Quantum chaos: an introduction via chains of interacting spins-1/2

NASA Astrophysics Data System (ADS)

Gubin, Aviva; Santos, Lea

2012-02-01

We discuss aspects of quantum chaos by focusing on spectral statistical properties and structures of eigenstates of quantum many-body systems. Quantum systems whose classical counterparts are chaotic have properties that differ from those of quantum systems whose classical counterparts are regular. One of the main signatures of what became known as quantum chaos is a spectrum showing repulsion of the energy levels. We show how level repulsion may develop in one-dimensional systems of interacting spins-1/2 which are devoid of random elements and involve only two-body interactions. We present a simple recipe to unfold the spectrum and emphasize the importance of taking into account the symmetries of the system. In addition to the statistics of eigenvalues, we analyze also how the structure of the eigenstates may indicate chaos. This is done by computing quantities that measure the level of delocalization of the eigenstates.

Quantum signature of chaos and thermalization in the kicked Dicke model

NASA Astrophysics Data System (ADS)

Ray, S.; Ghosh, A.; Sinha, S.

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Quantum signature of chaos and thermalization in the kicked Dicke model.

PubMed

Ray, S; Ghosh, A; Sinha, S

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Quantum chaos on a critical Fermi surface.

PubMed

Patel, Aavishkar A; Sachdev, Subir

2017-02-21

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of [Formula: see text] species of fermions at nonzero density coupled to a [Formula: see text] gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of [Formula: see text], the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.

Relativistic quantum chaos—An emergent interdisciplinary field

NASA Astrophysics Data System (ADS)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Controlling chaos-assisted directed transport via quantum resonance.

PubMed

Tan, Jintao; Zou, Mingliang; Luo, Yunrong; Hai, Wenhua

2016-06-01

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Controlling chaos-assisted directed transport via quantum resonance

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

Tan, Jintao; Zou, Mingliang; Luo, Yunrong

2016-06-15

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Can chaos be observed in quantum gravity?

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.

2017-06-01

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.

Strategic leadership: a view from quantum and chaos theories.

PubMed

McDaniel, R R

1997-01-01

Viewing health care from the perspective of chaos and quantum theories offers new insights into management techniques for effective and efficient delivery of health care services. This article introduces these concepts and gives specific prescriptions for managerial action.

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

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

Ren, Gang; Duan, Yi-Shi

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

DOE PAGES

Ren, Gang; Duan, Yi-Shi

2017-07-20

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

Chaos and random matrices in supersymmetric SYK

NASA Astrophysics Data System (ADS)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

Universality in quantum chaos and the one-parameter scaling theory.

PubMed

García-García, Antonio M; Wang, Jiao

2008-02-22

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.

Quantum ratchets, the orbital Josephson effect, and chaos in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando

2014-03-01

In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long-time dynamics of a driven interacting many-body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self-trapping and chaotic behavior. In the latter case, a full quantum many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number. Moreover, we find that chaos and entanglement, as defined by a variety of widely used and accepted measures, are overlapping but distinct notions. Funded by Spanish MINECO, the Ramon y Cajal program (CEC), the Comunidad de Madrid through Grant Microseres, the Heidelberg Center for Quantum Dynamics, and the NSF.

Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

ERIC Educational Resources Information Center

Salazar, R.; Tellez, G.

2012-01-01

We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

Chaos in quantum steering in high-dimensional systems

NASA Astrophysics Data System (ADS)

He, Guang Ping

2018-04-01

Quantum steering means that in some bipartite quantum systems the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems there exists a specific entangled state which can display a kind of chaos effect when being adopted for steering. That is, a subtle difference in the measurement results on one side can steer the other side into completely orthogonal states. Moreover, by expanding the result to infinite-dimensional systems, we find two sets of states for which, contrary to common belief, even though their density matrices approach being identical, the steering between them is impossible. This property makes them very useful for quantum cryptography.

Chaos-Assisted Quantum Tunneling and Delocalization Caused by Resonance or Near-Resonance

NASA Astrophysics Data System (ADS)

Liang, Danfu; Zhang, Jiawei; Zhang, Xili

2018-05-01

We investigate the quantum transport of a single particle trapped in a tilted optical lattice modulated with periodical delta kicks, and attempt to figure out the relationship between chaos and delocalization or quantum tunneling. We illustrate some resonant parameter lines existing in both chaotic and regular parameter regions, and discover the velocity of delocalization of particle tends to faster in the resonant line as well as the lines in which the lattice tilt is an integral multiple n of tilt driving frequency in chaotic region. While the degree of localization is linked to the distance between parameter points and resonant lines. Those useful results can be experimentally applied to control chaos-assisted transport of single particle held in optical lattices.

Collective diffusion and quantum chaos in holography

NASA Astrophysics Data System (ADS)

Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu

2018-05-01

We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Quantum Bound to Chaos and the Semiclassical Limit

NASA Astrophysics Data System (ADS)

Kurchan, Jorge

2018-06-01

We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as the corresponding one for the `Loschmidt echo'. The bound appears here as the impossibility to scatter a wave, by effect of the curvature, over characteristic lengths smaller than the deBroglie wavelength.

Quantum Regime of a Two-Dimensional Phonon Cavity

NASA Astrophysics Data System (ADS)

Bolgar, Aleksey N.; Zotova, Julia I.; Kirichenko, Daniil D.; Besedin, Ilia S.; Semenov, Aleksander V.; Shaikhaidarov, Rais S.; Astafiev, Oleg V.

2018-06-01

We realize the quantum regime of a surface acoustic wave (SAW) resonator by demonstrating vacuum Rabi mode splitting due to interaction with a superconducting artificial atom. Reaching the quantum regime is physically difficult and technologically challenging since SAW devices consist of large arrays of narrow metal strips. This work paves the way for realizing analogues of quantum optical phenomena with phonons and can be useful in on-chip quantum electronics.

Coherent perfect absorption in a quantum nonlinear regime of cavity quantum electrodynamics

NASA Astrophysics Data System (ADS)

Wei, Yang-hua; Gu, Wen-ju; Yang, Guoqing; Zhu, Yifu; Li, Gao-xiang

2018-05-01

Coherent perfect absorption (CPA) is investigated in the quantum nonlinear regime of cavity quantum electrodynamics (CQED), in which a single two-level atom couples to a single-mode cavity weakly driven by two identical laser fields. In the strong-coupling regime and due to the photon blockade effect, the weakly driven CQED system can be described as a quantum system with three polariton states. CPA is achieved at a critical input field strength when the frequency of the input fields matches the polariton transition frequency. In the quantum nonlinear regime, the incoherent dissipation processes such as atomic and photon decays place a lower bound for the purity of the intracavity quantum field. Our results show that under the CPA condition, the intracavity field always exhibits the quadrature squeezing property manifested by the quantum nonlinearity, and the outgoing photon flux displays the super-Poissonian distribution.

Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons.

PubMed

Aßmann, Marc; Thewes, Johannes; Fröhlich, Dietmar; Bayer, Manfred

2016-07-01

Symmetries are the underlying principles of fundamental interactions in nature. Chaos in a quantum system may emerge from breaking these symmetries. Compared to vacuum, crystals are attractive for studying quantum chaos, as they not only break spatial isotropy, but also lead to novel quasiparticles with modified interactions. Here we study yellow Rydberg excitons in cuprous oxide which couple strongly to the vacuum light field and interact significantly with crystal phonons, leading to inversion symmetry breaking. In a magnetic field, time-reversal symmetry is also broken and the exciton states show a complex splitting pattern, resulting in quadratic level repulsion for small splittings. In contrast to atomic chaotic systems in a magnetic field, which show only a linear level repulsion, this is a signature of a system where all anti-unitary symmetries are broken simultaneously. This behaviour can otherwise be found only for the electro-weak interaction or engineered billiards.

Studies of quantum dots in the quantum Hall regime

NASA Astrophysics Data System (ADS)

Goldmann, Eyal

We present two studies of quantum dots in the quantum Hall regime. In the first study, presented in Chapter 3, we investigate the edge reconstruction phenomenon believed to occur when the quantum dot filling fraction is n≲1 . Our approach involves the examination of large dots (≤40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction. In the second study, presented in Chapter 4, we investigate quantum dots in the fractional quantum Hall regime using a Hartree formulation of composite fermion theory. We find that under appropriate conditions, the chemical potential of the dots oscillates periodically with B due to the transfer of composite fermions between quasi-Landau bands. This effect is analogous the addition spectrum oscillations which occur in quantum dots in the integer quantum Hall regime. Period f0 oscillations are found in sharply confined dots with filling factors nu = 2/5 and nu = 2/3. Period 3 f0 oscillations are found in a parabolically confined nu = 2/5 dot. More generally, we argue that the oscillation period of dots with band pinning should vary continuously with B, whereas the period of dots without band pinning is f0 .

An investigation into possible quantum chaos in the H2 molecule under intense laser fields via Ehrenfest phase space (EPS) trajectories.

PubMed

Sadhukhan, Mainak; Deb, B M

2018-06-21

By employing the Ehrenfest "phase space" trajectory method for studying quantum chaos, developed in our laboratory, the present study reveals that the H 2 molecule under intense laser fields of three different intensities, I = 1 × 10 14  W/cm 2 , 5 × 10 14  W/cm 2 , and 1 × 10 15  W/cm 2 , does not show quantum chaos. A similar conclusion is also reached through the Loschmidt echo (also called quantum fidelity) calculations reported here for the first time for a real molecule under intense laser fields. Thus, a long-standing conjecture about the possible existence of quantum chaos in atoms and molecules under intense laser fields has finally been tested and not found to be valid in the present case.

Quantum Tunneling and Chaos in Classical Scale Walkers

NASA Astrophysics Data System (ADS)

Su, Jenny; Dijksman, Joshua; Ward, Jeremy; Behringer, Robert

2014-03-01

We study the behavior of `walkers' small droplets bouncing on a fluid layer vibrated at amplitudes just below the onset of Faraday instability. It was shown recently that despite their macroscopic size, the droplet dynamics are stochastic in nature and reminiscent of the dual particle-wave dynamics in the realm of quantum mechanics (Couder PRL 2006). We use these walkers to study how chaos, which is macroscopically unpredictable, will manifest in a quantum setting. Pecora showed in 2011 that tunneling for particles that have a chaotic ground state is different from tunneling for particles with a regular ground state (PRE 2011). In the experiment we gather data that illustrates the particle trajectory and tunneling behavior as particles transition across the barrier in the double well system with both integrable and chaotic shapes.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

Quantum no-scale regimes in string theory

NASA Astrophysics Data System (ADS)

Coudarchet, Thibaut; Fleming, Claude; Partouche, Hervé

2018-05-01

We show that in generic no-scale models in string theory, the flat, expanding cosmological evolutions found at the quantum level can be attracted to a "quantum no-scale regime", where the no-scale structure is restored asymptotically. In this regime, the quantum effective potential is dominated by the classical kinetic energies of the no-scale modulus and dilaton. We find that this natural preservation of the classical no-scale structure at the quantum level occurs when the initial conditions of the evolutions sit in a subcritical region of their space. On the contrary, supercritical initial conditions yield solutions that have no analogue at the classical level. The associated intrinsically quantum universes are sentenced to collapse and their histories last finite cosmic times. Our analysis is done at 1-loop, in perturbative heterotic string compactified on tori, with spontaneous supersymmetry breaking implemented by a stringy version of the Scherk-Schwarz mechanism.

