentials are derived by the force-matching method, and applied to compute the thermal conductivity of heavy water at ambient conditions. The problem of evaluating transport coefficients along with their accuracy from relatively short trajectories is finally addressed and discussed with a few representative examples. Partially funded by the European Union through the MaX Centre of Excellence (Grant No. 676598).

Trapped ion system for sympathetic cooling and non-equilibrium dynamics

NASA Astrophysics Data System (ADS)

Doret, Charlie; Jubin, Sierra; Stevenson, Sarah

2017-04-01

Atomic systems are superbly suited to the study of non-equilibrium dynamics. These systems' exquisite isolation from environmental perturbations leads to long relaxation times that enable exploration of far-from-equilibrium phenomena. We present progress towards trapping chains of multiple co-trapped calcium isotopes geared towards measuring thermal equilibration and sympathetic cooling rates. We also discuss plans for future experiments in non-equilibrium statistical mechanics, including exploration of the quantum-to-classical crossover between ballistic transport and diffusive, Fourier's Law conduction. This work is supported by Cottrell College Science Award from the Research Corporation for Science Advancement and by Williams College.

Role of Orbital Dynamics in Spin Relaxation and Weak Antilocalization in Quantum Dots

NASA Astrophysics Data System (ADS)

Zaitsev, Oleg; Frustaglia, Diego; Richter, Klaus

2005-01-01

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.

Archetypal dynamics, emergent situations, and the reality game.

PubMed

Sulis, William

2010-07-01

The classical approach to the modeling of reality is founded upon its objectification. Although successful dealing with inanimate matter, objectification has proven to be much less successful elsewhere, sometimes to the point of paradox. This paper discusses an approach to the modeling of reality based upon the concept of process as formulated within the framework of archetypal dynamics. Reality is conceptualized as an intermingling of information-transducing systems, together with the semantic frames that effectively describe and ascribe meaning to each system, along with particular formal representations of same which constitute the archetypes. Archetypal dynamics is the study of the relationships between systems, frames and their representations and the flow of information among these different entities. In this paper a specific formal representation of archetypal dynamics using tapestries is given, and a dynamics is founded upon this representation in the form of a combinatorial game called a reality game. Some simple examples are presented.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Quantum Spin Glasses, Annealing and Computation

NASA Astrophysics Data System (ADS)

Chakrabarti, Bikas K.; Inoue, Jun-ichi; Tamura, Ryo; Tanaka, Shu

2017-05-01

List of tables; List of figures, Preface; 1. Introduction; Part I. Quantum Spin Glass, Annealing and Computation: 2. Classical spin models from ferromagnetic spin systems to spin glasses; 3. Simulated annealing; 4. Quantum spin glass; 5. Quantum dynamics; 6. Quantum annealing; Part II. Additional Notes: 7. Notes on adiabatic quantum computers; 8. Quantum information and quenching dynamics; 9. A brief historical note on the studies of quantum glass, annealing and computation.

CONTIN XPCS: software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, calledCONTIN XPCS, is an extension of traditionalCONTINanalysis and accommodates the various dynamics encountered inmore » equilibrium XPCS measurements.« less

CONTIN XPCS: software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics

DOE PAGES

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; ...

2018-02-01

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, calledCONTIN XPCS, is an extension of traditionalCONTINanalysis and accommodates the various dynamics encountered inmore » equilibrium XPCS measurements.« less

Improved dynamic analysis method using load-dependent Ritz vectors

NASA Technical Reports Server (NTRS)

Escobedo-Torres, J.; Ricles, J. M.

1993-01-01

The dynamic analysis of large space structures is important in order to predict their behavior under operating conditions. Computer models of large space structures are characterized by having a large number of degrees of freedom, and the computational effort required to carry out the analysis is very large. Conventional methods of solution utilize a subset of the eigenvectors of the system, but for systems with many degrees of freedom, the solution of the eigenproblem is in many cases the most costly phase of the analysis. For this reason, alternate solution methods need to be considered. It is important that the method chosen for the analysis be efficient and that accurate results be obtainable. It is important that the method chosen for the analysis be efficient and that accurate results be obtainable. The load dependent Ritz vector method is presented as an alternative to the classical normal mode methods for obtaining dynamic responses of large space structures. A simplified model of a space station is used to compare results. Results show that the load dependent Ritz vector method predicts the dynamic response better than the classical normal mode method. Even though this alternate method is very promising, further studies are necessary to fully understand its attributes and limitations.

Linkages between Families and Political Extremism: A Theory of the Authoritarian Personality and Family System Dynamics.

ERIC Educational Resources Information Center

Gaziano, Cecilie

This paper seeks to integrate some ideas from family systems theory and attachment theory within a theory of public opinion and social movement. Citing the classic "The Authoritarian Personality," the paper states that the first authorities children know, their parents or other caregivers, shape children's attitudes toward all…

The Integration of Social-Ecological Resilience and Law

EPA Science Inventory

Growing recognition of the inherent uncertainty associated with the dynamics of ecological systems and their often non-linear and surprising behavior, however, presents a set of problems outside the scope of classic environmental law, and has lead to a fundamental understanding a...

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Lattice constants of pure methane and carbon dioxide hydrates at low temperatures. Implementing quantum corrections to classical molecular dynamics studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costandy, Joseph; Michalis, Vasileios K.; Economou, Ioannis G., E-mail: i.tsimpanogiannis@qatar.tamu.edu, E-mail: ioannis.economou@qatar.tamu.edu

2016-03-28

We introduce a simple correction to the calculation of the lattice constants of fully occupied structure sI methane or carbon dioxide pure hydrates that are obtained from classical molecular dynamics simulations using the TIP4PQ/2005 water force field. The obtained corrected lattice constants are subsequently used in order to obtain isobaric thermal expansion coefficients of the pure gas hydrates that exhibit a trend that is significantly closer to the experimental behavior than previously reported classical molecular dynamics studies.

Soliton Gases and Generalized Hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

2018-01-01

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

Optimal control of underactuated mechanical systems: A geometric approach

NASA Astrophysics Data System (ADS)

Colombo, Leonardo; Martín De Diego, David; Zuccalli, Marcela

2010-08-01

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.

Thermalization as an invisibility cloak for fragile quantum superpositions

NASA Astrophysics Data System (ADS)

Hahn, Walter; Fine, Boris V.

2017-07-01

We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions "fragile" if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition evolve under the internal thermalization dynamics of the system, followed by a time-reversal manipulation known as Loschmidt echo. The thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure. We validate the method by applying it to a cluster of spins ½.

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Amplification without instability: applying fluid dynamical insights in chemistry and biology

NASA Astrophysics Data System (ADS)

McCoy, Jonathan H.

2013-11-01

While amplification of small perturbations often arises from instability, transient amplification is possible locally even in asymptotically stable systems. That is, knowledge of a system's stability properties can mislead one's intuition for its transient behaviors. This insight, which has an interesting history in fluid dynamics, has more recently been rediscovered in ecology. Surprisingly, many nonlinear fluid dynamical and ecological systems share linear features associated with transient amplification of noise. This paper aims to establish that these features are widespread in many other disciplines concerned with noisy systems, especially chemistry, cell biology and molecular biology. Here, using classic nonlinear systems and the graphical language of network science, we explore how the noise amplification problem can be reframed in terms of activatory and inhibitory interactions between dynamical variables. The interaction patterns considered here are found in a great variety of systems, ranging from autocatalytic reactions and activator-inhibitor systems to influential models of nerve conduction, glycolysis, cell signaling and circadian rhythms.

Quantum decoherence and interlevel relations

NASA Astrophysics Data System (ADS)

Crull, Elise M.

Quantum decoherence is a dynamical process whereby a system's phase relations become delocalized due to interaction and subsequent entanglement with its environment. This delocalization, or decoherence, forces the quantum system into a state that is apparently classical (or apparently an eigenstate) by prodigiously suppressing features that typically give rise to so-called quantum behavior. Thus it has been frequently proposed by physicists and philosophers alike that decoherence explains the dynamical transition from quantum behavior to classical behavior. Statements like this assume the existence of distinct realms, however, and the present thesis is an exploration of the metaphysical consequences of quantum decoherence motivated by the question of the quantum-to-classical transition and interlevel relations: if there are in-principle "classical" and "quantum" levels, what are the relations between them? And if there are no such levels, what follows? Importantly, the following philosophical investigations are carried out by intentionally leaving aside the measurement problem and concerns about particular interpretations of quantum mechanics. Good philosophical work, it is argued, can be done without adopting a specific interpretational framework and without recourse to the measurement problem. After introducing the physics of decoherence and exploring the four canonical models applied to system-environment interactions, it is argued that, ontologically speaking, there exist no levels. This claim---called the "nontological thesis"---exposes as ill-posed questions regarding the transition from the quantum regime to the classical regime and reveals the inappropriateness of interlevel relations (like reduction, supervenience and emergence) operating within metaphysical frameworks. The nontological thesis has further important consequences regarding intralevel relations: not only are there no meaningful ways to carve the world into levels, but there are no meaningful ways to carve the world into parts and wholes either. These conclusions, supported by quantum decoherence and the empirical success of its models, drastically alter the philosophical terrain---not just in physics or in the philosophy of physics, but in traditional metaphysics as well.

DOE Office of Scientific and Technical Information (OSTI.GOV)

D’Arrigo, A., E-mail: antonio.darrigo@dmfci.unict.it; Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania; Centro Siciliano di Fisica Nucleare e Struttura della Materia

We investigate the phenomenon of bipartite entanglement revivals under purely local operations in systems subject to local and independent classical noise sources. We explain this apparent paradox in the physical ensemble description of the system state by introducing the concept of “hidden” entanglement, which indicates the amount of entanglement that cannot be exploited due to the lack of classical information on the system. For this reason this part of entanglement can be recovered without the action of non-local operations or back-transfer process. For two noninteracting qubits under a low-frequency stochastic noise, we show that entanglement can be recovered by localmore » pulses only. We also discuss how hidden entanglement may provide new insights about entanglement revivals in non-Markovian dynamics.« less

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

2006-11-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

1995-04-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

On the dynamic response of pressure transmission lines in the research of helium-charged free piston Stirling engines

NASA Technical Reports Server (NTRS)

Miller, Eric L.; Dudenhoefer, James E.

1989-01-01

In free piston Stirling engine research the integrity of both amplitude and phase of the dynamic pressure measurements is critical to the characterization of cycle dynamics and thermodynamics. It is therefore necessary to appreciate all possible sources of signal distortion when designing pressure measurement systems for this type of research. The signal distortion inherent to pressure transmission lines is discussed. Based on results from classical analysis, guidelines are formulated to describe the dynamic response properties of a volume-terminated transmission tube for applications involving helium-charged free piston Stirling engines. The scope and limitations of the dynamic response analysis are considered.

An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows.

PubMed

Oettinger, David; Haller, George

2016-10-01

Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ 2 (x 0 ), of the Cauchy-Green strain tensor. This ξ 2 -system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincaré maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ 2 -system to uncover both hyperbolic and elliptic LCSs from a single computation.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Hybrid classical/quantum simulation for infrared spectroscopy of water

NASA Astrophysics Data System (ADS)

Maekawa, Yuki; Sasaoka, Kenji; Ube, Takuji; Ishiguro, Takashi; Yamamoto, Takahiro

2018-05-01

We have developed a hybrid classical/quantum simulation method to calculate the infrared (IR) spectrum of water. The proposed method achieves much higher accuracy than conventional classical molecular dynamics (MD) simulations at a much lower computational cost than ab initio MD simulations. The IR spectrum of water is obtained as an ensemble average of the eigenvalues of the dynamical matrix constructed by ab initio calculations, using the positions of oxygen atoms that constitute water molecules obtained from the classical MD simulation. The calculated IR spectrum is in excellent agreement with the experimental IR spectrum.

A multi-state trajectory method for non-adiabatic dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tao, Guohua, E-mail: taogh@pkusz.edu.cn

2016-03-07

A multi-state trajectory approach is proposed to describe nuclear-electron coupled dynamics in nonadiabatic simulations. In this approach, each electronic state is associated with an individual trajectory, among which electronic transition occurs. The set of these individual trajectories constitutes a multi-state trajectory, and nuclear dynamics is described by one of these individual trajectories as the system is on the corresponding state. The total nuclear-electron coupled dynamics is obtained from the ensemble average of the multi-state trajectories. A variety of benchmark systems such as the spin-boson system have been tested and the results generated using the quasi-classical version of the method showmore » reasonably good agreement with the exact quantum calculations. Featured in a clear multi-state picture, high efficiency, and excellent numerical stability, the proposed method may have advantages in being implemented to realistic complex molecular systems, and it could be straightforwardly applied to general nonadiabatic dynamics involving multiple states.« less

Interaction and dynamics of ionic liquids based on choline and amino acid anions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campetella, M.; Bodo, E., E-mail: enrico.bodo@uniroma1.it; Caminiti, R., E-mail: ruggero.caminiti@uniroma1.it

2015-06-21

The combination of amino acid anions with the choline cation gives origin to a new and potentially important class of organic ionic liquids that might represent a viable and bio-compatible alternative with respect to the traditional ones. We present here a detailed study of the bulk phase of the prototype system composed of the simplest amino acid (alanine) anion and the choline cation, based on ab initio and classical molecular dynamics. Theoretical findings have been validated by comparing with accurate experimental X-ray diffraction data and infrared spectra. We find that hydrogen bonding (HB) features in these systems are crucial inmore » establishing their local geometric structure. We have also found that these HBs once formed are persistent and that the proton resides exclusively on the choline cation. In addition, we show that a classical force field description for this particular ionic liquid can be accurately performed by using a slightly modified version of the generalized AMBER force field.« less

Interaction and dynamics of ionic liquids based on choline and amino acid anions

NASA Astrophysics Data System (ADS)

Campetella, M.; Bodo, E.; Caminiti, R.; Martino, A.; D'Apuzzo, F.; Lupi, S.; Gontrani, L.

2015-06-01

The combination of amino acid anions with the choline cation gives origin to a new and potentially important class of organic ionic liquids that might represent a viable and bio-compatible alternative with respect to the traditional ones. We present here a detailed study of the bulk phase of the prototype system composed of the simplest amino acid (alanine) anion and the choline cation, based on ab initio and classical molecular dynamics. Theoretical findings have been validated by comparing with accurate experimental X-ray diffraction data and infrared spectra. We find that hydrogen bonding (HB) features in these systems are crucial in establishing their local geometric structure. We have also found that these HBs once formed are persistent and that the proton resides exclusively on the choline cation. In addition, we show that a classical force field description for this particular ionic liquid can be accurately performed by using a slightly modified version of the generalized AMBER force field.

Wavefront aberrations of x-ray dynamical diffraction beams.

PubMed

Liao, Keliang; Hong, Youli; Sheng, Weifan

2014-10-01

The effects of dynamical diffraction in x-ray diffractive optics with large numerical aperture render the wavefront aberrations difficult to describe using the aberration polynomials, yet knowledge of them plays an important role in a vast variety of scientific problems ranging from optical testing to adaptive optics. Although the diffraction theory of optical aberrations was established decades ago, its application in the area of x-ray dynamical diffraction theory (DDT) is still lacking. Here, we conduct a theoretical study on the aberration properties of x-ray dynamical diffraction beams. By treating the modulus of the complex envelope as the amplitude weight function in the orthogonalization procedure, we generalize the nonrecursive matrix method for the determination of orthonormal aberration polynomials, wherein Zernike DDT and Legendre DDT polynomials are proposed. As an example, we investigate the aberration evolution inside a tilted multilayer Laue lens. The corresponding Legendre DDT polynomials are obtained numerically, which represent balanced aberrations yielding minimum variance of the classical aberrations of an anamorphic optical system. The balancing of classical aberrations and their standard deviations are discussed. We also present the Strehl ratio of the primary and secondary balanced aberrations.

Ab initio molecular dynamics simulation of LiBr association in water

NASA Astrophysics Data System (ADS)

Izvekov, Sergei; Philpott, Michael R.

2000-12-01

A computationally economical scheme which unifies the density functional description of an ionic solute and the classical description of a solvent was developed. The density functional part of the scheme comprises Car-Parrinello and related formalisms. The substantial saving in the computer time is achieved by performing the ab initio molecular dynamics of the solute electronic structure in a relatively small basis set constructed from lowest energy Kohn-Sham orbitals calculated for a single anion in vacuum, instead of using plane wave basis. The methodology permits simulation of an ionic solution for longer time scales while keeping accuracy in the prediction of the solute electronic structure. As an example the association of the Li+-Br- ion-pair system in water is studied. The results of the combined molecular dynamics simulation are compared with that obtained from the classical simulation with ion-ion interaction described by the pair potential of Born-Huggins-Mayer type. The comparison reveals an important role played by the polarization of the Br- ion in the dynamics of ion pair association.

Functionality limit of classical simulated annealing

NASA Astrophysics Data System (ADS)

Hasegawa, M.

2015-09-01

By analyzing the system dynamics in the landscape paradigm, optimization function of classical simulated annealing is reviewed on the random traveling salesman problems. The properly functioning region of the algorithm is experimentally determined in the size-time plane and the influence of its boundary on the scalability test is examined in the standard framework of this method. From both results, an empirical choice of temperature length is plausibly explained as a minimum requirement that the algorithm maintains its scalability within its functionality limit. The study exemplifies the applicability of computational physics analysis to the optimization algorithm research.

Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise

NASA Astrophysics Data System (ADS)

Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius; Fouokeng, Georges Collince

2017-04-01

We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.

Parametric models to compute tryptophan fluorescence wavelengths from classical protein simulations.

PubMed

Lopez, Alvaro J; Martínez, Leandro

2018-02-26

Fluorescence spectroscopy is an important method to study protein conformational dynamics and solvation structures. Tryptophan (Trp) residues are the most important and practical intrinsic probes for protein fluorescence due to the variability of their fluorescence wavelengths: Trp residues emit in wavelengths ranging from 308 to 360 nm depending on the local molecular environment. Fluorescence involves electronic transitions, thus its computational modeling is a challenging task. We show that it is possible to predict the wavelength of emission of a Trp residue from classical molecular dynamics simulations by computing the solvent-accessible surface area or the electrostatic interaction between the indole group and the rest of the system. Linear parametric models are obtained to predict the maximum emission wavelengths with standard errors of the order 5 nm. In a set of 19 proteins with emission wavelengths ranging from 308 to 352 nm, the best model predicts the maximum wavelength of emission with a standard error of 4.89 nm and a quadratic Pearson correlation coefficient of 0.81. These models can be used for the interpretation of fluorescence spectra of proteins with multiple Trp residues, or for which local Trp environmental variability exists and can be probed by classical molecular dynamics simulations. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

A reformulation of mechanics and electrodynamics.

PubMed

Pinheiro, Mario J

2017-07-01

Classical mechanics, as commonly taught in engineering and science, are confined to the conventional Newtonian theory. But classical mechanics has not really changed in substance since Newton formulation, describing simultaneous rotation and translation of objects with somewhat complicate drawbacks, risking interpretation of forces in non-inertial frames. In this work we introduce a new variational principle for out-of-equilibrium, rotating systems, obtaining a set of two first order differential equations that introduces a thermodynamic-mechanistic time into Newton's dynamical equation, and revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. The results is a more consistent formulation of dynamics and electrodynamics, explaining natural phenomena as the outcome from a balance between energy and entropy, embedding translational with rotational motion into a single equation, showing centrifugal and Coriolis force as derivatives from the transport of angular momentum, and offering a natural method to handle variational problems, as shown with the brachistochrone problem. In consequence, a new force term appears, the topological torsion current, important for spacecraft dynamics. We describe a set of solved problems showing the potential of a competing technique, with significant interest to electrodynamics as well. We expect this new approach to have impact in a large class of scientific and technological problems.

Structure-based control of complex networks with nonlinear dynamics

NASA Astrophysics Data System (ADS)

Zanudo, Jorge G. T.; Yang, Gang; Albert, Reka

What can we learn about controlling a system solely from its underlying network structure? Here we use a framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors, regardless of the dynamic details and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of classical structural control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case, but not in specific model instances. This work was supported by NSF Grants PHY 1205840 and IIS 1160995. JGTZ is a recipient of a Stand Up To Cancer - The V Foundation Convergence Scholar Award.

Potentials Unbounded Below

NASA Astrophysics Data System (ADS)

Curtright, Thomas

2011-04-01

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V. Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the particle. The Beverton-Holt and Skellam models of population dynamics, and particular cases of the logistic map are used to illustrate these features.

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling.

PubMed

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H; Burghardt, Irene; Martinazzo, Rocco

2015-09-28

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonfanti, Matteo, E-mail: matteo.bonfanti@unimi.it; Jackson, Bret; Hughes, Keith H.

2015-09-28

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theorymore » for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.« less

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Effect of pairwise additivity on finite-temperature behavior of classical ideal gas

NASA Astrophysics Data System (ADS)

Shekaari, Ashkan; Jafari, Mahmoud

2018-05-01

Finite-temperature molecular dynamics simulations have been applied to inquire into the effect of pairwise additivity on the behavior of classical ideal gas within the temperature range of T = 250-4000 K via applying a variety of pair potentials and then examining the temperature dependence of a number of thermodynamical properties. Examining the compressibility factor reveals the most deviation from ideal-gas behavior for the Lennard-Jones system mainly due to the presence of both the attractive and repulsive terms. The systems with either attractive or repulsive intermolecular potentials are found to present no resemblance to real gases, but the most similarity to the ideal one as temperature rises.

Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter With Enhanced Numerical Stability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qi, Junjian; Sun, Kai; Wang, Jianhui

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKFGPS) is proposed and compared with five existing approaches, including UKFschol, UKF-kappa, UKFmodified, UKF-Delta Q, and the squareroot UKF (SRUKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is foundmore » that UKFschol, UKF-kappa, and UKF-Delta Q do not work well in some estimations while UKFGPS works well in most cases. UKFmodified and SRUKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.« less

Visualization of system dynamics using phasegrams

PubMed Central

Herbst, Christian T.; Herzel, Hanspeter; Švec, Jan G.; Wyman, Megan T.; Fitch, W. Tecumseh

2013-01-01

A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine. PMID:23697715

Chaotic dynamics of controlled electric power systems

NASA Astrophysics Data System (ADS)

Kozlov, V. N.; Trosko, I. U.

2016-12-01

The conditions for appearance of chaotic dynamics of electromagnetic and electromechanical processes in energy systems described by the Park-Gorev bilinear differential equations with account for lags of coordinates and restrictions on control have been formulated. On the basis of classical equations, the parameters of synchronous generators and power lines, at which the chaotic dynamics of energy systems appears, have been found. The qualitative and quantitative characteristics of chaotic processes in energy associations of two types, based on the Hopf theorem, and methods of nonstationary linearization and decompositions are given. The properties of spectral characteristics of chaotic processes have been investigated, and the qualitative similarity of bilinear equations of power systems and Lorentz equations have been found. These results can be used for modernization of the systems of control of energy objects. The qualitative and quantitative characteristics for power energy systems as objects of control and for some laws of control with the feedback have been established.

Stability enhancement of high Prandtl number chaotic convection in an anisotropic porous layer with feedback control

NASA Astrophysics Data System (ADS)

Mahmud, M. N.

2018-04-01

The chaotic dynamical behaviour of thermal convection in an anisotropic porous layer subject to gravity, heated from below and cooled from above, is studied based on theory of dynamical system in the presence of feedback control. The extended Darcy model, which includes the time derivative has been employed in the momentum equation to derive a low dimensional Lorenz-like equation by using Galerkin-truncated approximation. The classical fourth-order Runge-Kutta method is used to obtain the numerical solution in order to exemplify the dynamics of the nonlinear autonomous system. The results show that stability enhancement of chaotic convection is feasible via feedback control.

Gross-Pitaevski map as a chaotic dynamical system.

PubMed

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

The Next Generation of High-Speed Dynamic Stability Wind Tunnel Testing (Invited)

NASA Technical Reports Server (NTRS)

Tomek, Deborah M.; Sewall, William G.; Mason, Stan E.; Szchur, Bill W. A.

2006-01-01

Throughout industry, accurate measurement and modeling of dynamic derivative data at high-speed conditions has been an ongoing challenge. The expansion of flight envelopes and non-conventional vehicle design has greatly increased the demand for accurate prediction and modeling of vehicle dynamic behavior. With these issues in mind, NASA Langley Research Center (LaRC) embarked on the development and shakedown of a high-speed dynamic stability test technique that addresses the longstanding problem of accurately measuring dynamic derivatives outside the low-speed regime. The new test technique was built upon legacy technology, replacing an antiquated forced oscillation system, and greatly expanding the capabilities beyond classic forced oscillation testing at both low and high speeds. The modern system is capable of providing a snapshot of dynamic behavior over a periodic cycle for varying frequencies, not just a damping derivative term at a single frequency.

Quantum versus classical hyperfine-induced dynamics in a quantum dota)

NASA Astrophysics Data System (ADS)

Coish, W. A.; Loss, Daniel; Yuzbashyan, E. A.; Altshuler, B. L.

2007-04-01

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t <τc, after which they differ markedly.

Dynamics of Eastern Boundary Currents and Their Effects on Sound Speed Structure

DTIC Science & Technology

2006-06-01

Canary Current System (NCCS) off Morocco and the Iberian Peninsula , and the Leeuwin Current System (LCS) off Western Australia. These systems...Africa and the Iberian Peninsula . This system is considered a classical EBC and marks the closing eastern boundary of the North Atlantic Gyre...with several narrow filaments of cooler water extending off the coast of the Iberian Peninsula (Fiuza and Sousa, 1989) and Cape Ghir in northwest Africa

Stability analysis of spacecraft power systems

NASA Technical Reports Server (NTRS)

Halpin, S. M.; Grigsby, L. L.; Sheble, G. B.; Nelms, R. M.

1990-01-01

The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.

Femtosecond dynamics and laser control of charge transport in trans-polyacetylene.

PubMed

Franco, Ignacio; Shapiro, Moshe; Brumer, Paul

2008-06-28

The induction of dc electronic transport in rigid and flexible trans-polyacetylene oligomers according to the omega versus 2omega coherent control scenario is investigated using a quantum-classical mean field approximation. The approach involves running a large ensemble of mixed quantum-classical trajectories under the influence of omega+2omega laser fields and choosing the initial conditions by sampling the ground-state Wigner distribution function for the nuclei. The vibronic couplings are shown to change the mean single-particle spectrum, introduce ultrafast decoherence, and enhance intramolecular vibrational and electronic relaxation. Nevertheless, even in the presence of significant couplings, limited coherent control of the electronic dynamics is still viable, the most promising route involving the use of femtosecond pulses with a duration that is comparable to the electronic dephasing time. The simulations offer a realistic description of the behavior of a simple coherent control scenario in a complex system and provide a detailed account of the femtosecond photoinduced vibronic dynamics of a conjugated polymer.

Scaling relationships for nonadiabatic energy relaxation times in warm dense matter: toward understanding the equation of state.