Scalable quantum memory in the ultrastrong coupling regime.

PubMed

Kyaw, T H; Felicetti, S; Romero, G; Solano, E; Kwek, L-C

2015-03-02

Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances.

Scalable quantum memory in the ultrastrong coupling regime

PubMed Central

Kyaw, T. H.; Felicetti, S.; Romero, G.; Solano, E.; Kwek, L.-C.

2015-01-01

Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances. PMID:25727251

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops

NASA Astrophysics Data System (ADS)

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

2017-12-01

We consider two coupled quantum tops with angular momentum vectors L and M . The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems, which extends the well-known threefold way of Wigner and Dyson (referred to as "standard" symmetry classes here). We identify the nonstandard symmetry classes BD I0 (chiral orthogonal class with no zero modes), BD I1 (chiral orthogonal class with one zero mode), and C I (antichiral orthogonal class) as well as the standard symmetry class A I (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue, we show that the Feingold-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics, we show that these signatures disappear or strongly change.

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops.

PubMed

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

2017-12-01

We consider two coupled quantum tops with angular momentum vectors L and M. The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems, which extends the well-known threefold way of Wigner and Dyson (referred to as "standard" symmetry classes here). We identify the nonstandard symmetry classes BDI_{0} (chiral orthogonal class with no zero modes), BDI_{1} (chiral orthogonal class with one zero mode), and CI (antichiral orthogonal class) as well as the standard symmetry class AI (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue, we show that the Feingold-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics, we show that these signatures disappear or strongly change.

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory

NASA Astrophysics Data System (ADS)

Tzemos, Athanasios C.; Efthymiopoulos, Christos; Contopoulos, George

2018-04-01

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory.

PubMed

Tzemos, Athanasios C; Efthymiopoulos, Christos; Contopoulos, George

2018-04-01

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

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

Deterministic chaos in an ytterbium-doped mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Mélo, Lucas B. A.; Palacios, Guillermo F. R.; Carelli, Pedro V.; Acioli, Lúcio H.; Rios Leite, José R.; de Miranda, Marcio H. G.

2018-05-01

We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rossler map. A positive Lyapunov exponent $\\lambda = 0.14$ confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

Chaos and complexity by design

DOE PAGES

Roberts, Daniel A.; Yoshida, Beni

2017-04-20

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We also show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. In addition, we prove that these 2k-point correlators for Pauli operators completely determine the k-foldmore » channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.« less

Quantum chaos inside black holes

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2017-06-01

We show how semiclassical black holes can be reinterpreted as an effective geometry, composed of a large ensemble of horizonless naked singularities (eventually smoothed at the Planck scale). We call these new items frizzy-balls, which can be rigorously defined by Euclidean path integral approach. This leads to interesting implications about information paradoxes. We demonstrate that infalling information will chaotically propagate inside this system before going to the full quantum gravity regime (Planck scale).

The information geometry of chaos

NASA Astrophysics Data System (ADS)

Cafaro, Carlo

2008-10-01

In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already

Large quantum rings in the ν > 1 quantum Hall regime.

PubMed

Räsänen, E; Aichinger, M

2009-01-14

We study computationally the ground-state properties of large quantum rings in the filling-factor ν>1 quantum Hall regime. We show that the arrangement of electrons into different Landau levels leads to clear signatures in the total energies as a function of the magnetic field. In this context, we discuss possible approximations for the filling factor ν in the system. We are able to characterize integer-ν states in quantum rings in an analogy with conventional quantum Hall droplets. We also find a partially spin-polarized state between ν = 2 and 3. Despite the specific topology of a quantum ring, this state is strikingly reminiscent of the recently found ν = 5/2 state in a quantum dot.

Generic superweak chaos induced by Hall effect

NASA Astrophysics Data System (ADS)

Ben-Harush, Moti; Dana, Itzhack

2016-05-01

We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.

Embracing chaos and complexity: a quantum change for public health.

PubMed

Resnicow, Kenneth; Page, Scott E

2008-08-01

Public health research and practice have been guided by a cognitive, rational paradigm where inputs produce linear, predictable changes in outputs. However, the conceptual and statistical assumptions underlying this paradigm may be flawed. In particular, this perspective does not adequately account for nonlinear and quantum influences on human behavior. We propose that health behavior change is better understood through the lens of chaos theory and complex adaptive systems. Key relevant principles include that behavior change (1) is often a quantum event; (2) can resemble a chaotic process that is sensitive to initial conditions, highly variable, and difficult to predict; and (3) occurs within a complex adaptive system with multiple components, where results are often greater than the sum of their parts.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Spin squeezing as an indicator of quantum chaos in the Dicke model.

PubMed

Song, Lijun; Yan, Dong; Ma, Jian; Wang, Xiaoguang

2009-04-01

We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

MOND as a regime of quantum gravity

NASA Astrophysics Data System (ADS)

Smolin, Lee

2017-10-01

We propose that there is a regime of quantum gravity phenomena, for the case that the cosmological constant is small and positive, which concerns physics at temperatures below the de Sitter temperature, or length scales larger than the horizon. We observe that the standard form of the equivalence principle does not apply in this regime; we consider instead that a weakened form of the equivalence principle might hold in which the ratio of gravitational to inertial mass is a function of environmental parameters. We consider possible principles to determine that function. These lead to behavior that, in the limit of ℏ→0 and c →∞ , reproduces the modifications of Newtonian dynamics first proposed by Milgrom. Thus modified newtonian dynamics is elucidated as coding the physics of a novel regime of quantum gravity phenomena. We propose also an effective description of this regime in terms of a bimetric theory, valid in the approximation where the metric is static. This predicts a new effect, which modifies gravity for radial motions.

Dynamical thermalization in isolated quantum dots and black holes

NASA Astrophysics Data System (ADS)

Kolovsky, Andrey R.; Shepelyansky, Dima L.

2017-01-01

We study numerically a model of quantum dot with interacting fermions. At strong interactions with small conductance the model is reduced to the Sachdev-Ye-Kitaev black-hole model while at weak interactions and large conductance it describes a Landau-Fermi liquid in a regime of quantum chaos. We show that above the Åberg threshold for interactions there is an onset of dynamical themalization with the Fermi-Dirac distribution describing the eigenstates of an isolated dot. At strong interactions in the isolated black-hole regime there is also the onset of dynamical thermalization with the entropy described by the quantum Gibbs distribution. This dynamical thermalization takes place in an isolated system without any contact with a thermostat. We discuss the possible realization of these regimes with quantum dots of 2D electrons and cold ions in optical lattices.

Quantum rotor in nanostructured superconductors

PubMed Central

Lin, Shi-Hsin; Milošević, M. V.; Covaci, L.; Jankó, B.; Peeters, F. M.

2014-01-01

Despite its apparent simplicity, the idealized model of a particle constrained to move on a circle has intriguing dynamic properties and immediate experimental relevance. While a rotor is rather easy to set up classically, the quantum regime is harder to realize and investigate. Here we demonstrate that the quantum dynamics of quasiparticles in certain classes of nanostructured superconductors can be mapped onto a quantum rotor. Furthermore, we provide a straightforward experimental procedure to convert this nanoscale superconducting rotor into a regular or inverted quantum pendulum with tunable gravitational field, inertia, and drive. We detail how these novel states can be detected via scanning tunneling spectroscopy. The proposed experiments will provide insights into quantum dynamics and quantum chaos. PMID:24686241

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Does chaos assist localization or delocalization?

PubMed

Tan, Jintao; Lu, Gengbiao; Luo, Yunrong; Hai, Wenhua

2014-12-01

We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.

Chaos as the hub of systems dynamics. The part I-The attitude control of spacecraft by involving in the heteroclinic chaos

NASA Astrophysics Data System (ADS)

Doroshin, Anton V.

2018-06-01

In this work the chaos in dynamical systems is considered as a positive aspect of dynamical behavior which can be applied to change systems dynamical parameters and, moreover, to change systems qualitative properties. From this point of view, the chaos can be characterized as a hub for the system dynamical regimes, because it allows to interconnect separated zones of the phase space of the system, and to fulfill the jump into the desirable phase space zone. The concretized aim of this part of the research is to focus on developing the attitude control method for magnetized gyrostat-satellites, which uses the passage through the intentionally generated heteroclinic chaos. The attitude dynamics of the satellite/spacecraft in this case represents the series of transitions from the initial dynamical regime into the chaotic heteroclinic regime with the subsequent exit to the final target dynamical regime with desirable parameters of the attitude dynamics.

A bound on chaos

DOE PAGES

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas

2016-08-17

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Quantum plug n’ play: modular computation in the quantum regime

NASA Astrophysics Data System (ADS)

Thompson, Jayne; Modi, Kavan; Vedral, Vlatko; Gu, Mile

2018-01-01

Classical computation is modular. It exploits plug n’ play architectures which allow us to use pre-fabricated circuits without knowing their construction. This bestows advantages such as allowing parts of the computational process to be outsourced, and permitting individual circuit components to be exchanged and upgraded. Here, we introduce a formal framework to describe modularity in the quantum regime. We demonstrate a ‘no-go’ theorem, stipulating that it is not always possible to make use of quantum circuits without knowing their construction. This has significant consequences for quantum algorithms, forcing the circuit implementation of certain quantum algorithms to be rebuilt almost entirely from scratch after incremental changes in the problem—such as changing the number being factored in Shor’s algorithm. We develop a workaround capable of restoring modularity, and apply it to design a modular version of Shor’s algorithm that exhibits increased versatility and reduced complexity. In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked (or assembled) to implement various parts of a more complex quantum computation.

[Shedding light on chaos theory].

PubMed

Chou, Shieu-Ming

2004-06-01

Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.

Chaos Criminology: A critical analysis

NASA Astrophysics Data System (ADS)

McCarthy, Adrienne L.

There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.

Multimode optomechanical system in the quantum regime

NASA Astrophysics Data System (ADS)

Hvidtfelt Padkær Nielsen, William; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert

2017-01-01

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

Quantum chaos in ultracold collisions of gas-phase erbium atoms.

PubMed

Frisch, Albert; Mark, Michael; Aikawa, Kiyotaka; Ferlaino, Francesca; Bohn, John L; Makrides, Constantinos; Petrov, Alexander; Kotochigova, Svetlana

2014-03-27

Atomic and molecular samples reduced to temperatures below one microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating the interactions between their constituent particles. As a result of this resolution, atoms can be made to scatter resonantly on demand, through the precise control of a magnetic field. For simple atoms, such as alkalis, scattering resonances are extremely well characterized. However, ultracold physics is now poised to enter a new regime, where much more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense set of resonances in ultracold collision cross-sections will probably exhibit essentially random fluctuations, much as the observed energy spectra of nuclear scattering do. According to the Bohigas-Giannoni-Schmit conjecture, such fluctuations would imply chaotic dynamics of the underlying classical motion driving the collision. This would necessitate new ways of looking at the fundamental interactions in ultracold atomic and molecular systems, as well as perhaps new chaos-driven states of ultracold matter. Here we describe the experimental demonstration that random spectra are indeed found at ultralow temperatures. In the experiment, an ultracold gas of erbium atoms is shown to exhibit many Fano-Feshbach resonances, of the order of three per gauss for bosons. Analysis of their statistics verifies that their distribution of nearest-neighbour spacings is what one would expect from random matrix theory. The density and statistics of these resonances are explained by fully quantum mechanical scattering calculations that locate their origin in the anisotropy of the atoms' potential energy surface. Our results therefore reveal chaotic behaviour in the native interaction between ultracold atoms.

Edge mixing dynamics in graphene p–n junctions in the quantum Hall regime

PubMed Central

Matsuo, Sadashige; Takeshita, Shunpei; Tanaka, Takahiro; Nakaharai, Shu; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke

2015-01-01

Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p–n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p–n junction. PMID:26337445

Multimode optomechanical system in the quantum regime

PubMed Central

Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert

2017-01-01

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to −2.4 dB (−3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom. PMID:27999182

Multimode optomechanical system in the quantum regime.

PubMed

Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert

2017-01-03

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10 7 ) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

Fabry-Perot Interferometry in the Integer and Fractional Quantum Hall Regimes

NASA Astrophysics Data System (ADS)

McClure, Douglas; Chang, Willy; Kou, Angela; Marcus, Charles; Pfeiffer, Loren; West, Ken

2011-03-01

We present measurements of electronic Fabry-Perot interferometers in the integer and fractional quantum Hall regimes. Two classes of resistance oscillations may be seen as a function of magnetic field and gate voltage, as we have previously reported. In small interferometers in the integer regime, oscillations of the type associated with Coulomb interaction are ubiquitous, while those consistent with single-particle Aharonov-Bohm interference are seen to co-exist in some configurations. The amplitude scaling of both types with temperature and device size is consistent with a theoretical model. Oscillations are further observed in the fractional quantum Hall regime. Here the dependence of the period on the filling factors in the constrictions and bulk of the interferometer can shed light on the effective charge of the interfering quasiparticles, but care is needed to distinguish these oscillations from those associated with integer quantum Hall states. We acknowledge funding from Microsoft Project Q and IBM.

Optimization of edge state velocity in the integer quantum Hall regime

NASA Astrophysics Data System (ADS)

Sahasrabudhe, H.; Novakovic, B.; Nakamura, J.; Fallahi, S.; Povolotskyi, M.; Klimeck, G.; Rahman, R.; Manfra, M. J.

2018-02-01

Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here we present a new simulation method for designing heterostructures with high edge state velocity by realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. Using this simulation method, we also predict the filling factor at the center of QPCs and their conductance at different gate voltages. The 3D Schrödinger equation is split into 1D and 2D parts. Quasi-1D Schrödinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile, and quantum transport is used to solve for the edge state wave functions. The velocity of edge states is found to be /B , where is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double-sided delta doping have the highest edge state velocity among the structures considered.

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime.

PubMed

Braumüller, Jochen; Marthaler, Michael; Schneider, Andre; Stehli, Alexander; Rotzinger, Hannes; Weides, Martin; Ustinov, Alexey V

2017-10-03

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.

Disordered wires and quantum chaos in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Angonga, Jackson; Gadway, Bryce

2017-04-01

We present two topics: topological wires subjected to disorder and quantum chaos in a spin-J model. These studies are experimentally realized through the use of a momentum-space lattice, in which the dynamics of 87Rb atoms are recorded. In topological wires, a transition to a trivial phase is seen when disorder is applied to either the tunneling strengths or site energies. This transition is detected using both charge-pumping and Hamiltonian-quenching techniques. In the spin-J study we observe the effects of both linear and non-linear spin operations by measuring the linear entropy of the system as well as the out-of-time order correlation function. We further probe the chaotic signatures of the paradigmatic kicked top model.

Disorder-assisted quantum transport in suboptimal decoherence regimes

PubMed Central

Novo, Leonardo; Mohseni, Masoud; Omar, Yasser

2016-01-01

We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime. PMID:26726133

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic

Study of Quantum Chaos in the Framework of Triaxial Rotator Models

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

Proskurins, J.; Bavrins, K.; Andrejevs, A.

2009-01-28

Dynamical quantum chaos criteria--a perturbed wave function entropy W({psi}{sub i}) and a fragmentation width {kappa}({phi}{sub k}) of basis states were studied in two cases of nuclear rigid triaxial rotator models. The first model is characterized by deformation angle {gamma} only, while the second model depends on both quadrupole deformation parameters ({beta},{gamma}). The degree of chaoticity has been determined in the studies of the dependence of criteria W({psi}{sub i}) and {kappa}({phi}{sub k}) from nuclear spin values up to I{<=}101 for model parameters {gamma} and ({beta},{gamma}) correspondingly. The transition from librational to rotational type energy spectra has been considered for both modelsmore » as well.« less

Endoreversible quantum heat engines in the linear response regime.

PubMed

Wang, Honghui; He, Jizhou; Wang, Jianhui

2017-07-01

We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.

Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system

NASA Astrophysics Data System (ADS)

Weidinger, Simon A.; Knap, Michael

2017-04-01

We study the regimes of heating in the periodically driven O(N)-model, which is a well established model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green’s function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the system ceases to absorb, and at parametrically late times a thermalizing regime. Our simulations suggest that in the thermalizing regime the absorbed energy grows algebraically in time with an exponent that approaches the universal value of 1/2, and is thus significantly slower than linear Joule heating. Our results demonstrate the parametric stability of prethermal states in a many-body system driven at frequencies that are comparable to its microscopic scales. This paves the way for realizing exotic quantum phases, such as time crystals or interacting topological phases, in the prethermal regime of interacting Floquet systems.

Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory

NASA Astrophysics Data System (ADS)

Rui, Jun; Jiang, Yan; Yang, Sheng-Jun; Zhao, Bo; Bao, Xiao-Hui; Pan, Jian-Wei

2015-09-01

Spin echo is a powerful technique to extend atomic or nuclear coherence times by overcoming the dephasing due to inhomogeneous broadenings. However, there are disputes about the feasibility of applying this technique to an ensemble-based quantum memory at the single-quanta level. In this experimental study, we find that noise due to imperfections of the rephasing pulses has both intense superradiant and weak isotropic parts. By properly arranging the beam directions and optimizing the pulse fidelities, we successfully manage to operate the spin echo technique in the quantum regime by observing nonclassical photon-photon correlations as well as the quantum behavior of retrieved photons. Our work for the first time demonstrates the feasibility of harnessing the spin echo method to extend the lifetime of ensemble-based quantum memories at the single-quanta level.

Quantum interference magnetoconductance of polycrystalline germanium films in the variable-range hopping regime

NASA Astrophysics Data System (ADS)

Li, Zhaoguo; Peng, Liping; Zhang, Jicheng; Li, Jia; Zeng, Yong; Zhan, Zhiqiang; Wu, Weidong

2018-06-01

Direct evidence of quantum interference magnetotransport in polycrystalline germanium films in the variable-range hopping (VRH) regime is reported. The temperature dependence of the conductivity of germanium films fulfilled the Mott VRH mechanism with the form of ? in the low-temperature regime (?). For the magnetotransport behaviour of our germanium films in the VRH regime, a crossover, from negative magnetoconductance at the low-field to positive magnetoconductance at the high-field, is observed while the zero-field conductivity is higher than the critical value (?). In the regime of ?, the magnetoconductance is positive and quadratic in the field for some germanium films. These features are in agreement with the VRH magnetotransport theory based on the quantum interference effect among random paths in the hopping process.

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were

Nontrivial transition of transmission in a highly open quantum point contact in the quantum Hall regime

NASA Astrophysics Data System (ADS)

Hong, Changki; Park, Jinhong; Chung, Yunchul; Choi, Hyungkook; Umansky, Vladimir

2017-11-01

Transmission through a quantum point contact (QPC) in the quantum Hall regime usually exhibits multiple resonances as a function of gate voltage and high nonlinearity in bias. Such behavior is unpredictable and changes sample by sample. Here, we report the observation of a sharp transition of the transmission through an open QPC at finite bias, which was observed consistently for all the tested QPCs. It is found that the bias dependence of the transition can be fitted to the Fermi-Dirac distribution function through universal scaling. The fitted temperature matches quite nicely to the electron temperature measured via shot-noise thermometry. While the origin of the transition is unclear, we propose a phenomenological model based on our experimental results that may help to understand such a sharp transition. Similar transitions are observed in the fractional quantum Hall regime, and it is found that the temperature of the system can be measured by rescaling the quasiparticle energy with the effective charge (e*=e /3 ). We believe that the observed phenomena can be exploited as a tool for measuring the electron temperature of the system and for studying the quasiparticle charges of the fractional quantum Hall states.

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

NASA Astrophysics Data System (ADS)

Löck, Steffen; Bäcker, Arnd; Ketzmerick, Roland; Schlagheck, Peter

2010-03-01

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given ℏ regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system

NASA Astrophysics Data System (ADS)

Weidinger, Simon; Knap, Michael

We study the regimes of heating in the periodically driven O (N) -model, which represents a generic model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green's function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the system ceases to absorb, and at parametrically late times a thermalizing regime. Our simulations suggest that in the thermalizing regime the absorbed energy grows algebraically in time with an the exponent that approaches the universal value of 1 / 2 , and is thus significantly slower than linear Joule heating. Our results demonstrate the parametric stability of prethermal states in a generic many-body system driven at frequencies that are comparable to its microscopic scales. This paves the way for realizing exotic quantum phases, such as time crystals or interacting topological phases, in the prethermal regime of interacting Floquet systems. We acknowledge support from the Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under Grant agreement 291763, and from the DFG Grant No. KN 1254/1-1.

Maxwell’s demon in the quantum-Zeno regime and beyond

NASA Astrophysics Data System (ADS)

Engelhardt, G.; Schaller, G.

2018-02-01

The long-standing paradigm of Maxwell’s demon is till nowadays a frequently investigated issue, which still provides interesting insights into basic physical questions. Considering a single-electron transistor, where we implement a Maxwell demon by a piecewise-constant feedback protocol, we investigate quantum implications of the Maxwell demon. To this end, we harness a dynamical coarse-graining method, which provides a convenient and accurate description of the system dynamics even for high measurement rates. In doing so, we are able to investigate the Maxwell demon in a quantum-Zeno regime leading to transport blockade. We argue that there is a measurement rate providing an optimal performance. Moreover, we find that besides building up a chemical gradient, there can be also a regime where the feedback loop additionally extracts energy, which results from the energy non-conserving character of the projective measurement.

Relativistic laser-plasma interactions in the quantum regime.

PubMed

Eliasson, Bengt; Shukla, P K

2011-04-01

We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature.

Transient dynamics of a quantum-dot: From Kondo regime to mixed valence and to empty orbital regimes

NASA Astrophysics Data System (ADS)

Cheng, YongXi; Li, ZhenHua; Wei, JianHua; Nie, YiHang; Yan, YiJing

2018-04-01

Based on the hierarchical equations of motion approach, we study the time-dependent transport properties of a strongly correlated quantum dot system in the Kondo regime (KR), mixed valence regime (MVR), and empty orbital regime (EOR). We find that the transient current in KR shows the strongest nonlinear response and the most distinct oscillation behaviors. Both behaviors become weaker in MVR and diminish in EOR. To understand the physical insight, we examine also the corresponding dot occupancies and the spectral functions, with their dependence on the Coulomb interaction, temperature, and applied step bias voltage. The above nonlinear and oscillation behaviors could be understood as the interplay between dynamical Kondo resonance and single electron resonant-tunneling.