PubMed

Pradhan, Ekadashi; Magyar, Rudolph J; Akimov, Alexey V

2016-11-30

Understanding the dynamics of electron-ion energy transfer in warm dense (WD) matter is important to the measurement of equation of state (EOS) properties and for understanding the energy balance in dynamic simulations. In this work, we present a comprehensive investigation of nonadiabatic electron relaxation and thermal excitation dynamics in aluminum under high pressure and temperature. Using quantum-classical trajectory surface hopping approaches, we examine the role of nonadiabatic couplings and electronic decoherence in electron-nuclear energy transfer in WD aluminum. The computed timescales range from 400 fs to 4.0 ps and are consistent with existing experimental studies. We have derived general scaling relationships between macroscopic parameters of WD systems such as temperature or mass density and the timescales of energy redistribution between quantum and classical degrees of freedom. The scaling laws are supported by computational results. We show that electronic decoherence plays essential role and can change the functional dependencies qualitatively. The established scaling relationships can be of use in modelling of WD matter.

Symmetry aspects in emergent quantum mechanics

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2009-06-01

We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantum mechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

Entanglement revival can occur only when the system-environment state is not a Markov state

NASA Astrophysics Data System (ADS)

Sargolzahi, Iman

2018-06-01

Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will call strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the whole system-environment is a Markov state, then each localized dynamics of the whole system-environment reduces to a localized subdynamics of the system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system-environment state is not a Markov state. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system-environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.

In vitro dynamic model simulating the digestive tract of 6-month-old infants

PubMed Central

Gallo, Marianna; Tornatore, Fabio; Frasso, Annalisa; Saccone, Giulia; Budelli, Andrea; Barone, Maria V.

2017-01-01

Background In vivo assays cannot always be conducted because of ethical reasons, technical constraints or costs, but a better understanding of the digestive process, especially in infants, could be of great help in preventing food-related pathologies and in developing new formulas with health benefits. In this context, in vitro dynamic systems to simulate human digestion and, in particular, infant digestion could become increasingly valuable. Objective To simulate the digestive process through the use of a dynamic model of the infant gastroenteric apparatus to study the digestibility of starch-based infant foods. Design Using M.I.D.A (Model of an Infant Digestive Apparatus), the oral, gastric and intestinal digestibility of two starch-based products were measured: 1) rice starch mixed with distilled water and treated using two different sterilization methods (the classical method with a holding temperature of 121°C for 37 min and the HTST method with a holding temperature of 137°C for 70 sec) and 2) a rice cream with (premium product) or without (basic product) an aliquot of rice flour fermented by Lactobacillus paracasei CBA L74. After the digestion the foods were analyzed for the starch concentration, the amount of D-glucose released and the percentage of hydrolyzed starch. Results An in vitro dynamic system, which was referred to as M.I.D.A., was obtained. Using this system, the starch digestion occurred only during the oral and intestinal phase, as expected. The D-glucose released during the intestinal phase was different between the classical and HTST methods (0.795 grams for the HTST versus 0.512 for the classical product). The same analysis was performed for the basic and premium products. In this case, the premium product had a significant difference in terms of the starch hydrolysis percentage during the entire process. Conclusions The M.I.D.A. system was able to digest simple starches and a more complex food in the correct compartments. In this study, better digestibility of the premium product was revealed. PMID:29261742

Open-system dynamics of entanglement:a key issues review

NASA Astrophysics Data System (ADS)

Aolita, Leandro; de Melo, Fernando; Davidovich, Luiz

2015-04-01

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Open-system dynamics of entanglement: a key issues review.

PubMed

Aolita, Leandro; de Melo, Fernando; Davidovich, Luiz

2015-04-01

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Rotation in vibration, optimization, and aeroelastic stability problems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1974-01-01

The effects of rotation in the areas of vibrations, dynamic stability, optimization, and aeroelasticity were studied. The governing equations of motion for the study of vibration and dynamic stability of a rapidly rotating deformable body were developed starting from the nonlinear theory of elasticity. Some common features such as the limitations of the classical theory of elasticity, the choice of axis system, the property of self-adjointness, the phenomenon of frequency splitting, shortcomings of stability methods as applied to gyroscopic systems, and the effect of internal and external damping on stability in gyroscopic systems are identified and discussed, and are then applied to three specific problems.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

First experimental test of a trace formula for billiard systems showing mixed dynamics.

PubMed

Dembowski, C; Gräf, H D; Heine, A; Hesse, T; Rehfeld, H; Richter, A

2001-04-09

In general, trace formulas relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart. Here we report for the first time on a semiclassical description of microwave spectra taken from superconducting billiards of the Limaçon family showing mixed dynamics in terms of a generalized trace formula derived by Ullmo et al. [Phys. Rev. E 54, 136 (1996)]. This expression not only describes mixed-typed behavior but also the limiting cases of fully regular and fully chaotic systems and thus presents a continuous interpolation between the Berry-Tabor and Gutzwiller formulas.

Mesoscopic Dynamical Differences from Quantum State Preparation in a Bose-Hubbard Trimer

NASA Astrophysics Data System (ADS)

Olsen, M. K.; Neely, T. W.; Bradley, A. S.

2018-06-01

Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean-field classical equations. In this Letter we combine newly developed theoretical and experimental techniques to propose and analyze an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be detected by the simple measurements of atomic number.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrijević, Dragoljub D., E-mail: ddrag@pmf.ni.ac.rs; Djordjević, Goran S., E-mail: ddrag@pmf.ni.ac.rs; Milošević, Milan, E-mail: ddrag@pmf.ni.ac.rs

2014-11-24

We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking formore » a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.« less

Probability Simulations by Non-Lipschitz Chaos

NASA Technical Reports Server (NTRS)

Zak, Michail

1996-01-01

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Classical electromagnetic fields from quantum sources in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Holliday, Robert; McCarty, Ryan; Peroutka, Balthazar; Tuchin, Kirill

2017-01-01

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

Classical-to-Quantum Transition with Broadband Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Vered, Rafi Z.; Shaked, Yaakov; Ben-Or, Yelena; Rosenbluh, Michael; Pe'er, Avi

2015-02-01

A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband four-wave mixing over a large dynamic range of ˜80 dB in photon flux across the classical-to-quantum transition using a two-photon interference effect that distinguishes between classical and quantum behavior. We explore the quantum-classical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the four-wave mixing gain in the fiber becomes imaginary.

Superintegrable three-body systems on the line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chanu, Claudia; Degiovanni, Luca; Rastelli, Giovanni

2008-11-15

We consider classical three-body interactions on a Euclidean line depending on the reciprocal distance of the particles and admitting four functionally independent quadratic in the momentum first integrals. These systems are multiseparable, superintegrable, and equivalent (up to rescalings) to a one-particle system in the three-dimensional Euclidean space. Common features of the dynamics are discussed. We show how to determine quantum symmetry operators associated with the first integrals considered here but do not analyze the corresponding quantum dynamics. The conformal multiseparability is discussed and examples of conformal first integrals are given. The systems considered here in generality include the Calogero, Wolfes,more » and other three-body interactions widely studied in mathematical physics.« less

Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors

NASA Astrophysics Data System (ADS)

Bitter, M.; Milner, V.

2016-09-01

The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum—the hallmark of dynamical localization—is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.

Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors.

PubMed

Bitter, M; Milner, V

2016-09-30

The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum-the hallmark of dynamical localization-is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Structure and dynamics of the peptide strand KRFK from the thrombospondin TSP-1 in water.

PubMed

Taleb Bendiab, W; Benomrane, B; Bounaceur, B; Dauchez, M; Krallafa, A M

2018-02-14

Theoretical investigations of a solute in liquid water at normal temperature and pressure can be performed at different levels of theory. Static quantum calculations as well as classical and ab initio molecular dynamics are used to completely explore the conformational space for large solvated molecular systems. In the classical approach, it is essential to describe all of the interactions of the solute and the solvent in detail. Water molecules are very often described as rigid bodies when the most commonly used interaction potentials, such as the SPCE and the TIP4P models, are employed. Recently, a physical model based upon a cluster of rigid water molecules with a tetrahedral architecture (AB 4 ) was proposed that describes liquid water as a mixture of both TIP4P and SPCE molecular species that occur in the proportions implied by the tetrahedral architecture (one central molecule versus four outer molecules; i.e., 20% TIP4P versus 80% SPCE molecules). In this work, theoretical spectroscopic data for a peptide strand were correlated with the structural properties of the peptide strand solvated in water, based on data calculated using different theoretical approaches and physical models. We focused on a particular peptide strand, KRFK (lysine-arginine-phenylalanine-lysine), found in the thrombospondin TSP-1, due to its interesting properties. As the activity and electronic structure of this system is strongly linked to its structure, we correlated its structure with charge-density maps obtained using different semi-empirical charge Q eq equations. The structural and thermodynamic properties obtained from classical simulations were correlated with ab initio molecular dynamics (AIMD) data. Structural changes in the peptide strand were rationalized in terms of the motions of atoms and groups of atoms. To achieve this, conformational changes were investigated using calculated infrared spectra for the peptide in the gas phase and in water solvent. The calculated AIMD infrared spectrum for the peptide was correlated with static quantum calculations of the molecular system based on a harmonic approach as well as the VDOS (vibrational density of states) spectra obtained using various classical solvent models (SPCE, TIP4P, and AB 4 ) and charge maps.

Topological classification of the Goryachev integrable case in rigid body dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolaenko, S S

2016-01-31

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in othermore » words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.« less

Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walker, La Tonya Nicole; Malczynski, Leonard A.

DYNAMO is a computer program for building and running 'continuous' simulation models. It was developed by the Industrial Dynamics Group at the Massachusetts Institute of Technology for simulating dynamic feedback models of business, economic, and social systems. The history of the system dynamics method since 1957 includes many classic models built in DYANMO. It was not until the late 1980s that software was built to take advantage of the rise of personal computers and graphical user interfaces that DYNAMO was supplanted. There is much learning and insight to be gained from examining the DYANMO models and their accompanying research papers.more » We believe that it is a worthwhile exercise to convert DYNAMO models to more recent software packages. We have made an attempt to make it easier to turn these models into a more current system dynamics software language, Powersim © Studio produced by Powersim AS 2 of Bergen, Norway. This guide shows how to convert DYNAMO syntax into Studio syntax.« less

Effective model hierarchies for dynamic and static classical density functional theories

NASA Astrophysics Data System (ADS)

Majaniemi, S.; Provatas, N.; Nonomura, M.

2010-09-01

The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical density functional theories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced. To facilitate a more natural way of binding together the dynamics of the macrovariables and classical density functional theory, a dynamic generalization of density functional theory based on the nonequilibrium generating functional is suggested.

Classical Electrodynamics: Lecture notes

NASA Astrophysics Data System (ADS)

Likharev, Konstantin K.

2018-06-01

Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.

Lenard-Balescu calculations and classical molecular dynamics simulations of electrical and thermal conductivities of hydrogen plasmas

DOE PAGES

Whitley, Heather D.; Scullard, Christian R.; Benedict, Lorin X.; ...

2014-12-04

Here, we present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard-Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2-body quantum statistical potentials and compute both electrical and thermal conductivity from out particle trajectories using the Kubo approach. Our classical Lenard-Balescu results employing the identical statistical potentials agree well with the simulations.

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Classical trajectory studies of gas phase reaction dynamics and kinetics using ab initio potential energy surfaces

NASA Technical Reports Server (NTRS)

Jaffe, Richard L.; Pattengill, Merle D.; Schwenke, David W.

1989-01-01

Strategies for constructing global potential energy surfaces from a limited number of accurate ab initio electronic energy calculations are discussed. Generally, these data are concentrated in small regions of configuration space (e.g., in the vicinity of saddle points and energy minima) and difficulties arise in generating a potential function that is globally well-behaved. Efficient computer codes for carrying out classical trajectory calculations on vector and parallel processors are also described. Illustrations are given from recent work on the following chemical systems: Ca + HF yields CaF + H, H + H + H2 yields H2 + H2, N + O2 yields NO + O and O + N2 yields NO + N. The dynamics and kinetics of metathesis, dissociation, recombination, energy transfer and complex formation processes will be discussed.

Quantum cooling and squeezing of a levitating nanosphere via time-continuous measurements

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Zhang, Jinglei; Millen, James; Barker, Peter F.; Serafini, Alessio

2015-07-01

With the purpose of controlling the steady state of a dielectric nanosphere levitated within an optical cavity, we study its conditional dynamics under simultaneous sideband cooling and additional time-continuous measurement of either the output cavity mode or the nanosphere’s position. We find that the average phonon number, purity and quantum squeezing of the steady-states can all be made more non-classical through the addition of time-continuous measurement. We predict that the continuous monitoring of the system, together with Markovian feedback, allows one to stabilize the dynamics for any value of the laser frequency driving the cavity. By considering state of the art values of the experimental parameters, we prove that one can in principle obtain a non-classical (squeezed) steady-state with an average phonon number {n}{ph}≈ 0.5.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Redundant imprinting of information in non-ideal environments: Quantum Darwinism via a noisy channel

NASA Astrophysics Data System (ADS)

Zwolak, Michael; Quan, Haitao; Zurek, Wojciech

2011-03-01

Quantum Darwinism provides an information-theoretic framework for the emergence of the classical world from the quantum substrate. It recognizes that we - the observers - acquire our information about the ``systems of interest'' indirectly from their imprints on the environment. Objectivity, a key property of the classical world, arises via the proliferation of redundant information into the environment where many observers can then intercept it and independently determine the state of the system. While causing a system to decohere, environments that remain nearly invariant under the Hamiltonian dynamics, such as very mixed states, have a diminished ability to transmit information about the system, yet can still acquire redundant information about the system [1,2]. Our results show that Quantum Darwinism is robust with respect to non-ideal initial states of the environment. This research is supported by the U.S. Department of Energy through the LANL/LDRD Program.

Tuning quantum measurements to control chaos.

PubMed

Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R

2017-03-20

Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.

Long-time predictions in nonlinear dynamics

NASA Technical Reports Server (NTRS)

Szebehely, V.

1980-01-01

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

NASA Astrophysics Data System (ADS)

Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan

2017-05-01

Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.

Simulations of Probabilities for Quantum Computing

NASA Technical Reports Server (NTRS)

Zak, M.

1996-01-01

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Bifurcations and complete chaos for the diamagnetic Kepler problem

NASA Astrophysics Data System (ADS)

Hansen, Kai T.

1995-03-01

We describe the structure of bifurcations in the unbounded classical diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the nonwandering set is described by a complete trinary symbolic dynamics for scaled energies larger than ɛc=0.328 782. . ..

Hypertext: Behind the Hype. ERIC Digest.

ERIC Educational Resources Information Center

Bevilacqua, Ann F.

This digest begins by defining the concept of hypertext and describing the two types of hypertext--static and dynamic. Three prototype applications are then discussed: (1) Intermedia, a large-scale multimedia system at Brown University; (2) the Perseus Project at Harvard University, which is developing interactive courseware on classical Greek…

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D.

2016-04-01

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions agree with the numerical results of the quantum Chirikov map.

Hybrid annealing: Coupling a quantum simulator to a classical computer

NASA Astrophysics Data System (ADS)

Graß, Tobias; Lewenstein, Maciej

2017-05-01

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Quantum Game of Life

NASA Astrophysics Data System (ADS)

Glick, Aaron; Carr, Lincoln; Calarco, Tommaso; Montangero, Simone

2014-03-01

In order to investigate the emergence of complexity in quantum systems, we present a quantum game of life, inspired by Conway's classic game of life. Through Matrix Product State (MPS) calculations, we simulate the evolution of quantum systems, dictated by a Hamiltonian that defines the rules of our quantum game. We analyze the system through a number of measures which elicit the emergence of complexity in terms of spatial organization, system dynamics, and non-local mutual information within the network. Funded by NSF

Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures

NASA Astrophysics Data System (ADS)

Bishop, Kevin P.; Roy, Pierre-Nicholas

2018-03-01

Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.

Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures.

PubMed

Bishop, Kevin P; Roy, Pierre-Nicholas

2018-03-14

Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.

Dynamics of embedded curves by doubly-nonlocal reaction-diffusion systems

NASA Astrophysics Data System (ADS)

von Brecht, James H.; Blair, Ryan

2017-11-01

We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of complexity for embedded curves. This line of investigation culminates in a family of complexity bounds that relate a rather broad class of models to a generalized, or weighted, variant of the crossing number. Our dynamic results include global well-posedness of the associated partial differential equations, regularity of equilibria for these flows as well as a more detailed investigation of dynamics near such equilibria. Finally, we explore a few global dynamical properties of these models numerically.

Applications of Density Functional Theory in Soft Condensed Matter

NASA Astrophysics Data System (ADS)

Löwen, Hartmut

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

On the dynamics of a generalized predator-prey system with Z-type control.

PubMed

Lacitignola, Deborah; Diele, Fasma; Marangi, Carmela; Provenzale, Antonello

2016-10-01

We apply the Z-control approach to a generalized predator-prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter λ for the successful application of the method is stressed and related to specific dynamical properties of the Z-controlled model. Critical values of the design parameter are also found, delimiting the λ-range for the effectiveness of the Z-method. Analytical results are then numerically validated by the means of two ecological models: the classical Lotka-Volterra model and a model related to a case study of the wolf-wild boar dynamics in the Alta Murgia National Park. Investigations on these models also highlight how the Z-control method acts in respect to different dynamical regimes of the uncontrolled model. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Universal attractor in a highly occupied non-Abelian plasma

NASA Astrophysics Data System (ADS)

Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R.

2014-06-01

We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The nonequilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Phys. Rev. D 89, 074011 (2014), 10.1103/PhysRevD.89.074011 along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the nonequilibrium evolution on large time scales both for nonexpanding and expanding non-Abelian plasmas. The turbulent attractor for a nonexpanding plasma drives the system close to thermal equilibrium on a time scale t ˜Q-1αs-7/4. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the "bottom up" thermalization scenario [R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001), 10.1016/S0370-2693(01)00191-5]. While the focus of this paper is to understand the nonequilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.

Universality classes of fluctuation dynamics in hierarchical complex systems

NASA Astrophysics Data System (ADS)

Macêdo, A. M. S.; González, Iván R. Roa; Salazar, D. S. P.; Vasconcelos, G. L.

2017-03-01

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

Ratchet effect in the quantum kicked rotor and its destruction by dynamical localization

NASA Astrophysics Data System (ADS)

Hainaut, Clément; Rançon, Adam; Clément, Jean-François; Garreau, Jean Claude; Szriftgiser, Pascal; Chicireanu, Radu; Delande, Dominique

2018-06-01

We study experimentally a quantum kicked rotor with broken parity symmetry, supporting a ratchet effect due to the presence of a classical accelerator mode. We show that the short-time dynamics is very well described by the classical dynamics, characterized by a strongly asymmetric momentum distribution with directed motion on one side, and an anomalous diffusion on the other. At longer times, quantum effects lead to dynamical localization, causing an asymptotic resymmetrization of the wave function.

Wigner's quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

Enhanced energy transport in genetically engineered excitonic networks.

PubMed

Park, Heechul; Heldman, Nimrod; Rebentrost, Patrick; Abbondanza, Luigi; Iagatti, Alessandro; Alessi, Andrea; Patrizi, Barbara; Salvalaggio, Mario; Bussotti, Laura; Mohseni, Masoud; Caruso, Filippo; Johnsen, Hannah C; Fusco, Roberto; Foggi, Paolo; Scudo, Petra F; Lloyd, Seth; Belcher, Angela M

2016-02-01

One of the challenges for achieving efficient exciton transport in solar energy conversion systems is precise structural control of the light-harvesting building blocks. Here, we create a tunable material consisting of a connected chromophore network on an ordered biological virus template. Using genetic engineering, we establish a link between the inter-chromophoric distances and emerging transport properties. The combination of spectroscopy measurements and dynamic modelling enables us to elucidate quantum coherent and classical incoherent energy transport at room temperature. Through genetic modifications, we obtain a significant enhancement of exciton diffusion length of about 68% in an intermediate quantum-classical regime.

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Classical scattering calculations for diatomic molecules: A general procedure and application to the microwave spectrum O2

NASA Technical Reports Server (NTRS)

Mingelgrin, U.

1972-01-01

Many properties of gaseous systems such as electromagnetic absorption and emission, sound dispersion and absorption, may be elucidated if the nature of collisions between the particles in the system is understood. A procedure for the calculation of the classical trajectories of two interacting diatomic molecules is described. The dynamics of the collision will be assumed to be that of two rigid rotors moving in a specified potential. The actual outcome of a representative sample of many trajectories at 298K was computed, and the use of these values at any temperature for calculations of various molecular properties will be described. Calculations performed for the O2 microwave spectrum are given to demonstrate the use of the procedure described.

Quantum chemistry simulation on quantum computers: theories and experiments.

PubMed

Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng

2012-07-14

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

Improved direct torque control of an induction generator used in a wind conversion system connected to the grid.

PubMed

Abdelli, Radia; Rekioua, Djamila; Rekioua, Toufik; Tounzi, Abdelmounaïm

2013-07-01

This paper presents a modulated hysteresis direct torque control (MHDTC) applied to an induction generator (IG) used in wind energy conversion systems (WECs) connected to the electrical grid through a back-to-back converter. The principle of this strategy consists in superposing to the torque reference a triangular signal, as in the PWM strategy, with the desired switching frequency. This new modulated reference is compared to the estimated torque by using a hysteresis controller as in the classical direct torque control (DTC). The aim of this new approach is to lead to a constant frequency and low THD in grid current with a unit power factor and a minimum voltage variation despite the wind variation. To highlight the effectiveness of the proposed method, a comparison was made with classical DTC and field oriented control method (FOC). The obtained simulation results, with a variable wind profile, show an adequate dynamic of the conversion system using the proposed method compared to the classical approaches. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Hamiltonian flow over saddles for exploring molecular phase space structures

NASA Astrophysics Data System (ADS)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

PubMed

Lemkul, Justin A; MacKerell, Alexander D

2017-05-09

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Dynamical Crossovers in Prethermal Critical States.

PubMed

Chiocchetta, Alessio; Gambassi, Andrea; Diehl, Sebastian; Marino, Jamir

2017-03-31

We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.

Classical Electrodynamics: Problems with solutions; Problems with solutions

NASA Astrophysics Data System (ADS)

Likharev, Konstantin K.

2018-06-01

l Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.

The dance of molecules: new dynamical perspectives on highly excited molecular vibrations.

PubMed

Kellman, Michael E; Tyng, Vivian

2007-04-01

At low energies, molecular vibrational motion is described by the normal modes model. This model breaks down at higher energy, with strong coupling between normal modes and onset of chaotic dynamics. New anharmonic modes are born in bifurcations, or branchings of the normal modes. Knowledge of these new modes is obtained through the window of frequency-domain spectroscopy, using techniques of nonlinear classical dynamics. It may soon be possible to "watch" molecular rearrangement reactions spectroscopically. Connections are being made with reaction rate theories, condensed phase systems, and motions of electrons in quantum dots.

On the effect of gyroscopic forces on the instability of certain fluid-elastic systems. Part 1: Definitions

NASA Astrophysics Data System (ADS)

Kornecki, A.

1983-09-01

This study was motivated by work on the stability of nonconservative elastic systems and flutter of certain fluid-elastic systems. A literature review revealed that the concepts of conservative forces (and systems) and gyroscopic forces (and systems) need clarifications, and the definitions formulated by different authors for the forces and systems are sometimes conflicting. In this report, these controversies are thoroughly discussed and conservative and gyroscopic systems are redefined within the framework of the classical dynamics of a system of particles.

Dynamic stabilization of classical Rayleigh-Taylor instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piriz, A. R.; Piriz, S. A.; Tahir, N. A.

2011-09-15

Dynamic stabilization of classical Rayleigh-Taylor instability is studied by modeling the interface vibration with the simplest possible wave form, namely, a sequence of Dirac deltas. As expected, stabilization results to be impossible. However, in contradiction to previously reported results obtained with a sinusoidal driving, it is found that in general the perturbation amplitude is larger than in the classical case. Therefore, no beneficial effect can be obtained from the vertical vibration of a Rayleigh-Taylor unstable interface between two ideal fluids.

System dynamics of subcellular transport.

PubMed

Chen, Vivien Y; Khersonsky, Sonya M; Shedden, Kerby; Chang, Young Tae; Rosania, Gus R

2004-01-01

In pharmacokinetic experiments, interpretations often hinge on treating cells as a "black box": a single, lumped compartment or boundary. Here, a combinatorial library of fluorescent small molecules was used to visualize subcellular transport pathways in living cells, using a kinetic, high content imaging system to monitor spatiotemporal variations of intracellular probe distribution. Most probes accumulate in cytoplasmic vesicles and probe kinetics conform to a nested, two-compartment dynamical system. At steady state, probes preferentially partition from the extracellular medium to the cytosol, and from the cytosol to cytoplasmic vesicles, with hydrophobic molecules favoring sequestration. Altogether, these results point to a general organizing principle underlying the system dynamics of subcellular, small molecule transport. In addition to plasma membrane permeability, subcellular transport phenomena can determine the active concentration of small molecules in the cytosol and the efflux of small molecules from cells. Fundamentally, direct observation of intracellular probe distribution challenges the simple boundary model of classical pharmacokinetics, which considers cells as static permeability barriers.

Anomalous dynamics of interstitial dopants in soft crystals

PubMed Central

Tauber, Justin; Higler, Ruben; Sprakel, Joris

2016-01-01

The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant–dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopant–dopant interactions into account. PMID:27856751

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1995-01-01

During this year, we concentrated our efforts on the design of controllers for lateral/directional control using mu synthesis. This proved to be a more difficult task than we anticipated and we are still working on the designs. In the lateral-directional control problem, the inputs are pilot lateral stick and pedal commands and the outputs are roll rate about the velocity vector and side slip angle. The control effectors are ailerons, rudder deflection, and directional thrust vectoring vane deflection which produces a yawing moment about the body axis. Our math model does not contain any provision for thrust vectoring of rolling moment. This has resulted in limitations of performance at high angles of attack. During 1994-95, the following tasks for the lateral-directional controllers were accomplished: (1) Designed both inner and outer loop dynamic inversion controllers. These controllers are implemented using accelerometer outputs rather than an a priori model of the vehicle aerodynamics; (2) Used classical techniques to design controllers for the system linearized by dynamics inversion. These controllers acted to control roll rate and Dutch roll response; (3) Implemented the inner loop dynamic inversion and classical controllers on the six DOF simulation; (4) Developed a lateral-directional control allocation scheme based on minimizing required control effort among the ailerons, rudder, and directional thrust vectoring; and (5) Developed mu outer loop controllers combined with classical inner loop controllers.

Microscopic Electron Dynamics in Metal Nanoparticles for Photovoltaic Systems.