Cavity quantum electrodynamics in the nonperturbative regime

NASA Astrophysics Data System (ADS)

De Bernardis, Daniele; Jaako, Tuomas; Rabl, Peter

2018-04-01

We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode L C resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.

Low-temperature physics: Chaos in the cold

NASA Astrophysics Data System (ADS)

Julienne, Paul S.

2014-03-01

A marriage between theory and experiment has shown that ultracold erbium atoms trapped with laser light and subjected to a magnetic field undergo collisions that are characterized by quantum chaos. See Letter p.475

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

Diffractive paths for weak localization in quantum billiards

NASA Astrophysics Data System (ADS)

Březinová, Iva; Stampfer, Christoph; Wirtz, Ludger; Rotter, Stefan; Burgdörfer, Joachim

2008-04-01

We study the weak-localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity (when approaching the lead mouths from the cavity interior) to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding antipeak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.

Atomic quantum corrals for Bose-Einstein condensates

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

Xiong Hongwei; Kavli Institute for Theoretical Physics China, Chinese Academy of Sciences, Beijing 100190; Wu Biao

2010-11-15

We consider the dynamics of Bose-Einstein condensates in a corral-like potential. Compared to the electronic quantum corrals, the atomic quantum corrals have the advantages of allowing direct and convenient observation of the wave dynamics, together with adjustable interaction strength. Our numerical study shows that these advantages not only allow exploration of the rich dynamical structures in the density distribution but also make the corrals useful in many other aspects. In particular, the corrals for atoms can be arranged into a stadium shape for the experimental visualization of quantum chaos, which has been elusive with electronic quantum corrals. The density correlationmore » is used to describe quantitatively the dynamical quantum chaos. Furthermore, we find that the interatomic interaction can greatly enhance the dynamical quantum chaos, for example, inducing a chaotic behavior even in circle-shaped corrals.« 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.

Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology

NASA Astrophysics Data System (ADS)

Dhamala, Mukeshwar; Lai, Ying-Cheng

1999-02-01

Transient chaos is a common phenomenon in nonlinear dynamics of many physical, biological, and engineering systems. In applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos. We address how to sustain transient chaos in deterministic flows. We utilize a simple and practical method, based on extracting the fundamental dynamics from time series, to maintain chaos. The method can result in control of trajectories from almost all initial conditions in the original basin of the chaotic attractor from which transient chaos is created. We apply our method to three problems: (1) voltage collapse in electrical power systems, (2) species preservation in ecology, and (3) elimination of undesirable bursting behavior in a chemical reaction system.

Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime.

PubMed

Press, David; Götzinger, Stephan; Reitzenstein, Stephan; Hofmann, Carolin; Löffler, Andreas; Kamp, Martin; Forchel, Alfred; Yamamoto, Yoshihisa

2007-03-16

We observe antibunching in the photons emitted from a strongly coupled single quantum dot and pillar microcavity in resonance. When the quantum dot was spectrally detuned from the cavity mode, the cavity emission remained antibunched, and also anticorrelated from the quantum dot emission. Resonant pumping of the selected quantum dot via an excited state enabled these observations by eliminating the background emitters that are usually coupled to the cavity. This device demonstrates an on-demand single-photon source operating in the strong coupling regime, with a Purcell factor of 61+/-7 and quantum efficiency of 97%.

Quantum simulation of disordered systems with cold atoms

NASA Astrophysics Data System (ADS)

Garreau, Jean-Claude

2017-01-01

This paper reviews the physics of quantum disorder in relation with a series of experiments using laser-cooled atoms exposed to "kicks" of a standing wave, realizing a paradigmatic model of quantum chaos, the kicked rotor. This dynamical system can be mapped onto a tight-binding Hamiltonian with pseudo-disorder, formally equivalent to the Anderson model of quantum disorder, with quantum chaos playing the role of disorder. This provides a very good quantum simulator for the Anderson physics. xml:lang="fr"

Signatures of chaos in the Brillouin zone.

PubMed

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Evolution of Plasmonic Metamolecule Modes in the Quantum Tunneling Regime.

PubMed

Scholl, Jonathan A; Garcia-Etxarri, Aitzol; Aguirregabiria, Garikoitz; Esteban, Ruben; Narayan, Tarun C; Koh, Ai Leen; Aizpurua, Javier; Dionne, Jennifer A

2016-01-26

Plasmonic multinanoparticle systems exhibit collective electric and magnetic resonances that are fundamental for the development of state-of-the-art optical nanoantennas, metamaterials, and surface-enhanced spectroscopy substrates. While electric dipolar modes have been investigated in both the classical and quantum realm, little attention has been given to magnetic and other "dark" modes at the smallest dimensions. Here, we study the collective electric, magnetic, and dark modes of colloidally synthesized silver nanosphere trimers with varying interparticle separation using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). This technique enables direct visualization and spatially selective excitation of individual trimers, as well as manipulation of the interparticle distance into the subnanometer regime with the electron beam. Our experiments reveal that bonding electric and magnetic modes are significantly impacted by quantum effects, exhibiting a relative blueshift and reduced EELS amplitude compared to classical predictions. In contrast, the trimer's electric dark mode is not affected by quantum tunneling for even Ångström-scale interparticle separations. We employ a quantum-corrected model to simulate the effect of electron tunneling in the trimer which shows excellent agreement with experimental results. This understanding of classical and quantum-influenced hybridized modes may impact the development of future quantum plasmonic materials and devices, including Fano-like molecular sensors and quantum metamaterials.

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

NASA Astrophysics Data System (ADS)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior

Convergence of moment expansions for expectation values with embedded random matrix ensembles and quantum chaos

NASA Astrophysics Data System (ADS)

Kota, V. K. B.

2003-07-01

Smoothed forms for expectation values < K> E of positive definite operators K follow from the K-density moments either directly or in many other ways each giving a series expansion (involving polynomials in E). In large spectroscopic spaces one has to partition the many particle spaces into subspaces. Partitioning leads to new expansions for expectation values. It is shown that all the expansions converge to compact forms depending on the nature of the operator K and the operation of embedded random matrix ensembles and quantum chaos in many particle spaces. Explicit results are given for occupancies < ni> E, spin-cutoff factors < JZ2> E and strength sums < O†O> E, where O is a one-body transition operator.

Information processing in echo state networks at the edge of chaos.

PubMed

Boedecker, Joschka; Obst, Oliver; Lizier, Joseph T; Mayer, N Michael; Asada, Minoru

2012-09-01

We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.

Electrostatic and Quantum Transport Simulations of Quantum Point Contacts in the Integer Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Sahasrabudhe, Harshad; Fallahi, Saeed; Nakamura, James; Povolotskyi, Michael; Novakovic, Bozidar; Rahman, Rajib; Manfra, Michael; Klimeck, Gerhard

Quantum Point Contacts (QPCs) are extensively used in semiconductor devices for charge sensing, tunneling and interference experiments. Fabry-Pérot interferometers containing 2 QPCs have applications in quantum computing, in which electrons/quasi-particles undergo interference due to back-scattering from the QPCs. Such experiments have turned out to be difficult because of the complex structure of edge states near the QPC boundary. We present realistic simulations of the edge states in QPCs based on GaAs/AlGaAs heterostructures, which can be used to predict conductance and edge state velocities. Conduction band profile is obtained by solving decoupled effective mass Schrödinger and Poisson equations self-consistently on a finite element mesh of a realistic geometry. In the integer quantum Hall regime, we obtain compressible and in-compressible regions near the edges. We then use the recursive Green`s function algorithm to solve Schrödinger equation with open boundary conditions for calculating transmission and local current density in the QPCs. Impurities are treated by inserting bumps in the potential with a Gaussian distribution. We compare observables with experiments for fitting some adjustable parameters. The authors would like to thank Purdue Research Foundation and Purdue Center for Topological Materials for their support.

How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?

PubMed Central

Gelens, Lendert; Huang, Kerwyn Casey; Ferrell, James E.

2015-01-01

Summary Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume, and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration, and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells. PMID:26212326

Thermal diffusivity and chaos in metals without quasiparticles

NASA Astrophysics Data System (ADS)

Blake, Mike; Davison, Richard A.; Sachdev, Subir

2017-11-01

We study the thermal diffusivity DT in models of metals without quasiparticle excitations ("strange metals"). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infrared fixed points DT is always related to parameters characterizing many-body quantum chaos: the butterfly velocity vB and Lyapunov time τL through DT˜vB2τL. The relationship holds independently of the charge density, periodic potential strength, or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime and is otherwise insensitive to the profile of any matter fields.

Leakage of The Quantum Dot Hybrid Qubit in The Strong Driving Regime

NASA Astrophysics Data System (ADS)

Yang, Yuan-Chi; Friesen, Mark; Coppersmith, S. N.

Recent experimental demonstrations of high-fidelity single-qubit gates suggest that the quantum dot hybrid qubit is a promising candidate for large-scale quantum computing. The qubit is comprised of three electrons in a double quantum dot, and can be protected from charge noise by operating in an extended sweet-spot regime. Gate operations are based on exchange interactions mediated by an excited state. However, strong resonant driving causes unwanted leakage into the excited state. Here, we theoretically analyze leakage caused by strong driving, and explore methods for increasing gate fidelities. This work was supported in part by ARO (W911NF-12-0607), NSF (PHY-1104660), ONR (N00014-15-1-0029), and the University of Wisconsin-Madison.

Quantum resource theory of non-stabilizer states in the one-shot regime

NASA Astrophysics Data System (ADS)

Ahmadi, Mehdi; Dang, Hoan; Gour, Gilad; Sanders, Barry

Universal quantum computing is known to be impossible using only stabilizer states and stabilizer operations. However, addition of non-stabilizer states (also known as magic states) to quantum circuits enables us to achieve universality. The resource theory of non-stablizer states aims at quantifying the usefulness of non-stabilizer states. Here, we focus on a fundamental question in this resource theory in the so called single-shot regime: Given two resource states, is there a free quantum channel that will (approximately or exactly) convert one to the other?. To provide an answer, we phrase the question as a semidefinite program with constraints on the Choi matrix of the corresponding channel. Then, we use the semidefinite version of the Farkas lemma to derive the necessary and sufficient conditions for the conversion between two arbitrary resource states via a free quantum channel. BCS appreciates financial support from Alberta Innovates, NSERC, China's 1000 Talent Plan and the Institute for Quantum Information and Matter.

Chaos in nuclei: Theory and experiment

NASA Astrophysics Data System (ADS)

Muñoz, L.; Molina, R. A.; Gómez, J. M. G.

2018-05-01

During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.

Laser-induced polarization of a quantum spin system in the steady-state regime

NASA Astrophysics Data System (ADS)

Zvyagin, A. A.