PubMed

Kluczyk, Katarzyna; Jacak, Lucjan; Jacak, Witold; David, Christin

2018-06-25

Nanoparticles—regularly patterned or randomly dispersed—are a key ingredient for emerging technologies in photonics. Of particular interest are scattering and field enhancement effects of metal nanoparticles for energy harvesting and converting systems. An often neglected aspect in the modeling of nanoparticles are light interaction effects at the ultimate nanoscale beyond classical electrodynamics. Those arise from microscopic electron dynamics in confined systems, the accelerated motion in the plasmon oscillation and the quantum nature of the free electron gas in metals, such as Coulomb repulsion and electron diffusion. We give a detailed account on free electron phenomena in metal nanoparticles and discuss analytic expressions stemming from microscopic (Random Phase Approximation—RPA) and semi-classical (hydrodynamic) theories. These can be incorporated into standard computational schemes to produce more reliable results on the optical properties of metal nanoparticles. We combine these solutions into a single framework and study systematically their joint impact on isolated Au, Ag, and Al nanoparticles as well as dimer structures. The spectral position of the plasmon resonance and its broadening as well as local field enhancement show an intriguing dependence on the particle size due to the relevance of additional damping channels.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

NASA Astrophysics Data System (ADS)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-01

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.

PubMed

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE PAGES

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Ab initio and classical molecular dynamics studies of the structural and dynamical behavior of water near a hydrophobic graphene sheet.

PubMed

Rana, Malay Kumar; Chandra, Amalendu

2013-05-28

The behavior of water near a graphene sheet is investigated by means of ab initio and classical molecular dynamics simulations. The wetting of the graphene sheet by ab initio water and the relation of such behavior to the strength of classical dispersion interaction between surface atoms and water are explored. The first principles simulations reveal a layered solvation structure around the graphene sheet with a significant water density in the interfacial region implying no drying or cavitation effect. It is found that the ab initio results of water density at interfaces can be reproduced reasonably well by classical simulations with a tuned dispersion potential between the surface and water molecules. Calculations of vibrational power spectrum from ab initio simulations reveal a shift of the intramolecular stretch modes to higher frequencies for interfacial water molecules when compared with those of the second solvation later or bulk-like water due to the presence of free OH modes near the graphene sheet. Also, a weakening of the water-water hydrogen bonds in the vicinity of the graphene surface is found in our ab initio simulations as reflected in the shift of intermolecular vibrational modes to lower frequencies for interfacial water molecules. The first principles calculations also reveal that the residence and orientational dynamics of interfacial water are somewhat slower than those of the second layer or bulk-like molecules. However, the lateral diffusion and hydrogen bond relaxation of interfacial water molecules are found to occur at a somewhat faster rate than that of the bulk-like water molecules. The classical molecular dynamics simulations with tuned Lennard-Jones surface-water interaction are found to produce dynamical results that are qualitatively similar to those of ab initio molecular dynamics simulations.

Quantum Darwinism in hazy environments

NASA Astrophysics Data System (ADS)

Zwolak, Michael; Quan, H. T.; Zurek, Wojciech

2010-03-01

Quantum Darwinism provides an information-theoretic framework for the emergence of the classical world from the quantum substrate. It recognizes that we - the observers - acquire our information about the ``systems of interest'' indirectly from their imprints on the environment. Objectivity, a key property of the classical world, arises via the proliferation of redundant information into the environment where many observers can then intercept it and independently determine the state of the system. After a general introduction to this framework, we demonstrate how non-ideal initial states of the environment (e.g., mixed states) affect its ability to act as a communication channel for information about the system. The environment's capacity for transmitting information is directly related to its ability to increase its entropy. Therefore, environments that remain nearly invariant under the Hamiltonian dynamics, such as very mixed states, have a diminished ability to transmit information. However, despite this, the environment almost always redundantly transmits information about the system.

An Improved Fast Self-Calibration Method for Hybrid Inertial Navigation System under Stationary Condition

PubMed Central

Liu, Bingqi; Wei, Shihui; Su, Guohua; Wang, Jiping; Lu, Jiazhen

2018-01-01

The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible. PMID:29695041

An Improved Fast Self-Calibration Method for Hybrid Inertial Navigation System under Stationary Condition.

PubMed

Liu, Bingqi; Wei, Shihui; Su, Guohua; Wang, Jiping; Lu, Jiazhen

2018-04-24

The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible.

Coherent Two-Mode Dynamics of a Nanowire Force Sensor

NASA Astrophysics Data System (ADS)

Braakman, Floris R.; Rossi, Nicola; Tütüncüoglu, Gözde; Morral, Anna Fontcuberta i.; Poggio, Martino

2018-05-01

Classically coherent dynamics analogous to those of quantum two-level systems are studied in the setting of force sensing. We demonstrate quantitative control over the coupling between two orthogonal mechanical modes of a nanowire cantilever through measurement of avoided crossings as we deterministically position the nanowire inside an electric field. Furthermore, we demonstrate Rabi oscillations between the two mechanical modes in the strong-coupling regime. These results give prospects of implementing coherent two-mode control techniques for force-sensing signal enhancement.

Simulation of quantum dynamics based on the quantum stochastic differential equation.

PubMed

Li, Ming

2013-01-01

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Quantumness-generating capability of quantum dynamics

NASA Astrophysics Data System (ADS)

Li, Nan; Luo, Shunlong; Mao, Yuanyuan

2018-04-01

We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

NASA Astrophysics Data System (ADS)

Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger

2018-04-01

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

NASA Astrophysics Data System (ADS)

Lorenzen, F.; de Ponte, M. A.; Moussa, M. H. Y.

2009-09-01

In this paper, employing the Itô stochastic Schrödinger equation, we extend Bell’s beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm’s causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm’s causal dynamics regarding stationary states in quantum mechanics.

Quantum Bohmian model for financial market

NASA Astrophysics Data System (ADS)

Choustova, Olga Al.

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

NASA Astrophysics Data System (ADS)

Schubert, Alexander; Falvo, Cyril; Meier, Christoph

2016-08-01

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1996-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1999-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high-order characteristics of the system. In this paper only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles of attack: 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of the identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the estimated closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Lyapounov variable: Entropy and measurement in quantum mechanics

PubMed Central

Misra, B.; Prigogine, I.; Courbage, M.

1979-01-01

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables—i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantum mechanics. PMID:16578757

Immunity by equilibrium.

PubMed

Eberl, Gérard

2016-08-01

The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.

Parametric representation of open quantum systems and cross-over from quantum to classical environment.

PubMed

Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I; Verrucchi, Paola

2013-04-23

The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the s = 1/2 Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables (θ, ϕ), and broadened according to their quantum probability distribution. Such distribution is independent of ϕ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because ϕ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field.

Normalization in Lie algebras via mould calculus and applications

NASA Astrophysics Data System (ADS)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach

NASA Technical Reports Server (NTRS)

Pei, Jing; Newsome, Jerry R.

2015-01-01

Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.

Experimental demonstration of chaotic scattering of microwaves

NASA Astrophysics Data System (ADS)

Doron, E.; Smilansky, U.; Frenkel, A.

1990-12-01

Reflection of microwaves from a cavity is measured in a frequency domain where the underlying classical chaotic scattering leaves a clear mark on the wave dynamics. We check the hypothesis that the fluctuations of the S matrix can be described in terms of parameters characterizing the chaotic classical scatteirng. Absorption of energy in the cavity walls is shown to significantly affect the results, and is linked to time-domain properties of the scattering in a general way. We also show that features whose origin is entirely due to wave dynamics (e.g., the enhancement of the Wigner time delay due to time-reversal symmetry) coexist with other features which characterize the underlying classical dynamics.

Indeterminism in Classical Dynamics of Particle Motion

NASA Astrophysics Data System (ADS)

Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian; Aluie, Hussein; Kanov, Kalin; Burns, Randal; Meneveau, Charles; Szalay, Alex

2013-03-01

We show that ``God plays dice'' not only in quantum mechanics but also in the classical dynamics of particles advected by turbulent fluids. With a fixed deterministic flow velocity and an exactly known initial position, the particle motion is nevertheless completely unpredictable! In analogy with spontaneous magnetization in ferromagnets which persists as external field is taken to zero, the particle trajectories in turbulent flow remain random as external noise vanishes. The necessary ingredient is a rough advecting field with a power-law energy spectrum extending to smaller scales as noise is taken to zero. The physical mechanism of ``spontaneous stochasticity'' is the explosive dispersion of particle pairs proposed by L. F. Richardson in 1926, so the phenomenon should be observable in laboratory and natural turbulent flows. We present here the first empirical corroboration of these effects in high Reynolds-number numerical simulations of hydrodynamic and magnetohydrodynamic fluid turbulence. Since power-law spectra are seen in many other systems in condensed matter, geophysics and astrophysics, the phenomenon should occur rather widely. Fast reconnection in solar flares and other astrophysical systems can be explained by spontaneous stochasticity of magnetic field-line motion

Exact sampling hardness of Ising spin models

NASA Astrophysics Data System (ADS)

Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.

2017-09-01

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osovski, Shmuel; Moiseyev, Nimrod

The recent pioneering experiments of the [Nature 412, 52 (2001)] and [Science, 293, 274 (2001)] groups have demonstrated the dynamical tunneling of cold atoms interacting with standing electromagnetic waves. It has been shown [Phys. Rev. Lett. 89, 253201 (2002)], that the tunneling oscillations observed in these experiments correspondingly stems from two- and three-Floquet quantum state mechanism and can be controlled by varying the experimental parameters. The question where are the fingerprints of the classical chaotic dynamics in a quantum dynamical process which is controlled by 2 or 3 quantum states remains open. Our calculations show that although the effective ({Dirac_h}/2{pi})more » associated with the two experiments is large, and the quantum system is far from its semiclassical limit, the quantum Floquet-Bloch quasienergy states still can be classified as regular and chaotic states. In both experiments the quantum and the classical phase-space entropies are quite similar, although the classical phase space is a mixed regular-chaotic space. It is also shown that as the wave packet which is initially localized at one of the two inner regular islands oscillates between them through the chaotic sea, it accumulates a random phase which causes the decay of the amplitude of the oscillating mean momentum, , as measured in both experiments. The extremely high sensitivity of the rate of decay of the oscillations of to the very small changes in the population of different Floquet-Bloch states, is another type of fingerprint of chaos in quantum dynamics that presumably was measured in the NIST and AUSTIN experiments for the first time.« less

On information, negentropy and H-theorem

NASA Astrophysics Data System (ADS)

Chakrabarti, C. G.; Sarker, N. G.

1983-09-01

The paper deals with the imprtance of the Kullback descrimination information in the statistical characterization of negentropy of non-equilibrium state and the irreversibility of a classical dynamical system. The theory based on the Kullback discrimination information as the H-function gives new insight into the interrelation between the concepts of coarse-graining and the principle of sufficiency leading to important statistical characterization of thermal equilibrium of a closed system.

Analytical Solution for Low-Thrust Minimum Time Control of a Satellite Formation

DTIC Science & Technology

2004-09-01

The Classical Clohessy - Wiltshire Equations . . . . . . . . . A-1 A.1 Hill’s Rotating Coordinate Frame . . . . . . . . . . . . . . . A-1 A.2 Kinematics...9 A.1. The Clohessy and Wiltshire coordinate frame with x in the radial direction and y in the velocity direction. . . . . . . . . . . . . . . . A-1 B...coordinate system and approx- imations made by Clohessy and Wiltshire , combined with body-fixed thruster control, result in a linearized dynamic system. The

On whole Abelian model dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600

2012-09-24

Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics orientedmore » through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.« less

Torsional vibrations of shafts of mechanical systems

NASA Astrophysics Data System (ADS)

Gulevsky, V. A.; Belyaev, A. N.; Trishina, T. V.

2018-03-01

The aim of the research is to compare the calculated dependencies for determining the equivalent rigidity of a mechanical system and to come to an agreement on the methods of compiling dynamic models for systems with elastic reducer couplings in applied and classical oscillation theories. As a result of the analysis, it was revealed that most of the damage in the mechanisms and their details is due to the appearance of oscillations due to the dynamic impact of various factors: shock and alternating loads, unbalanced parts of machines, etc. Therefore, the designer at the design stage, and the engineer in the process of operation should provide the possibility of regulating the oscillatory processes both in details and machines by means of creating rational designs, as well as the use of special devices such as vibration dampers, various vibrators with optimal characteristics. A method is proposed for deriving a formula for determining the equivalent stiffness of a double-mass oscillating system of a multistage reducer with elastic reducer links without taking into account the internal losses and inertia of its elements, which gives a result completely coinciding with the result obtained by the classical theory of small mechanical oscillations and allows eliminating formulas for reducing the moments of inertia of the flywheel masses and the stiffness of the shafts.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Characterizing popularity dynamics of online videos

NASA Astrophysics Data System (ADS)

Ren, Zhuo-Ming; Shi, Yu-Qiang; Liao, Hao

2016-07-01

Online popularity has a major impact on videos, music, news and other contexts in online systems. Characterizing online popularity dynamics is nature to explain the observed properties in terms of the already acquired popularity of each individual. In this paper, we provide a quantitative, large scale, temporal analysis of the popularity dynamics in two online video-provided websites, namely MovieLens and Netflix. The two collected data sets contain over 100 million records and even span a decade. We characterize that the popularity dynamics of online videos evolve over time, and find that the dynamics of the online video popularity can be characterized by the burst behaviors, typically occurring in the early life span of a video, and later restricting to the classic preferential popularity increase mechanism.

Cerebrospinal Fluid Mechanics and Its Coupling to Cerebrovascular Dynamics

NASA Astrophysics Data System (ADS)

Linninger, Andreas A.; Tangen, Kevin; Hsu, Chih-Yang; Frim, David

2016-01-01

Cerebrospinal fluid (CSF) is not stagnant but displays fascinating oscillatory flow patterns inside the ventricular system and reversing fluid exchange between the cranial vault and spinal compartment. This review provides an overview of the current knowledge of pulsatile CSF motion. Observations contradicting classical views about its bulk production and clearance are highlighted. A clinical account of diseases of abnormal CSF flow dynamics, including hydrocephalus, syringomyelia, Chiari malformation type 1, and pseudotumor cerebri, is also given. We survey medical imaging modalities used to observe intracranial dynamics in vivo. Additionally, we assess the state of the art in predictive models of CSF dynamics. The discussion addresses open questions regarding CSF dynamics as they relate to the understanding and management of diseases.

Molecular Studies of Complex Soil Organic Matter Interactions with Metal Ions and Mineral Surfaces using Classical Molecular Dynamics and Quantum Chemistry Methods

NASA Astrophysics Data System (ADS)

Andersen, A.; Govind, N.; Laskin, A.

2017-12-01

Mineral surfaces have been implicated as potential protectors of soil organic matter (SOM) against decomposition and ultimate mineralization to small molecules which can provide nutrients for plants and soil microbes and can also contribute to the Earth's elemental cycles. SOM is a complex mixture of organic molecules of biological origin at varying degrees of decomposition and can, itself, self-assemble in such a way as to expose some biomolecule types to biotic and abiotic attack while protecting other biomolecule types. The organization of SOM and SOM with mineral surfaces and solvated metal ions is driven by an interplay of van der Waals and electrostatic interactions leading to partitioning of hydrophilic (e.g. sugars) and hydrophobic (e.g., lipids) SOM components that can be bridged with amphiphilic molecules (e.g., proteins). Classical molecular dynamics simulations can shed light on assemblies of organic molecules alone or complexation with mineral surfaces. The role of chemical reactions is also an important consideration in potential chemical changes of the organic species such as oxidation/reduction, degradation, chemisorption to mineral surfaces, and complexation with solvated metal ions to form organometallic systems. For the study of chemical reactivity, quantum chemistry methods can be employed and combined with structural insight provided by classical MD simulations. Moreover, quantum chemistry can also simulate spectroscopic signatures based on chemical structure and is a valuable tool in interpreting spectra from, notably, x-ray absorption spectroscopy (XAS). In this presentation, we will discuss our classical MD and quantum chemistry findings on a model SOM system interacting with mineral surfaces and solvated metal ions.

Dynamic changes in the numbers of different subsets of peripheral blood NK cells in patients with systemic lupus erythematosus following classic therapy.

PubMed

Ma, Hongshuang; Zhao, Ling; Jiang, Zhenyu; Jiang, Yanfang; Feng, Li; Ye, Zhuang

2014-11-01

Imbalance of natural killer (NK) cells is associated with the development of systemic lupus erythematosus (SLE). However, little is known about the dynamic changes on NK cells following therapy. This study aimed at examining the impact of classic therapies on the numbers of different subsets of NK cells in new-onset SLE patients. The numbers of different subsets of peripheral blood NK cells in 24 new-onset SLE patients before, 4 and 12 weeks post the classic therapies, and 7 healthy controls were determined by flow cytometry. The potential correlation between the numbers of NK cells and the values of clinical measures was analyzed. In comparison with that before treatment, the numbers of NK, NKG2C+, and KIR2DL3+ NK cells were significantly increased while the numbers of NKp46+ and NKG2A + NK cells significantly decreased at 4 and/or 12 weeks post the treatment only in the drug well-responding patients, but not in those poor responders (P < 0.05 for all). The numbers of NKG2C + NK cells were correlated positively with the levels of serum C3 while the numbers of KIR2DL3+ NK cells were correlated negatively with the scores of SLEDAI in these patients at 4 weeks post the treatment. The classic therapies modulated the numbers of some subsets of NK cells in drug well-responding SLE patients. The changes in the numbers of some subsets of NK cells may serve as biomarkers for evaluating the therapeutic responses of SLE.

Classical simulation of quantum many-body systems

NASA Astrophysics Data System (ADS)

Huang, Yichen

Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance. It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood. Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods. Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).

From strings to coils: Rotational dynamics of DNA-linked colloidal chains

NASA Astrophysics Data System (ADS)

Kuei, Steve; Garza, Burke; Biswal, Sibani Lisa

2017-10-01

We investigate the dynamical behavior of deformable filaments experimentally using a tunable model system consisting of linked paramagnetic colloidal particles, where the persistence length lp, the contour length lc, and the strength and frequency of the external driving force are controlled. We find that upon forcing by an external magnetic field, a variety of structural and conformational regimes exist. Depending on the competition of forces and torques on the chain, we see classic rigid rotator behavior, as well as dynamically rich wagging, coiling, and folding behavior. Through a combination of experiments, computational models, and theoretical calculations, we are able to observe, classify, and predict these dynamics as a function of the dimensionless Mason and magnetoelastic numbers.

Generalized Bell states map physical systems’ quantum evolution into a grammar for quantum information processing

NASA Astrophysics Data System (ADS)

Delgado, Francisco

2017-12-01

Quantum information processing should be generated through control of quantum evolution for physical systems being used as resources, such as superconducting circuits, spinspin couplings in ions and artificial anyons in electronic gases. They have a quantum dynamics which should be translated into more natural languages for quantum information processing. On this terrain, this language should let to establish manipulation operations on the associated quantum information states as classical information processing does. This work shows how a kind of processing operations can be settled and implemented for quantum states design and quantum processing for systems fulfilling a SU(2) reduction in their dynamics.

Quasi-classical approaches to vibronic spectra revisited

NASA Astrophysics Data System (ADS)

Karsten, Sven; Ivanov, Sergei D.; Bokarev, Sergey I.; Kühn, Oliver

2018-03-01

The framework to approach quasi-classical dynamics in the electronic ground state is well established and is based on the Kubo-transformed time correlation function (TCF), being the most classical-like quantum TCF. Here we discuss whether the choice of the Kubo-transformed TCF as a starting point for simulating vibronic spectra is as unambiguous as it is for vibrational ones. Employing imaginary-time path integral techniques in combination with the interaction representation allowed us to formulate a method for simulating vibronic spectra in the adiabatic regime that takes nuclear quantum effects and dynamics on multiple potential energy surfaces into account. Further, a generalized quantum TCF is proposed that contains many well-established TCFs, including the Kubo one, as particular cases. Importantly, it also provides a framework to construct new quantum TCFs. Applying the developed methodology to the generalized TCF leads to a plethora of simulation protocols, which are based on the well-known TCFs as well as on new ones. Their performance is investigated on 1D anharmonic model systems at finite temperatures. It is shown that the protocols based on the new TCFs may lead to superior results with respect to those based on the common ones. The strategies to find the optimal approach are discussed.

Perspective: Memcomputing: Leveraging memory and physics to compute efficiently

NASA Astrophysics Data System (ADS)

Di Ventra, Massimiliano; Traversa, Fabio L.

2018-05-01

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this perspective, we discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that are scalable. DMMs can be realized with non-linear dynamical systems with memory. The latter property allows the realization of a new type of Boolean logic, one that is self-organizing. Self-organizing logic gates are "terminal-agnostic," namely, they do not distinguish between the input and output terminals. When appropriately assembled to represent a given combinatorial/optimization problem, the corresponding self-organizing circuit converges to the equilibrium points that express the solutions of the problem at hand. In doing so, DMMs take advantage of the long-range order that develops during the transient dynamics. This collective dynamical behavior, reminiscent of a phase transition, or even the "edge of chaos," is mediated by families of classical trajectories (instantons) that connect critical points of increasing stability in the system's phase space. The topological character of the solution search renders DMMs robust against noise and structural disorder. Since DMMs are non-quantum systems described by ordinary differential equations, not only can they be built in hardware with the available technology, they can also be simulated efficiently on modern classical computers. As an example, we will show the polynomial-time solution of the subset-sum problem for the worst cases, and point to other types of hard problems where simulations of DMMs' equations of motion on classical computers have already demonstrated substantial advantages over traditional approaches. We conclude this article by outlining further directions of study.

Statistical benchmark for BosonSampling

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Kuipers, Jack; Urbina, Juan-Diego; Mayer, Klaus; Tichy, Malte Christopher; Richter, Klaus; Buchleitner, Andreas

2016-03-01

Boson samplers—set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modes—promise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.

Perpetual extraction of work from a nonequilibrium dynamical system under Markovian feedback control

NASA Astrophysics Data System (ADS)

Kosugi, Taichi

2013-09-01

By treating both control parameters and dynamical variables as probabilistic variables, we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a Markovian feedback control. It is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of Markov chain in the higher-dimensional phase space. We derive a version of the detailed fluctuation theorem, which was originally derived for classical nonequilibrium systems by Horowitz and Vaikuntanathan [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061120 82, 061120 (2010)], in a form suitable for the analyses of perpetual extraction of work. Since our theory is formulated for generic dynamics of probability distribution function in phase space, its application to a physical system is straightforward. As simple applications of the theory, two exactly solvable models are analyzed. The one is a nonequilibrium two-state system and the other is a particle confined to a one-dimensional harmonic potential in thermal equilibrium. For the former example, it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted. For the latter example, it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement. The validity of our version of the detailed fluctuation theorem, which determines the upper bound of the expected work in the stationary state, is also confirmed for both examples. These observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment.

Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model

NASA Astrophysics Data System (ADS)

Xu, Yang; Song, Kai; Shi, Qiang

2018-03-01

The hydride transfer reaction catalyzed by dihydrofolate reductase is studied using a recently developed mixed quantum-classical method to investigate the nuclear quantum effects on the reaction. Molecular dynamics simulation is first performed based on a two-state empirical valence bond potential to map the atomistic model to an effective double-well potential coupled to a harmonic bath. In the mixed quantum-classical simulation, the hydride degree of freedom is quantized, and the effective harmonic oscillator modes are treated classically. It is shown that the hydride transfer reaction rate using the mapped effective double-well/harmonic-bath model is dominated by the contribution from the ground vibrational state. Further comparison with the adiabatic reaction rate constant based on the Kramers theory confirms that the reaction is primarily vibrationally adiabatic, which agrees well with the high transmission coefficients found in previous theoretical studies. The calculated kinetic isotope effect is also consistent with the experimental and recent theoretical results.

Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

DOE PAGES

Remmen, Grant N.; Bao, Ning; Pollack, Jason

2016-07-11

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less

Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Remmen, Grant N.; Bao, Ning; Pollack, Jason

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

Spin polarization of two-dimensional electron system in parabolic potential

NASA Astrophysics Data System (ADS)

Miyake, Takashi; Totsuji, Chieko; Nakanishi, Kenta; Tsuruta, Kenji; Totsuji, Hiroo

2008-09-01

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of r estimated from the average density is as low as r∼0.4 which is much smaller than the r value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical r value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at r∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects.

PubMed

Sumner, Isaiah; Iyengar, Srinivasan S

2007-10-18

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donangelo, R.J.

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, andmore » therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.« less

Quantized Detector Networks

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2017-12-01

Preface; Acronyms; 1. Introduction; 2. Questions and answers; 3. Classical bits; 4. Quantum bits; 5. Classical and quantum registers; 6. Classical register mechanics; 7. Quantum register dynamics; 8. Partial observations; 9. Mixed states and POVMs; 10. Double-slit experiments; 11. Modules; 12. Computerization and computer algebra; 13. Interferometers; 14. Quantum eraser experiments; 15. Particle decays; 16. Non-locality; 17. Bell inequalities; 18. Change and persistence; 19. Temporal correlations; 20. The Franson experiment; 21. Self-intervening networks; 22. Separability and entanglement; 23. Causal sets; 24. Oscillators; 25. Dynamical theory of observation; 26. Conclusions; Appendix; Index.

Transition from the mechanics of material points to the mechanics of structured particles

NASA Astrophysics Data System (ADS)

Somsikov, V. M.

2016-01-01

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

Generalized relative entropies in the classical limit

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Martin, M. T.; Plastino, A.

2015-03-01

Our protagonists are (i) the Cressie-Read family of divergences (characterized by the parameter γ), (ii) Tsallis' generalized relative entropies (characterized by the q one), and, as a particular instance of both, (iii) the Kullback-Leibler (KL) relative entropy. In their normalized versions, we ascertain the equivalence between (i) and (ii). Additionally, we employ these three entropic quantifiers in order to provide a statistical investigation of the classical limit of a semiclassical model, whose properties are well known from a purely dynamic viewpoint. This places us in a good position to assess the appropriateness of our statistical quantifiers for describing involved systems. We compare the behaviour of (i), (ii), and (iii) as one proceeds towards the classical limit. We determine optimal ranges for γ and/or q. It is shown the Tsallis-quantifier is better than KL's for 1.5 < q < 2.5.

Neuromorphic Implementation of Attractor Dynamics in a Two-Variable Winner-Take-All Circuit with NMDARs: A Simulation Study

PubMed Central

You, Hongzhi; Wang, Da-Hui

2017-01-01

Neural networks configured with winner-take-all (WTA) competition and N-methyl-D-aspartate receptor (NMDAR)-mediated synaptic dynamics are endowed with various dynamic characteristics of attractors underlying many cognitive functions. This paper presents a novel method for neuromorphic implementation of a two-variable WTA circuit with NMDARs aimed at implementing decision-making, working memory and hysteresis in visual perceptions. The method proposed is a dynamical system approach of circuit synthesis based on a biophysically plausible WTA model. Notably, slow and non-linear temporal dynamics of NMDAR-mediated synapses was generated. Circuit simulations in Cadence reproduced ramping neural activities observed in electrophysiological recordings in experiments of decision-making, the sustained activities observed in the prefrontal cortex during working memory, and classical hysteresis behavior during visual discrimination tasks. Furthermore, theoretical analysis of the dynamical system approach illuminated the underlying mechanisms of decision-making, memory capacity and hysteresis loops. The consistence between the circuit simulations and theoretical analysis demonstrated that the WTA circuit with NMDARs was able to capture the attractor dynamics underlying these cognitive functions. Their physical implementations as elementary modules are promising for assembly into integrated neuromorphic cognitive systems. PMID:28223913

Neuromorphic Implementation of Attractor Dynamics in a Two-Variable Winner-Take-All Circuit with NMDARs: A Simulation Study.