2016-05-01

The effect of the circularly polarized laser field on quantum spin systems in the steady-state regime, in which relaxation plays the central role, has been studied. The dynamical mean-field-like theory predicts several general results for the behavior of the time-average magnetization caused by the laser field. The induced magnetization oscillates with the frequency of the laser field (while Rabi-like oscillations, which modulate the latter in the dynamical regime, are damped by the relaxation in the steady-state regime). At high frequencies, that magnetization is determined by the value to which the relaxation process is directed. At low frequencies the slope of that magnetization as a function of the frequency is determined by the strength of the laser field. The anisotropy determines the resonance behavior of the time-averaged magnetization in both the ferromagnetic and antiferromagnetic cases with nonzero magnetic anisotropy. Nonlinear effects (in the magnitude of the laser field) have been considered. The effect of the laser field on quantum spin systems is maximal in resonance, where the time-averaged magnetization, caused by the laser field, is changed essentially. Out of resonance the changes in the magnetization are relatively small. The resonance effect is caused by the nonzero magnetic anisotropy. The resonance frequency is small (proportional to the anisotropy value) for spin systems with ferromagnetic interactions and enhanced by exchange interactions in the spin systems with antiferromagnetic couplings. We show that it is worthwhile to study the laser-field-induced magnetization of quantum spin systems caused by the high-frequency laser field in the steady-state regime in "easy-axis" antiferromagnetic spin systems (e.g., in Ising-like antiferromagnetic spin-chain materials). The effects of the Dzyaloshinskii-Moriya interaction and the spin-frustration couplings (in the case of the zigzag spin chain) have been analyzed.

Extended linear regime of cavity-QED enhanced optical circular birefringence induced by a charged quantum dot

NASA Astrophysics Data System (ADS)

Hu, C. Y.; Rarity, J. G.

2015-02-01

Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al., Phys. Rev. B 78, 085307 (2008), 10.1103/PhysRevB.78.085307; Hu et al., Phys. Rev. B 80, 205326 (2009), 10.1103/PhysRevB.80.205326]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [Tan, J. Opt. B 1, 424 (1999), 10.1088/1464-4266/1/4/312]. We find that the GFR and GCB around the cavity resonance in the strong-coupling regime are input field independent at intermediate powers and can be well described by the semiclassical approximation. Those associated with the dressed state resonances in the strong-coupling regime or merging with the cavity resonance in the Purcell regime are sensitive to input field at intermediate powers, and cannot be well described by the semiclassical approximation due to the quantum-dot saturation. As the GFR and GCB around the cavity resonance are relatively immune to the saturation effects, the rapid readout of single-electron spins can be carried out with coherent state and other statistically fluctuating light fields. This also shows that high-speed quantum entangling gates, robust against input power variations, can be built exploiting these linear effects.

Multimode Regimes in Quantum Cascade Lasers: From Coherent Instabilities to Spatial Hole Burning

DTIC Science & Technology

2009-02-10

from which absorption can take place; and although not very significant, there is always bulk n2 of the material. 1 A. E. Siegman , Lasers ...2007 4. TI11.E AND SUBTITI..E 5a. CONTRACT NUMBER Multimode regimes in quantum cascade lasers : from coherent W91INF-04-I-0253 instabilities to spatial...quantum cascade lasers (QCLs). In narrow devices it is found that above a second threshold the laser spectrwn dramatically broadens showing multimode

Bias voltage dependence of the electron spin depolarization in quantum wires in the quantum Hall regime detected by the resistively detected NMR

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

Chida, K.; Yamauchi, Y.; Arakawa, T.

2013-12-04

We performed the resistively-detected nuclear magnetic resonance (RDNMR) to study the electron spin polarization in the non-equilibrium quantum Hall regime. By measuring the Knight shift, we derive source-drain bias voltage dependence of the electron spin polarization in quantum wires. The electron spin polarization shows minimum value around the threshold voltage of the dynamic nuclear polarization.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

NASA Astrophysics Data System (ADS)

Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.; Balaz, Antun

2016-03-01

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

PubMed Central

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

Long-lasting quantum memories: Extending the coherence time of superconducting artificial atoms in the ultrastrong-coupling regime

NASA Astrophysics Data System (ADS)

Stassi, Roberto; Nori, Franco

2018-03-01

Quantum systems are affected by interactions with their environments, causing decoherence through two processes: pure dephasing and energy relaxation. For quantum information processing it is important to increase the coherence time of Josephson qubits and other artificial two-level atoms. We show theoretically that if the coupling between these qubits and a cavity field is longitudinal and in the ultrastrong-coupling regime, the system is strongly protected against relaxation. Vice versa, if the coupling is transverse and in the ultrastrong-coupling regime, the system is protected against pure dephasing. Taking advantage of the relaxation suppression, we show that it is possible to enhance their coherence time and use these qubits as quantum memories. Indeed, to preserve the coherence from pure dephasing, we prove that it is possible to apply dynamical decoupling. We also use an auxiliary atomic level to store and retrieve quantum information.

Discovery of Dozy Chaos and Discovery of Quanta: Analogy Being in Science and Perhaps in Human Progress

NASA Astrophysics Data System (ADS)

Egorov, Vladimir V.

The concept of a dozy chaos in the theory of quantum transitions and its applications are discussed in a historical context. Conjectured that dozy chaos is of primary importance to the dynamic self-organization of any living organism and concentrated in its brain. A hypothesis of the physical origin of cancer is put forward. Surmised that dozy chaos is the physical origin of life and driving force of its evolution.

Transition to Chaos in Random Neuronal Networks

NASA Astrophysics Data System (ADS)

Kadmon, Jonathan; Sompolinsky, Haim

2015-10-01

Firing patterns in the central nervous system often exhibit strong temporal irregularity and considerable heterogeneity in time-averaged response properties. Previous studies suggested that these properties are the outcome of the intrinsic chaotic dynamics of the neural circuits. Indeed, simplified rate-based neuronal networks with synaptic connections drawn from Gaussian distribution and sigmoidal nonlinearity are known to exhibit chaotic dynamics when the synaptic gain (i.e., connection variance) is sufficiently large. In the limit of an infinitely large network, there is a sharp transition from a fixed point to chaos, as the synaptic gain reaches a critical value. Near the onset, chaotic fluctuations are slow, analogous to the ubiquitous, slow irregular fluctuations observed in the firing rates of many cortical circuits. However, the existence of a transition from a fixed point to chaos in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work, we investigate rate-based dynamics of neuronal circuits composed of several subpopulations with randomly diluted connections. Nonzero connections are either positive for excitatory neurons or negative for inhibitory ones, while single neuron output is strictly positive with output rates rising as a power law above threshold, in line with known constraints in many biological systems. Using dynamic mean field theory, we find the phase diagram depicting the regimes of stable fixed-point, unstable-dynamic, and chaotic-rate fluctuations. We focus on the latter and characterize the properties of systems near this transition. We show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as the single population with Gaussian connectivity. In these architectures, the large mean excitatory and inhibitory inputs dynamically balance each other, amplifying the effect of the residual fluctuations. Importantly, the existence of a transition to chaos

The quantum N-body problem in the mean-field and semiclassical regime

NASA Astrophysics Data System (ADS)

Golse, François

2018-04-01

The present work discusses the mean-field limit for the quantum N-body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti. This article is part of the themed issue `Hilbert's sixth problem'.

Adaptive Schools in a Quantum Universe.

ERIC Educational Resources Information Center

Garmston, Robert; Wellman, Bruce

1995-01-01

Information from quantum mechanics, chaos theory, fractal geometry, and the new biology can help educators rethink school-improvement approaches. Chaos and order exist simultaneously. Adaptability, the central operating principle of successful organizations, stems from five human energy fields: efficacy, flexibility, craftsmanship, consciousness,…

Cavity Quantum Acoustic Device in the Multimode Strong Coupling Regime

NASA Astrophysics Data System (ADS)

Moores, Bradley A.; Sletten, Lucas R.; Viennot, Jeremie J.; Lehnert, K. W.

2018-06-01

We demonstrate an acoustical analog of a circuit quantum electrodynamics system that leverages acoustic properties to enable strong multimode coupling in the dispersive regime while suppressing spontaneous emission to unconfined modes. Specifically, we fabricate and characterize a device that comprises a flux tunable transmon coupled to a 300 μ m long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches 6.5 MHz, exceeding the cavity loss rate (200 kHz), qubit linewidth (1.1 MHz), and the cavity free spectral range (4.8 MHz), placing the device in both the strong coupling and strong multimode regimes. With the qubit detuned from the confined modes of the cavity, we observe that the qubit linewidth strongly depends on its frequency, as expected for spontaneous emission of phonons, and we identify operating frequencies where this emission rate is suppressed.

Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

PubMed

Wang, Hongli; Ouyang, Qi

2007-11-23

The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons

NASA Astrophysics Data System (ADS)

Scammell, H. D.; Sushkov, O. P.

2017-01-01

Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.

Localization-delocalization transition in a system of quantum kicked rotors.

PubMed

Creffield, C E; Hur, G; Monteiro, T S

2006-01-20

The quantum dynamics of atoms subjected to pairs of closely spaced delta kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single delta-kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power L approximately h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation summation2(L) approximately or equal to chi(L) approximately 1/2 (1-nu)L, where nu approximately 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximately 0.75 exponent is analyzed.

Local quenches and quantum chaos from higher spin perturbations

NASA Astrophysics Data System (ADS)

David, Justin R.; Khetrapal, Surbhi; Kumar, S. Prem

2017-10-01

We study local quenches in 1+1 dimensional conformal field theories at large- c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ back-ground, we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as | q| /c < E 2 /c 2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two-sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4 π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity.

Cavity Quantum Acoustic Device in the Multimode Strong Coupling Regime.

PubMed

Moores, Bradley A; Sletten, Lucas R; Viennot, Jeremie J; Lehnert, K W

2018-06-01

We demonstrate an acoustical analog of a circuit quantum electrodynamics system that leverages acoustic properties to enable strong multimode coupling in the dispersive regime while suppressing spontaneous emission to unconfined modes. Specifically, we fabricate and characterize a device that comprises a flux tunable transmon coupled to a 300  μm long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches 6.5 MHz, exceeding the cavity loss rate (200 kHz), qubit linewidth (1.1 MHz), and the cavity free spectral range (4.8 MHz), placing the device in both the strong coupling and strong multimode regimes. With the qubit detuned from the confined modes of the cavity, we observe that the qubit linewidth strongly depends on its frequency, as expected for spontaneous emission of phonons, and we identify operating frequencies where this emission rate is suppressed.

Route to chaos in porous-medium thermal convection

NASA Astrophysics Data System (ADS)

Kimura, S.; Schubert, G.; Straus, J. M.

1986-05-01

The transition to chaos in two-dimensional single-cell time-dependent convection in a square cross section of porous material saturated with fluid and heated from below is investigated theoretically by means of pseudospectral numerical simulations. The results are presented graphically and discussed in terms of the time-averaged Nusselt number, the oscillation mechanism, and similarities to Hele-Shaw convection. As the Rayleigh number (R) increases, the system is found to proceed from the steady state to a simply periodic state, a quasi-periodic state with two basic frequencies, a second simply periodic state, and finally to chaos. The transitions occur at R = 4 pi squared, 380-400, 500-520, 560-570, and 850-1000. The intermediate and chaotic regimes are characterized in detail.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Regimes of external optical feedback in 5.6 μm distributed feedback mid-infrared quantum cascade lasers

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

Jumpertz, L., E-mail: louise.jumpertz@telecom-paristech.fr; Alcatel Thales III-V Lab, Campus de Polytechnique, 1 avenue Augustin Fresnel, 91767 Palaiseau; Carras, M.