PubMed

You, Hongzhi; Wang, Da-Hui

2017-01-01

Neural networks configured with winner-take-all (WTA) competition and N-methyl-D-aspartate receptor (NMDAR)-mediated synaptic dynamics are endowed with various dynamic characteristics of attractors underlying many cognitive functions. This paper presents a novel method for neuromorphic implementation of a two-variable WTA circuit with NMDARs aimed at implementing decision-making, working memory and hysteresis in visual perceptions. The method proposed is a dynamical system approach of circuit synthesis based on a biophysically plausible WTA model. Notably, slow and non-linear temporal dynamics of NMDAR-mediated synapses was generated. Circuit simulations in Cadence reproduced ramping neural activities observed in electrophysiological recordings in experiments of decision-making, the sustained activities observed in the prefrontal cortex during working memory, and classical hysteresis behavior during visual discrimination tasks. Furthermore, theoretical analysis of the dynamical system approach illuminated the underlying mechanisms of decision-making, memory capacity and hysteresis loops. The consistence between the circuit simulations and theoretical analysis demonstrated that the WTA circuit with NMDARs was able to capture the attractor dynamics underlying these cognitive functions. Their physical implementations as elementary modules are promising for assembly into integrated neuromorphic cognitive systems.

Explaining electric conductivity using the particle-in-a-box model: quantum superposition is the key

NASA Astrophysics Data System (ADS)

Sivanesan, Umaseh; Tsang, Kin; Izmaylov, Artur F.

2017-12-01

Most of the textbooks explaining electric conductivity in the context of quantum mechanics provide either incomplete or semi-classical explanations that are not connected with the elementary concepts of quantum mechanics. We illustrate the conduction phenomena using the simplest model system in quantum dynamics, a particle in a box (PIB). To induce the particle dynamics, a linear potential tilting the bottom of the box is introduced, which is equivalent to imposing a constant electric field for a charged particle. Although the PIB model represents a closed system that cannot have a flow of electrons through the system, we consider the oscillatory dynamics of the particle probability density as the analogue of the electric current. Relating the amplitude and other parameters of the particle oscillatory dynamics with the gap between the ground and excited states of the PIB model allows us to demonstrate one of the most basic dependencies of electric conductivity on the valence-conduction band gap of the material.

Coherence penalty functional: A simple method for adding decoherence in Ehrenfest dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akimov, Alexey V., E-mail: alexvakimov@gmail.com, E-mail: oleg.prezhdo@rochester.edu; Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973; Long, Run

2014-05-21

We present a new semiclassical approach for description of decoherence in electronically non-adiabatic molecular dynamics. The method is formulated on the grounds of the Ehrenfest dynamics and the Meyer-Miller-Thoss-Stock mapping of the time-dependent Schrödinger equation onto a fully classical Hamiltonian representation. We introduce a coherence penalty functional (CPF) that accounts for decoherence effects by randomizing the wavefunction phase and penalizing development of coherences in regions of strong non-adiabatic coupling. The performance of the method is demonstrated with several model and realistic systems. Compared to other semiclassical methods tested, the CPF method eliminates artificial interference and improves agreement with the fullymore » quantum calculations on the models. When applied to study electron transfer dynamics in the nanoscale systems, the method shows an improved accuracy of the predicted time scales. The simplicity and high computational efficiency of the CPF approach make it a perfect practical candidate for applications in realistic systems.« less

Evaluating the Classical Versus an Emerging Conceptual Model of Peatland Methane Dynamics

Treesearch

Wendy H. Yang; Gavin McNicol; Yit Arn Teh; Katerina Estera-Molina; Tana E. Wood; Whendee L. Silver

2017-01-01

Methane (CH4) is a potent greenhouse gas that is both produced and consumed in soils by microbially mediated processes sensitive to soil redox. We evaluated the classical conceptual model of peatland CH4 dynamics—in which the water table position determines the vertical distribution of methanogenesis and methanotrophy—...

Classical and quantum dynamics of a kicked relativistic particle in a box

NASA Astrophysics Data System (ADS)

Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

2018-03-01

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

PubMed

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Modeling and characterization of an electromagnetic system for the estimation of Frequency Response Function of spindle

NASA Astrophysics Data System (ADS)

Tlalolini, David; Ritou, Mathieu; Rabréau, Clément; Le Loch, Sébastien; Furet, Benoit

2018-05-01

The paper presents an electromagnetic system that has been developed to measure the quasi-static and dynamic behavior of machine-tool spindle, at different spindle speeds. This system consists in four Pulse Width Modulation amplifiers and four electromagnets to produce magnetic forces of ± 190 N for the static mode and ± 80 N for the dynamic mode up to 5 kHz. In order to measure the Frequency Response Function (FRF) of spindle, the applied force is required, which is a key issue. A dynamic force model is proposed in order to obtain the load from the measured current in the amplifiers. The model depends on the exciting frequency and on the magnetic characteristics of the system. The predicted force at high speed is validated with a specific experiment and the performance limits of the experimental device are investigated. The FRF obtained with the electromagnetic system is compared to a classical tap test measurement.

Thermalization and its mechanism for generic quantum isolated systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim; Dunjko, Vanja; Rigol, Marcos

2008-05-01

Time dynamics of isolated many-body quantum systems has long been an elusive subject, perhaps most urgently needed in the foundations of quantum statistical mechanics. In generic systems, one expects the nonequilibrium dynamics to lead to thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. The relaxation mechanism is not obvious, however; dynamical chaos cannot play the key role as it does in classical systems since quantum evolution is linear. Here we demonstrateootnotetextM. Rigol, V. Dunjko, and M. Olshanii, to appear in Nature (2008), using the results of an ab initio numerical experiment with 5 hard-core bosons moving in a 5x5 lattice, that in quantum systems thermalization happens not in course of time evolution but instead at the level of individual eigenstates, as first proposed by DeutschootnotetextJ. M. Deutsch, Phys.Rev. A 43, 2046 (1991) and SrednickiootnotetextM. Srednicki, Phys. Rev. E 50, 888 (1994).

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

Nonlinear Synergistic Emergence and Predictability in Complex Systems: Theory and Hydro-Climatic Applications

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter

2017-04-01

Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is confirmed with robust nonlinear information diagnostics.

Complex Systems

PubMed Central

Goldberger, Ary L.

2006-01-01

Physiologic systems in health and disease display an extraordinary range of temporal behaviors and structural patterns that defy understanding based on linear constructs, reductionist strategies, and classical homeostasis. Application of concepts and computational tools derived from the contemporary study of complex systems, including nonlinear dynamics, fractals and “chaos theory,” is having an increasing impact on biology and medicine. This presentation provides a brief overview of an emerging area of biomedical research, including recent applications to cardiopulmonary medicine and chronic obstructive lung disease. PMID:16921107

Gyrotron collector systems: Types and capabilities

NASA Astrophysics Data System (ADS)

Manuilov, V. N.; Morozkin, M. V.; Luksha, O. I.; Glyavin, M. Yu

2018-06-01

A classification and a comparative analysis of the collector systems of gyrotrons of different frequency ranges and power levels are presented. Both the classical schemes of gyrotron collectors with an adiabatic magnetic field and new ones, including the systems with dynamic scanning of the electron beam, collectors with a highly nonuniform field, as well as multistage recovery schemes, are considered. Recommendations on the use of this or that type of collectors, depending on the output power of the device and the pulse width, are given.

Experimental and analytical investigation of inertial propulsion mechanisms and motion simulation of rigid multi-body mechanical systems

NASA Astrophysics Data System (ADS)

Almesallmy, Mohammed

Methodologies are developed for dynamic analysis of mechanical systems with emphasis on inertial propulsion systems. This work adopted the Lagrangian methodology. Lagrangian methodology is the most efficient classical computational technique, which we call Equations of Motion Code (EOMC). The EOMC is applied to several simple dynamic mechanical systems for easier understanding of the method and to aid other investigators in developing equations of motion of any dynamic system. In addition, it is applied to a rigid multibody system, such as Thomson IPS [Thomson 1986]. Furthermore, a simple symbolic algorithm is developed using Maple software, which can be used to convert any nonlinear n-order ordinary differential equation (ODE) systems into 1st-order ODE system in ready format to be used in Matlab software. A side issue, but equally important, we have started corresponding with the U.S. Patent office to persuade them that patent applications, claiming gross linear motion based on inertial propulsion systems should be automatically rejected. The precedent is rejection of patent applications involving perpetual motion machines.

Quantum Bose-Hubbard model with an evolving graph as a toy model for emergent spacetime

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Markopoulou, Fotini; Lloyd, Seth; Caravelli, Francesco; Severini, Simone; Markström, Klas

2010-05-01

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.

Analysis of airframe/engine interactions - An integrated control perspective

NASA Technical Reports Server (NTRS)

Schmidt, David K.; Schierman, John D.; Garg, Sanjay

1990-01-01

Techniques for the analysis of the dynamic interactions between airframe/engine dynamical systems are presented. Critical coupling terms are developed that determine the significance of these interactions with regard to the closed loop stability and performance of the feedback systems. A conceptual model is first used to indicate the potential sources of the coupling, how the coupling manifests itself, and how the magnitudes of these critical coupling terms are used to quantify the effects of the airframe/engine interactions. A case study is also presented involving an unstable airframe with thrust vectoring for attitude control. It is shown for this system with classical, decentralized control laws that there is little airframe/engine interaction, and the stability and performance with those control laws is not affected. Implications of parameter uncertainty in the coupling dynamics is also discussed, and effects of these parameter variations are also demonstrated to be small for this vehicle configuration.

Investigations of quantum pendulum dynamics in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We investigate the quantum spin dynamics of a spin-1 BEC initialized to an unstable critical point of the dynamical phase space. The subsequent evolution of the collective states of the system is analogous to an inverted simple pendulum in the quantum limit and yields non-classical states with quantum correlations. For short evolution times in the low depletion limit, we observe squeezed states and for longer times beyond the low depletion limit we observe highly non-Gaussian distributions. C.D. Hamley, C.S. Gerving, T.M. Hoang, E.M. Bookjans, and M.S. Chapman, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Superamphiphilic nanocontainers based on the resorcinarene - Cationic surfactant system: Synergetic self-assembling behavior

NASA Astrophysics Data System (ADS)

Gaynanova, Gulnara A.; Bekmukhametova, Alina M.; Kashapov, Ruslan R.; Ziganshina, Albina Yu.; Zakharova, Lucia Ya.

2016-05-01

Self-organization in the mixed system based on water-soluble aminomethylated calix[4]arene with sulfonatoethyl groups at the lower rim and classical cationic surfactant cetyltrimethylammonium bromide has been studied by the methods of tensiometry, conductometry, spectrophotometry, dynamic and electrophoretic light scattering. The values of the critical association concentration, the size and zeta potential values, and the solubilization capacity of mixed aggregates toward the hydrophobic probe (Sudan I) were determined.

Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems

NASA Astrophysics Data System (ADS)

Moca, Cǎtǎlin Paşcu; Kormos, Márton; Zaránd, Gergely

2017-09-01

We develop a hybrid semiclassical method to study the time evolution of one-dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time-evolving block decimation method while treating orbital quasiparticle motion classically. We can follow dynamics up to time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel-coupled one-dimensional Bose condensates. We demonstrate the emergence of soliton-collision-induced phase propagation, soliton-entropy production, and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.

Frenetic Bounds on the Entropy Production

NASA Astrophysics Data System (ADS)

Maes, Christian

2017-10-01

We give a systematic derivation of positive lower bounds for the expected entropy production (EP) rate in classical statistical mechanical systems obeying a dynamical large deviation principle. The logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance. We recover there recently studied "uncertainty" relations for the EP, appearing in studies about the effectiveness of mesoscopic machines. In general our refinement of the positivity of the expected EP rate is obtained in terms of a positive and even function of the expected current(s) which measures the dynamical activity in the system, a time-symmetric estimate of the changes in the system's configuration. Also underdamped diffusions can be included in the analysis.

THERMODYNAMICS OF FE-CU ALLOYS AS DESCRIBED BY A CLASSIC POTENTIALS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caro, A; Caro, M; Lopasso, E M

2005-04-14

The Fe-Cu system is of relevance to the nuclear industry because of the deleterious consequences of Cu precipitates in the mechanical properties of Fe. Several sets of classical potentials are used in molecular dynamics simulations studies of this system, in particular that proposed by Ludwig et al. (Modelling Simul. Mater. Sci. Eng. 6, 19 (1998)). In this work we extract thermodynamic information from this interatomic potentials. We obtain equilibrium phase diagram and find a reasonable agreement with the experimental phases in the regions of relevance to radiation damage studies. We compare the results with the predicted phase diagram based onmore » other potential, as calculated in previous work. We discuss the disagreements found between the phase diagram calculated here and experimental results, focusing on the pure components and discuss the applicability of these potentials; finally we suggest an approach to improve existing potentials for this system.« less

Realistic finite temperature simulations of magnetic systems using quantum statistics

NASA Astrophysics Data System (ADS)

Bergqvist, Lars; Bergman, Anders

2018-01-01

We have performed realistic atomistic simulations at finite temperatures using Monte Carlo and atomistic spin dynamics simulations incorporating quantum (Bose-Einstein) statistics. The description is much improved at low temperatures compared to classical (Boltzmann) statistics normally used in these kind of simulations, while at higher temperatures the classical statistics are recovered. This corrected low-temperature description is reflected in both magnetization and the magnetic specific heat, the latter allowing for improved modeling of the magnetic contribution to free energies. A central property in the method is the magnon density of states at finite temperatures, and we have compared several different implementations for obtaining it. The method has no restrictions regarding chemical and magnetic order of the considered materials. This is demonstrated by applying the method to elemental ferromagnetic systems, including Fe and Ni, as well as Fe-Co random alloys and the ferrimagnetic system GdFe3.

Endogenous Price Bubbles in a Multi-Agent System of the Housing Market

PubMed Central

2015-01-01

Economic history shows a large number of boom-bust cycles, with the U.S. real estate market as one of the latest examples. Classical economic models have not been able to provide a full explanation for this type of market dynamics. Therefore, we analyze home prices in the U.S. using an alternative approach, a multi-agent complex system. Instead of the classical assumptions of agent rationality and market efficiency, agents in the model are heterogeneous, adaptive, and boundedly rational. We estimate the multi-agent system with historical house prices for the U.S. market. The model fits the data well and a deterministic version of the model can endogenously produce boom-and-bust cycles on the basis of the estimated coefficients. This implies that trading between agents themselves can create major price swings in absence of fundamental news. PMID:26107740

Based on Artificial Neural Network to Realize K-Parameter Analysis of Vehicle Air Spring System

NASA Astrophysics Data System (ADS)

Hung, San-Shan; Hsu, Chia-Ning; Hwang, Chang-Chou; Chen, Wen-Jan

2017-10-01

In recent years, because of the air-spring control technique is more mature, that air- spring suspension systems already can be used to replace the classical vehicle suspension system. Depend on internal pressure variation of the air-spring, thestiffnessand the damping factor can be adjusted. Because of air-spring has highly nonlinear characteristic, therefore it isn’t easy to construct the classical controller to control the air-spring effectively. The paper based on Artificial Neural Network to propose a feasible control strategy. By using offline way for the neural network design and learning to the air-spring in different initial pressures and different loads, offline method through, predict air-spring stiffness parameter to establish a model. Finally, through adjusting air-spring internal pressure to change the K-parameter of the air-spring, realize the well dynamic control performance of air-spring suspension.

A novel word spotting method based on recurrent neural networks.

PubMed

Frinken, Volkmar; Fischer, Andreas; Manmatha, R; Bunke, Horst

2012-02-01

Keyword spotting refers to the process of retrieving all instances of a given keyword from a document. In the present paper, a novel keyword spotting method for handwritten documents is described. It is derived from a neural network-based system for unconstrained handwriting recognition. As such it performs template-free spotting, i.e., it is not necessary for a keyword to appear in the training set. The keyword spotting is done using a modification of the CTC Token Passing algorithm in conjunction with a recurrent neural network. We demonstrate that the proposed systems outperform not only a classical dynamic time warping-based approach but also a modern keyword spotting system, based on hidden Markov models. Furthermore, we analyze the performance of the underlying neural networks when using them in a recognition task followed by keyword spotting on the produced transcription. We point out the advantages of keyword spotting when compared to classic text line recognition.

Quantum and classical dynamics in adiabatic computation

NASA Astrophysics Data System (ADS)

Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.

2014-10-01

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.

Experimental recovery of quantum correlations in absence of system-environment back-action

PubMed Central

Xu, Jin-Shi; Sun, Kai; Li, Chuan-Feng; Xu, Xiao-Ye; Guo, Guang-Can; Andersson, Erika; Lo Franco, Rosario; Compagno, Giuseppe

2013-01-01

Revivals of quantum correlations in composite open quantum systems are a useful dynamical feature against detrimental effects of the environment. Their occurrence is attributed to flows of quantum information back and forth from systems to quantum environments. However, revivals also show up in models where the environment is classical, thus unable to store quantum correlations, and forbids system-environment back-action. This phenomenon opens basic issues about its interpretation involving the role of classical environments, memory effects, collective effects and system-environment correlations. Moreover, an experimental realization of back-action-free quantum revivals has applicative relevance as it leads to recover quantum resources without resorting to more demanding structured environments and correction procedures. Here we introduce a simple two-qubit model suitable to address these issues. We then report an all-optical experiment which simulates the model and permits us to recover and control, against decoherence, quantum correlations without back-action. We finally give an interpretation of the phenomenon by establishing the roles of the involved parties. PMID:24287554

Experimental recovery of quantum correlations in absence of system-environment back-action.

PubMed

Xu, Jin-Shi; Sun, Kai; Li, Chuan-Feng; Xu, Xiao-Ye; Guo, Guang-Can; Andersson, Erika; Lo Franco, Rosario; Compagno, Giuseppe

2013-01-01

Revivals of quantum correlations in composite open quantum systems are a useful dynamical feature against detrimental effects of the environment. Their occurrence is attributed to flows of quantum information back and forth from systems to quantum environments. However, revivals also show up in models where the environment is classical, thus unable to store quantum correlations, and forbids system-environment back-action. This phenomenon opens basic issues about its interpretation involving the role of classical environments, memory effects, collective effects and system-environment correlations. Moreover, an experimental realization of back-action-free quantum revivals has applicative relevance as it leads to recover quantum resources without resorting to more demanding structured environments and correction procedures. Here we introduce a simple two-qubit model suitable to address these issues. We then report an all-optical experiment which simulates the model and permits us to recover and control, against decoherence, quantum correlations without back-action. We finally give an interpretation of the phenomenon by establishing the roles of the involved parties.

Method for construction of a biased potential for hyperdynamic simulation of atomic systems

NASA Astrophysics Data System (ADS)

Duda, E. V.; Kornich, G. V.

2017-10-01

An approach to constructing a biased potential for hyperdynamic simulation of atomic systems is considered. Using this approach, the diffusion of an atom adsorbed on the surface of a two-dimensional crystal and a vacancy in the bulk of the crystal are simulated. The influence of the variation in the potential barriers due to thermal vibrations of atoms on the results of calculations is discussed. It is shown that the bias of the potential in the hyperdynamic simulation makes it possible to obtain statistical samples of transitions of atomic systems between states, similar to those given by classical molecular dynamics. However, hyperdynamics significantly accelerates computations in comparison with molecular dynamics in the case of temperature-activated transitions and the associated processes in atomic systems.

Towards a physics of evolution: Critical diversity dynamics at the edges of collapse and bursts of diversification

NASA Astrophysics Data System (ADS)

Hanel, Rudolf; Kauffman, Stuart A.; Thurner, Stefan

2007-09-01

Systems governed by the standard mechanisms of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find an analogy with classical thermodynamic systems. In particular, we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two phases have been subject to previous work, here we focus on the destructive aspects—in particular the phase diagram—of evolutionary dynamics. The main message is that within a critical region, massive loss of diversity can be triggered by very small external fluctuations. We further propose a dynamical model of diversity which captures spontaneous creation and destruction processes fully respecting the phase diagrams of evolutionary systems. The emergent time series show rich diversity dynamics, including power laws as observed in actual economical data, e.g., firm bankruptcy data. We believe the present model presents a possibility to cast the famous qualitative picture of Schumpeterian economic evolution, into a quantifiable and testable framework.

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schubert, Alexander, E-mail: schubert@irsamc.ups-tlse.fr; Meier, Christoph; Falvo, Cyril

2016-08-07

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the “surfaces” for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking themore » molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.« less

Insights into structural and dynamical features of water at halloysite interfaces probed by DFT and classical molecular dynamics simulations.

PubMed

Presti, Davide; Pedone, Alfonso; Mancini, Giordano; Duce, Celia; Tiné, Maria Rosaria; Barone, Vincenzo

2016-01-21

Density functional theory calculations and classical molecular dynamics simulations have been used to investigate the structure and dynamics of water molecules on kaolinite surfaces and confined in the interlayer of a halloysite model of nanometric dimension. The first technique allowed us to accurately describe the structure of the tetrahedral-octahedral slab of kaolinite in vacuum and in interaction with water molecules and to assess the performance of two widely employed empirical force fields to model water/clay interfaces. Classical molecular dynamics simulations were used to study the hydrogen bond network structure and dynamics of water adsorbed on kaolinite surfaces and confined in the halloysite interlayer. The results are in nice agreement with the few experimental data available in the literature, showing a pronounced ordering and reduced mobility of water molecules at the hydrophilic octahedral surfaces of kaolinite and confined in the halloysite interlayer, with respect to water interacting with the hydrophobic tetrahedral surfaces and in the bulk. Finally, this investigation provides new atomistic insights into the structural and dynamical properties of water-clay interfaces, which are of fundamental importance for both natural processes and industrial applications.

Differential dynamic microscopy to characterize Brownian motion and bacteria motility

NASA Astrophysics Data System (ADS)

Germain, David; Leocmach, Mathieu; Gibaud, Thomas

2016-03-01

We have developed a lab module for undergraduate students, which involves the process of quantifying the dynamics of a suspension of microscopic particles using Differential Dynamic Microscopy (DDM). DDM is a relatively new technique that constitutes an alternative method to more classical techniques such as dynamic light scattering (DLS) or video particle tracking (VPT). The technique consists of imaging a particle dispersion with a standard light microscope and a camera and analyzing the images using a digital Fourier transform to obtain the intermediate scattering function, an autocorrelation function that characterizes the dynamics of the dispersion. We first illustrate DDM in the textbook case of colloids under Brownian motion, where we measure the diffusion coefficient. Then we show that DDM is a pertinent tool to characterize biological systems such as motile bacteria.

Hamiltonization of Solids of Revolution Through Reduction

NASA Astrophysics Data System (ADS)

Balseiro, Paula

2017-12-01

In this paper, we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of Balseiro (Arch Ration Mech Anal 214:453-501, 2014) and Balseiro and Garcia-Naranjo (Arch Ration Mech Anal 205(1):267-310, 2012). We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using the existence of two conserved quantities we obtain, by means of gauge transformations and symmetry reduction, genuine Poisson brackets describing the reduced dynamics.

Molecular dynamics studies of displacement cascades in Fe-Y{sub 2}TiO{sub 5} system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dholakia, Manan, E-mail: manan@igcar.gov.in; Chandra, Sharat; Jaya, S. Mathi

The effect of displacement cascade on Fe-Y{sub 2}TiO{sub 5} bilayer is studied using classical molecular dynamics simulations. Different PKA species – Fe, Y, Ti and O – with the same PKA energy of 8 keV are used to produce displacement cascades that encompass the interface. It is shown that Ti atom has the highest movement in the ballistic regime of cascades which can lead to Ti atoms moving out of the oxide clusters into the Fe matrix in ODS alloys.

(Super)symmetries of semiclassical models in theoretical and condensed matter physics

NASA Astrophysics Data System (ADS)

Ngome, J.-P.

2011-03-01

Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.

Robust Control Analysis of Hydraulic Turbine Speed

NASA Astrophysics Data System (ADS)

Jekan, P.; Subramani, C.

2018-04-01

An effective control strategy for the hydro-turbine governor in time scenario is adjective for this paper. Considering the complex dynamic characteristic and the uncertainty of the hydro-turbine governor model and taking the static and dynamic performance of the governing system as the ultimate goal, the designed logic combined the classical PID control theory with artificial intelligence used to obtain the desired output. The used controller will be a variable control techniques, therefore, its parameters can be adaptively adjusted according to the information about the control error signal.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Dynamics of cancerous tissue correlates with invasiveness

NASA Astrophysics Data System (ADS)

West, Ann-Katrine Vransø; Wullkopf, Lena; Christensen, Amalie; Leijnse, Natascha; Tarp, Jens Magelund; Mathiesen, Joachim; Erler, Janine Terra; Oddershede, Lene Broeng

2017-03-01

Two of the classical hallmarks of cancer are uncontrolled cell division and tissue invasion, which turn the disease into a systemic, life-threatening condition. Although both processes are studied, a clear correlation between cell division and motility of cancer cells has not been described previously. Here, we experimentally characterize the dynamics of invasive and non-invasive breast cancer tissues using human and murine model systems. The intrinsic tissue velocities, as well as the divergence and vorticity around a dividing cell correlate strongly with the invasive potential of the tissue, thus showing a distinct correlation between tissue dynamics and aggressiveness. We formulate a model which treats the tissue as a visco-elastic continuum. This model provides a valid reproduction of the cancerous tissue dynamics, thus, biological signaling is not needed to explain the observed tissue dynamics. The model returns the characteristic force exerted by an invading cell and reveals a strong correlation between force and invasiveness of breast cancer cells, thus pinpointing the importance of mechanics for cancer invasion.

Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model

NASA Technical Reports Server (NTRS)

Parker, Robert G.; Agashe, Vinayak; Vijayakar, Sandeep M.

2000-01-01

The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotation mode response is shown to be more sensitive to input torque than translational mode response.

Parity-time symmetry breaking in magnetic systems

DOE PAGES

Galda, Alexey; Vinokur, Valerii M.

2016-07-14

The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. By focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. Here, we reveal the spin-transfer torque-drivenmore » parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. These findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.« less

Studies of perturbed three vortex dynamics

NASA Astrophysics Data System (ADS)

Blackmore, Denis; Ting, Lu; Knio, Omar

2007-06-01

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated with completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half plane, three coaxial slender vortex rings in three space, and "restricted" four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser- and Poincaré-Birkhoff-type arguments and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.

Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators

PubMed Central

Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong

2016-01-01

Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962