2014-09-29

External optical feedback is studied experimentally in mid-infrared quantum cascade lasers. These structures exhibit a dynamical response close to that observed in interband lasers, with threshold reduction and optical power enhancement when increasing the feedback ratio. The study of the optical spectrum proves that the laser undergoes five distinct regimes depending on the phase and amplitude of the reinjected field. These regimes are mapped in the plane of external cavity length and feedback strength, revealing unstable behavior only for a very narrow range of operation, making quantum cascade lasers much more stable than their interband counterparts.

Characterization of Carrier Transport Properties in Strained Crystalline Si Wall-Like Structures as a Function of Scaling into the Quasi-Quantum Regime

DTIC Science & Technology

2017-05-03

AS A FUNCTION OF SCALING INTO THE QUASI -QUANTUM REGIME Naz Islam University of Missouri Electrical and Computer Engineering 319 Engineering...Carrier Transport Properties in Strained Crystalline Si Wall-Like Structures as a Function of Scaling into the Quasi -Quantum Regime 5b. GRANT NUMBER...curves) and their comparisons with experimental data (black dots in both panels......................................... 16 Approved for public

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

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

Khomitsky, D. V., E-mail: khomitsky@phys.unn.ru; Chubanov, A. A.; Konakov, A. A.

2016-12-15

The dynamics of Dirac–Weyl spin-polarized wavepackets driven by a periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of the two-dimensional HgTe/CdTe topological insulator with Dirac–Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It is observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics in both coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within themore » quasiclassical approach by means of the Ince–Strutt diagram for the Mathieu equation, and is supported by full quantum-mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics, which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We find that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in the fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spindependent phenomena in nanostructures based on topological insulators.« less

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

NASA Astrophysics Data System (ADS)

Khomitsky, D. V.; Chubanov, A. A.; Konakov, A. A.

2016-12-01

The dynamics of Dirac-Weyl spin-polarized wavepackets driven by a periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of the two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It is observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics in both coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince-Strutt diagram for the Mathieu equation, and is supported by full quantum-mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics, which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We find that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in the fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spindependent phenomena in nanostructures based on topological insulators.

Neutral line chaos and phase space structure

NASA Technical Reports Server (NTRS)

Burkhart, Grant R.; Speiser, Theodore W.; Martin, Richard F., Jr.; Dusenbery, Paul B.

1991-01-01

Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.

Deterministic chaos in entangled eigenstates

NASA Astrophysics Data System (ADS)

Schlegel, K. G.; Förster, S.

2008-05-01

We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

Admittance measurements in the quantum Hall effect regime

NASA Astrophysics Data System (ADS)

Hernández, C.; Consejo, C.; Chaubet, C.

2014-11-01

In this work we present an admittance study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. We have studied several Hall bars in different contacts configurations in the frequency range 100 Hz-1 MHz. Our interpretation is based on the Landauer-Büttiker theory and takes into account both the capacitance and the topology of the coaxial cables which are connected to the sample holder. We show that we always observe losses through the capacitive impedance of the coaxial cables, except in the two contacts configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the 2DEG and show its dependence with the filling factor ν.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

NASA Astrophysics Data System (ADS)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

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.

Chaos and Cryptography: A new dimension in secure communications

NASA Astrophysics Data System (ADS)

Banerjee, Santo; Kurths, J.

2014-06-01

This issue is a collection of contributions on recent developments and achievements of cryptography and communications using chaos. The various contributions report important and promising results such as synchronization of networks and data transmissions; image cipher; optical and TDMA communications, quantum keys etc. Various experiments and applications such as FPGA, smartphone cipher, semiconductor lasers etc, are also included.

Chaos-assisted tunneling in the presence of Anderson localization.

PubMed

Doggen, Elmer V H; Georgeot, Bertrand; Lemarié, Gabriel

2017-10-01

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case, for both a deterministic and a disordered model. We develop a single-parameter scaling description which accurately describes the numerical data. Several possible experimental implementations using cold atoms, photonic lattices, or microwave billiards are discussed.

Semi-Poisson statistics in quantum chaos.

PubMed

García-García, Antonio M; Wang, Jiao

2006-03-01

We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques.

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

NASA Astrophysics Data System (ADS)

Shul'ga, N. F.; Syshchenko, V. V.; Tarnovsky, A. I.; Solovyev, I. I.; Isupov, A. Yu.

2018-01-01

The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed.

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Magnetic chaos healing in the helical reversed-field pinch: indications from the volume-preserving field line tracing code NEMATO

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Veranda, M.; Cappello, S.; Chacón, L.; Spizzo, G.

2010-11-01

The emergence of a self-organized reversed-field pinch (RFP) helical regime, first shown by 3D MHD numerical simulations, has been highlighted in the RFX-mod experiment at high current operation (IP above 1 MA). In fact, a quasi-stationary helical configuration spontaneously appears, characterized by strong internal electron transport barriers. In such regime electron temperature and density become, to a very good approximation, functions of the helical flux coordinate related to the dominant helical magnetic component. In addition, this regime is diagnosed to be associated with the topological transition to a single-helical-axis (SHAx) state, achieved after the expulsion of the separatrix of the dominant mode's magnetic island. The SHAx state is theoretically predicted to be resilient to the magnetic chaos induced by secondary modes. In this paper, we present initial results of the volume-preserving field line tracing code NEMATO [Finn J M and Chacón L 2005 Phys. Plasmas 12 054503] applied to study the magnetic topology resulting from 3D MHD simulations of the RFP. First, a successful 2D verification test of the code is shown, then, initial application to a systematic study of chaos healing in the helical RFP is discussed. The separatrix disappearance is confirmed to play an essential role for chaos healing. The triggering effect of a reversed magnetic shear for the formation of ordered surfaces within magnetic chaos is also diagnosed.

Magnetic chaos healing in hte helical reversed-field pinch: indications from the volume-preserving field line tracing code NEMATO

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

Bonfiglio, Daniele; Veranda, M.; Cappello, Susanna

2010-01-01

The emergence of a self-organized reversed-field pinch (RFP) helical regime, first shown by 3D MHD numerical simulations, has been highlighted in the RFX-mod experiment at high current operation (IP above 1 MA). In fact, a quasi-stationary helical configuration spontaneously appears, characterized by strong internal electron transport barriers. In such regime electron temperature and density become, to a very good approximation, functions of the helical flux coordinate related to the dominant helical magnetic component. In addition, this regime is diagnosed to be associated with the topological transition to a single-helical-axis (SHAx) state, achieved after the expulsion of the separatrix of themore » dominant mode's magnetic island. The SHAx state is theoretically predicted to be resilient to the magnetic chaos induced by secondary modes. In this paper, we present initial results of the volume-preserving field line tracing code nemato [Finn J M and Chacon L 2005 Phys. Plasmas 12 054503] applied to study the magnetic topology resulting from 3D MHD simulations of the RFP. First, a successful 2D verification test of the code is shown, then, initial application to a systematic study of chaos healing in the helical RFP is discussed. The separatrix disappearance is confirmed to play an essential role for chaos healing. The triggering effect of a reversed magnetic shear for the formation of ordered surfaces within magnetic chaos is also diagnosed.« less

Chaos and Chaos Control of the Frenkel-Kontorova Model with Dichotomous Noise

NASA Astrophysics Data System (ADS)

Lei, Youming; Zheng, Fan; Shao, Xizhen

Chaos and chaos control of the Frenkel-Kontorova (FK) model with dichotomous noise are studied theoretically and numerically. The threshold conditions for the onset of chaos in the FK model are firstly derived by applying the random Melnikov method with a mean-square criterion to the soliton equation, which is a fundamental topological mode of the FK model and accounts for its nonlinear phenomena. We found that dichotomous noise can induce stochastic chaos in the FK model, and the threshold of noise amplitude for the onset of chaos increases with the increase of its transition rate. Then the analytical criterion of chaos control is obtained by means of the time-delay feedback method. Since the time-delay feedback control raises the threshold of noise amplitude for the onset of chaos, chaos in the FK model is effectively suppressed. Through numerical simulations including the mean top Lyapunov exponent and the safe basin, we demonstrate the validity of the analytical predictions of chaos. Furthermore, time histories and phase portraits are utilized to verify the effectiveness of the proposed control.

Crossover to the anomalous quantum regime in the extrinsic spin Hall effect of graphene

NASA Astrophysics Data System (ADS)

Ferreira, Aires; Milletari, Mirco

Recent reports of spin-orbit coupling enhancement in chemically modified graphene have opened doors to studies of the spin Hall effect with massless chiral fermions. Here, we theoretically investigate the interaction and impurity density dependence of the extrinsic spin Hall effect in spin-orbit coupled graphene. We present a nonperturbative quantum diagrammatic calculation of the spin Hall response function in the strong-coupling regime that incorporates skew scattering and anomalous impurity density-independent contributions on equal footing. The spin Hall conductivity dependence on Fermi energy and electron-impurity interaction strength reveals the existence of experimentally accessible regions where anomalous quantum processes dominate. Our findings suggest that spin-orbit-coupled graphene is an ideal model system for probing the competition between semiclassical and bona fide quantum scattering mechanisms underlying the spin Hall effect. A.F. gratefully acknowledges the financial support of the Royal Society (U.K.).

Chaos and Localization in Dieterich-Ruina Friction

NASA Astrophysics Data System (ADS)

Erickson, B. A.; Birnir, B.; Lavallee, D.

2009-12-01

We consider two models derived from a 1-D Burridge-Knopoff chain of spring connected blocks subject to the Dieterich-Ruina (D-R) friction law. We analyze both the discrete ordinary differential equations, as well as the continuum model. Preliminary investigation into the ODEs shows evidence of the Dieterich-Ruina law exhibiting chaos, dependent on the size of the system. Periodic behavior occurs when considering chains of 3 or 5 blocks, while a chain of 10 blocks with the same parameter values results in chaotic motion. The continuum model (PDE) undergoes a transition to chaos when a specific parameter is increased and the chaotic regime is reached for smaller critical values than in the case of a single block (see Erickson et. al. 2008). This parameter, epsilon is the ratio of the stress parameters (B-A) and A in the D-R friction law. The parameter A is a measure of the direct velocity dependence (sometimes called the "direct effect") while (A-B) is a measure of the steady-state velocity dependence. When compared to the slip weakening friction law, the parameter (B-A) plays a role of a stress drop while A corresponds to the strength excess. In the case of a single block, transitions to chaos occur when epsilon = 11, a value too high for applications in seismology. For the continuum model however, the chaotic regime is reached for epsilon = 1. That the transition to chaos ensues for smaller parameter values than in the case of a single block may also be an indication that a careful rescaling of the friction law is necessary, similar to the conclusions made by Schmittbuhl et. al. (1996) who studied a "hierarchical array of blocks" and found that velocity weakening friction was scale dependent. We also observe solutions to both the discrete and the continuous model where the slip remains localized in space, suggesting the presence of solitonic behavior. Initial data in the form of a gaussian pulse tends to remain localized under certain parameter values and we

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Chaos, Complexity and Deterrence

DTIC Science & Technology

2000-04-19

populations of adversary countries but which seldom affect their leadership . Conclusion The jury is still out on the applicability of chaos theory to...Advent of Chaos Chaos theory in the West (considerable work on chaos was also conducted in the Soviet Union) developed from the 1960s work of...predicted by his model over time.1 This discovery, sensitivity to initial conditions, is one of the fundamental characteristics of chaos theory . Lorenz

Quasibound states in a triple Gaussian potential

NASA Astrophysics Data System (ADS)

Reichl, L. E.; Porter, Max D.

2018-04-01

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos. We also derive an exact expression for the non-Hermitian Hamiltonian whose eigenvalues give quasibound state energies and lifetimes of the system.

Nitrite-Oxidizing Bacteria Community Composition and Diversity Are Influenced by Fertilizer Regimes, but Are Independent of the Soil Aggregate in Acidic Subtropical Red Soil.

PubMed

Han, Shun; Li, Xiang; Luo, Xuesong; Wen, Shilin; Chen, Wenli; Huang, Qiaoyun

2018-01-01

Nitrification is the two-step aerobic oxidation of ammonia to nitrate via nitrite in the nitrogen-cycle on earth. However, very limited information is available on how fertilizer regimes affect the distribution of nitrite oxidizers, which are involved in the second step of nitrification, across aggregate size classes in soil. In this study, the community compositions of nitrite oxidizers ( Nitrobacter and Nitrospira ) were characterized from a red soil amended with four types of fertilizer regimes over a 26-year fertilization experiment, including control without fertilizer (CK), swine manure (M), chemical fertilization (NPK), and chemical/organic combined fertilization (MNPK). Our results showed that the addition of M and NPK significantly decreased Nitrobacter Shannon and Chao1 index, while M and MNPK remarkably increased Nitrospira Shannon and Chao1 index, and NPK considerably decreased Nitrospira Shannon and Chao1 index, with the greatest diversity achieved in soils amended with MNPK. However, the soil aggregate fractions had no impact on that alpha-diversity of Nitrobacter and Nitrospira under the fertilizer treatment. Soil carbon, nitrogen and phosphorus in the soil had a significant correlation with Nitrospira Shannon and Chao1 diversity index, while total potassium only had a significant correlation with Nitrospira Shannon diversity index. However, all of them had no significant correlation with Nitrobacter Shannon and Chao1 diversity index. The resistance indices for alpha-diversity indexes (Shannon and Chao1) of Nitrobacter were higher than those of Nitrospira in response to the fertilization regimes. Manure fertilizer is important in enhancing the Nitrospira Shannon and Chao1 index resistance. Principal co-ordinate analysis revealed that Nitrobacter - and Nitrospira -like NOB communities under four fertilizer regimes were differentiated from each other, but soil aggregate fractions had less effect on the nitrite oxidizers community. Redundancy analysis

Nitrite-Oxidizing Bacteria Community Composition and Diversity Are Influenced by Fertilizer Regimes, but Are Independent of the Soil Aggregate in Acidic Subtropical Red Soil

PubMed Central

Han, Shun; Li, Xiang; Luo, Xuesong; Wen, Shilin; Chen, Wenli; Huang, Qiaoyun

2018-01-01

Nitrification is the two-step aerobic oxidation of ammonia to nitrate via nitrite in the nitrogen-cycle on earth. However, very limited information is available on how fertilizer regimes affect the distribution of nitrite oxidizers, which are involved in the second step of nitrification, across aggregate size classes in soil. In this study, the community compositions of nitrite oxidizers (Nitrobacter and Nitrospira) were characterized from a red soil amended with four types of fertilizer regimes over a 26-year fertilization experiment, including control without fertilizer (CK), swine manure (M), chemical fertilization (NPK), and chemical/organic combined fertilization (MNPK). Our results showed that the addition of M and NPK significantly decreased Nitrobacter Shannon and Chao1 index, while M and MNPK remarkably increased Nitrospira Shannon and Chao1 index, and NPK considerably decreased Nitrospira Shannon and Chao1 index, with the greatest diversity achieved in soils amended with MNPK. However, the soil aggregate fractions had no impact on that alpha-diversity of Nitrobacter and Nitrospira under the fertilizer treatment. Soil carbon, nitrogen and phosphorus in the soil had a significant correlation with Nitrospira Shannon and Chao1 diversity index, while total potassium only had a significant correlation with Nitrospira Shannon diversity index. However, all of them had no significant correlation with Nitrobacter Shannon and Chao1 diversity index. The resistance indices for alpha-diversity indexes (Shannon and Chao1) of Nitrobacter were higher than those of Nitrospira in response to the fertilization regimes. Manure fertilizer is important in enhancing the Nitrospira Shannon and Chao1 index resistance. Principal co-ordinate analysis revealed that Nitrobacter- and Nitrospira-like NOB communities under four fertilizer regimes were differentiated from each other, but soil aggregate fractions had less effect on the nitrite oxidizers community. Redundancy analysis and

Embrace the Chaos

ERIC Educational Resources Information Center

Huwe, Terence K.

2009-01-01

"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…

rf Quantum Capacitance of the Topological Insulator Bi2Se3 in the Bulk Depleted Regime for Field-Effect Transistors

NASA Astrophysics Data System (ADS)

Inhofer, A.; Duffy, J.; Boukhicha, M.; Bocquillon, E.; Palomo, J.; Watanabe, K.; Taniguchi, T.; Estève, I.; Berroir, J. M.; Fève, G.; Plaçais, B.; Assaf, B. A.

2018-02-01

A metal-dielectric topological-insulator capacitor device based on hexagonal-boron-nitrate- (h -BN) encapsulated CVD-grown Bi2Se3 is realized and investigated in the radio-frequency regime. The rf quantum capacitance and device resistance are extracted for frequencies as high as 10 GHz and studied as a function of the applied gate voltage. The superior quality h -BN gate dielectric combined with the optimized transport characteristics of CVD-grown Bi2Se3 (n ˜1018 cm-3 in 8 nm) on h -BN allow us to attain a bulk depleted regime by dielectric gating. A quantum-capacitance minimum and a linear variation of the capacitance with the chemical potential are observed revealing a Dirac regime. The topological surface state in proximity to the gate is seen to reach charge neutrality, but the bottom surface state remains charged and capacitively coupled to the top via the insulating bulk. Our work paves the way toward implementation of topological materials in rf devices.

Relativistic Quantum Transport in Graphene Systems

DTIC Science & Technology

2015-07-09

which is desirable in the development of nanoscale devices such as graphene-based resonant- tunneling diodes . Details of this work can be found in • L... tunneling , etc. The AFOSR support helped create a new field of interdisciplinary research: Relativistic Quantum Chaos, which studies the relativistic quantum...Objectives 2 2 List of Publications 2 3 Accomplishments and New Findings 3 3.1 Solutions of Dirac equation, relativistic quantum tunneling and

Chaos in neurons and its application: perspective of chaos engineering.

PubMed

Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

2012-12-01

We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

PubMed

Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J

2013-06-01

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

A quantum Rosetta Stone for the information paradox

NASA Astrophysics Data System (ADS)

Pando Zayas, Leopoldo A.

2014-11-01

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

Chaos in Environmental Education.

ERIC Educational Resources Information Center

Hardy, Joy

1999-01-01

Explores chaos theory, the evolutionary capacity of chaotic systems, and the philosophical implications of chaos theory in general and for education. Compares the relationships between curriculum vision based on chaos theory and critical education for the environment. (Author/CCM)

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity.

PubMed

Choi, Daeyoung; Wishon, Michael J; Chang, C Y; Citrin, D S; Locquet, A

2018-01-01

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

Superpersistent Currents in Dirac Fermion Systems

DTIC Science & Technology

2017-03-06

development of quantum mechanics,, but also to quantum information processing and computing . Exploiting various physical systems to realize two-level...Here, using the QSD method, we calculated the dynamical trajectories of the system in the quantum regime. Our computations extending to the long time...currents in 2D Dirac material systems and pertinent phenomena in the emerging field of relativistic quantum nonlinear dynamics and chaos. Systematic

Squeezing Enhances Quantum Synchronization.

PubMed

Sonar, Sameer; Hajdušek, Michal; Mukherjee, Manas; Fazio, Rosario; Vedral, Vlatko; Vinjanampathy, Sai; Kwek, Leong-Chuan

2018-04-20

It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.

Squeezing Enhances Quantum Synchronization

NASA Astrophysics Data System (ADS)

Sonar, Sameer; Hajdušek, Michal; Mukherjee, Manas; Fazio, Rosario; Vedral, Vlatko; Vinjanampathy, Sai; Kwek, Leong-Chuan

2018-04-01

It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

NASA Astrophysics Data System (ADS)

Lv, Dingshun; An, Shuoming; Liu, Zhenyu; Zhang, Jing-Ning; Pedernales, Julen S.; Lamata, Lucas; Solano, Enrique; Kim, Kihwan

2018-04-01

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong-coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

PHYSICAL EFFECTS OCCURRING DURING GENERATION AND AMPLIFICATION OF LASER RADIATION: Dynamic chaos in a laser with a bleachable filter and dimensionality

NASA Astrophysics Data System (ADS)

Samson, A. M.; Kotomtseva, L. A.; Grigor'eva, E. V.

1989-02-01

A theoretical study of the dynamics of a laser with a bleachable filter revealed chaotic lasing regimes and ranges of bistable states of parameters close to those found in reality. It is shown how a transition to chaos occurs as a result of period-doubling bifurcation. A study is reported of the degree of chaos and of the structure of the resultant strange attractor by calculation of its fractal dimensionality and of the Lyapunov indices.

Scanned gate microscopy of inter-edge channel scattering in the quantum Hall regime

NASA Astrophysics Data System (ADS)

Woodside, Michael T.; Vale, Chris; McEuen, Paul L.; Kadow, C.; Maranowski, K. D.; Gossard, A. C.

2000-03-01

Novel scanned probe techniques have recently been used to study in detail the microscopic properties of 2D electron gases in the quantum Hall regime [1]. We report local measurements of the scattering between edge states in a quantum Hall conductor with non-equilibrium edge state populations. Using an atomic force microscope (AFM) tip as a local gate to perturb the edge states, we find that the scattering is dominated by individual, microscopic scattering sites, which we directly image and characterise. The dependence of the scattering on the AFM tip voltage reveals that it involves tunneling both through quasi-bound impurity states and through disorder-induced weak links between the edge states. [1] S. H. Tessmer et al., Nature 392, 51 (1998); K. L. McCormick et al., Phys. Rev. B 59, 4654 (1999); A. Yacoby et al., Solid State Comm. 111, 1 (1999).

How to couple identical ring oscillators to get quasiperiodicity, extended chaos, multistability, and the loss of symmetry

NASA Astrophysics Data System (ADS)

Hellen, Edward H.; Volkov, Evgeny

2018-09-01

We study the dynamical regimes demonstrated by a pair of identical 3-element ring oscillators (reduced version of synthetic 3-gene genetic Repressilator) coupled using the design of the 'quorum sensing (QS)' process natural for interbacterial communications. In this work QS is implemented as an additional network incorporating elements of the ring as both the source and the activation target of the fast diffusion QS signal. This version of indirect nonlinear coupling, in cooperation with the reasonable extension of the parameters which control properties of the isolated oscillators, exhibits the formation of a very rich array of attractors. Using a parameter-space defined by the individual oscillator amplitude and the coupling strength, we found the extended area of parameter-space where the identical oscillators demonstrate quasiperiodicity, which evolves to chaos via the period doubling of either resonant limit cycles or complex antiphase symmetric limit cycles with five winding numbers. The symmetric chaos extends over large parameter areas up to its loss of stability, followed by a system transition to an unexpected mode: an asymmetric limit cycle with a winding number of 1:2. In turn, after long evolution across the parameter-space, this cycle demonstrates a period doubling cascade which restores the symmetry of dynamics by formation of symmetric chaos, which nevertheless preserves the memory of the asymmetric limit cycles in the form of stochastic alternating "polarization" of the time series. All stable attractors coexist with some others, forming remarkable and complex multistability including the coexistence of torus and limit cycles, chaos and regular attractors, symmetric and asymmetric regimes. We traced the paths and bifurcations leading to all areas of chaos, and presented a detailed map of all transformations of the dynamics.

Quantum turing machine and brain model represented by Fock space

NASA Astrophysics Data System (ADS)

Iriyama, Satoshi; Ohya, Masanori

2016-05-01

The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.

Bounding the space of holographic CFTs with chaos

DOE PAGES

Perlmutter, Eric

2016-10-13

In this study, thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ L ≤ 2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ L = 2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge andmore » a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS 3 higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W ∞[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ L = 0. Independently, we show that such theories violate unitarity for |λ| > 2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.« less

Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Jo, Insun; Deng, Hao; Liu, Yang; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.

2018-01-01

We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled lowest Landau level, while the lower-density (bottom) layer forms a Wigner crystal (WC) as its filling becomes very small. Owing to the interlayer interaction, the CFs in the top layer feel the periodic Coulomb potential of the WC in the bottom layer. We measure the magnetoresistance of the top layer while changing the bottom-layer density. As the WC layer density increases, the resistance peaks separating the adjacent fractional quantum Hall states in the top layer change nonmonotonically and attain maximum values when the cyclotron orbit of the CFs encloses one WC lattice point. These features disappear at T =275 mK when the WC melts. The observation of such geometric resonance features is unprecedented and surprising as it implies that the CFs retain a well-defined cyclotron orbit and Fermi wave vector even deep in the fractional quantum Hall regime, far from half-filling.

Defining chaos.

PubMed

Hunt, Brian R; Ott, Edward

2015-09-01

In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

Qubit-flip-induced cavity mode squeezing in the strong dispersive regime of the quantum Rabi model

PubMed Central

Joshi, Chaitanya; Irish, Elinor K.; Spiller, Timothy P.

2017-01-01

Squeezed states of light are a set of nonclassical states in which the quantum fluctuations of one quadrature component are reduced below the standard quantum limit. With less noise than the best stabilised laser sources, squeezed light is a key resource in the field of quantum technologies and has already improved sensing capabilities in areas ranging from gravitational wave detection to biomedical applications. In this work we propose a novel technique for generating squeezed states of a confined light field strongly coupled to a two-level system, or qubit, in the dispersive regime. Utilising the dispersive energy shift caused by the interaction, control of the qubit state produces a time-dependent change in the frequency of the light field. An appropriately timed sequence of sudden frequency changes reduces the quantum noise fluctuations in one quadrature of the field well below the standard quantum limit. The degree of squeezing and the time of generation are directly controlled by the number of frequency shifts applied. Even in the presence of realistic noise and imperfections, our protocol promises to be capable of generating a useful degree of squeezing with present experimental capabilities. PMID:28358025

Nonlinear Dynamics and Chaos in Astrophysics: A Festschrift in Honor of George Contopoulos

NASA Astrophysics Data System (ADS)

Buchler, J. Robert; Gottesman, Stephen T.; Kandrup, Henry E.

1998-12-01

The annals of the New York Academy of Sciences is a compilation of work in the area of nonlinear dynamics and chaos in Astrophysics. Sections included are: From Quasars to Extraordinary N-body Problems; Dynamical Spectra and the Onset of Chaos; Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systems; Bifurcations of Periodic Orbits in Axisymmetric Scalefree Potentials; Irregular Period-Tripling Bifurcations in Axisymmetric Scalefree Potentials; Negative Energy Modes and Gravitational Instability of Interpenetrating Fluids; Invariants and Labels in Lie-Poisson Systems; From Jupiter's Great Red Spot to the Structure of Galaxies: Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems; N-Body Simulations of Galaxies and Groups of Galaxies with the Marseille GRAPE Systems; On Nonlinear Dynamics of Three-Dimensional Astrophysical Disks; Satellites as Probes of the Masses of Spiral Galaxies; Chaos in the Centers of Galaxies; Counterrotating Galaxies and Accretion Disks; Global Spiral Patterns in Galaxies: Complexity and Simplicity; Candidates for Abundance Gradients at Intermediate Red-Shift Clusters; Scaling Regimes in the Distribution of Galaxies; Recent Progress in the Study of One-Dimensional Gravitating Systems; Modeling the Time Variability of Black Hole Candidates; Stellar Oscillons; Chaos in Cosmological Hamiltonians; and Phase Space Transport in Noisy Hamiltonian Systems.

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

NASA Astrophysics Data System (ADS)

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond.

PubMed

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E G D

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

Regimes of turbulence without an energy cascade

PubMed Central

Barenghi, C. F.; Sergeev, Y. A.; Baggaley, A. W.

2016-01-01

Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics. PMID:27761005

Particle chaos and pitch angle scattering

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Dusenbery, P. B.; Speiser, T. W.

1995-01-01

Pitch angle scattering is a factor that helps determine the dawn-to-dusk current, controls particle energization, and it has also been used as a remote probe of the current sheet structure. Previous studies have interpreted their results under the exception that randomization will be greatest when the ratio of the two timescales of motion (gyration parallel to and perpendicular to the current sheet) is closet to one. Recently, the average expotential divergence rate (AEDR) has been calculated for particle motion in a hyperbolic current sheet (Chen, 1992). It is claimed that this AEDR measures the degree of chaos and therefore may be thought to measure the randomization. In contrast to previous expectations, the AEDR is not maximized when Kappa is approximately equal to 1 but instead increases with decreasing Kappa. Also contrary to previous expectations, the AEDR is dependent upon the parameter b(sub z). In response to the challenge to previous expectations that has been raised by this calculation of the AEDR, we have investigated the dependence of a measure of particle pitch angle scattering on both the parameters Kappa and b(sub z). We find that, as was previously expected, particle pitch angle scattering is maximized near Kappa = 1 provided that Kappa/b(sub z) greater than 1. In the opposite regime, Kappa/b(sub z) less than 1, we find that particle pitch angle scattering is still largest when the two timescales are equal, but the ratio of the timescales is proportional to b(sub z). In this second regime, particle pitch angle scattering is not due to randomization, but is instead due to a systematic pitch angle change. This result shows that particle pitch angle scattering need not be due to randomization and indicates how a measure of pitch angle scattering can exhibit a different behavior than a measure of chaos.

Topological chaos, braiding and bifurcation of almost-cyclic sets.

PubMed

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity.

PubMed

Cantrell, John H; Adler, Laszlo; Yost, William T

2015-02-01

Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.

Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain

NASA Astrophysics Data System (ADS)

Lin, Cheng-Ju; Motrunich, Olexei I.

2017-02-01

The eigenstate thermalization hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Bañuls, Cirac, and Hastings, Phys. Rev. Lett. 106, 050405 (2007), 10.1103/PhysRevLett.106.050405] of a nonintegrable quantum Ising model with longitudinal field under such a quench setting found different behaviors for different initial quantum states. One particular case called the "weak-thermalization" regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We note that the corresponding initial state has low energy density relative to the ground state of the model. We then use perturbation theory near the ground state and identify the oscillation frequency as essentially a quasiparticle gap. With this quasiparticle picture, we can then address the long-time behavior of the oscillations. Upon making additional approximations which intuitively should only make thermalization weaker, we argue that the oscillations nevertheless decay in the long-time limit. As part of our arguments, we also consider a quench from a BEC to a hard-core boson model in one dimension. We find that the expectation value of a single-boson creation operator oscillates but decays exponentially in time, while a pair-boson creation operator has oscillations with a t-3 /2 decay in time. We also study dependence of the decay time on the density of bosons in the low-density regime and use this to estimate decay time for oscillations in the original spin model.

Fine Grained Chaos in AdS2 Gravity

NASA Astrophysics Data System (ADS)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS_{2} Gravity.

PubMed

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Quantum internet using code division multiple access

PubMed Central

Zhang, Jing; Liu, Yu-xi; Özdemir, Şahin Kaya; Wu, Re-Bing; Gao, Feifei; Wang, Xiang-Bin; Yang, Lan; Nori, Franco

2013-01-01

A crucial open problem inS large-scale quantum networks is how to efficiently transmit quantum data among many pairs of users via a common data-transmission medium. We propose a solution by developing a quantum code division multiple access (q-CDMA) approach in which quantum information is chaotically encoded to spread its spectral content, and then decoded via chaos synchronization to separate different sender-receiver pairs. In comparison to other existing approaches, such as frequency division multiple access (FDMA), the proposed q-CDMA can greatly increase the information rates per channel used, especially for very noisy quantum channels. PMID:23860488

Chaos Modeling: An Introduction and Research Application.

ERIC Educational Resources Information Center

Newman, Isadore; And Others

1993-01-01

Introduces the basic concepts of chaos theory and chaos modeling. Relates chaos theory to qualitative research and factor analysis. Describes some current research in education and psychology using chaos theory. Claims that the philosophical implications of chaos theory have been misapplied in practical terms. (KS)

Quantum description of the high-order harmonic generation in multiphoton and tunneling regimes

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

Perez-Hernandez, J. A.; Plaja, L.

2007-08-15

We employ a recently developed S-matrix approach [L. Plaja and J. A. Perez-Hernandez, Opt. Express 15, 3629 (2007)] to investigate the process of harmonic generation in tunnel and multiphoton ionization regimes. In contrast with most of the previous approaches, this model is developed without the stationary phase approximation and including the relevant continuum-continuum transitions. Therefore, it provides a full quantum description of the harmonic generation process in these two ionization regimes, with a good quantitative accuracy with the exact results of the time-dependent Schroedinger equation. We show how this model can be used to investigate the contribution of the electronicmore » population ionized at different times, thus giving a time-resolved description that, up to now, was reserved only to semiclassical models. In addition, we will show some aspects of harmonic generation beyond the semiclassical predictions as, for instance, the emission of radiation while the electron is leaving the parent ion and the generation of harmonics in semiclassically forbidden situations.« less

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

NASA Astrophysics Data System (ADS)

Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella

2017-03-01

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

Scrambling of quantum information in quantum many-body systems

NASA Astrophysics Data System (ADS)

Iyoda, Eiki; Sagawa, Takahiro

2018-04-01

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Death and revival of chaos.

PubMed

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2016-12-01

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.

Noise tolerant spatiotemporal chaos computing.

PubMed

Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L

2014-12-01

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Noise tolerant spatiotemporal chaos computing

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

Kia, Behnam; Kia, Sarvenaz; Ditto, William L.

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Relativistic chaos is coordinate invariant.

PubMed

Motter, Adilson E

2003-12-05

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.

Method of controlling chaos in laser equations

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-01-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Emel'yanov, V. V.; Kuznetsov, S. P.; Ryskin, N. M.

2010-12-01

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.

Asynchronous Rate Chaos in Spiking Neuronal Circuits

PubMed Central

Harish, Omri; Hansel, David

2015-01-01

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679

Teaching as Chaos

ERIC Educational Resources Information Center

Moseley, Bryan; Dustin, Daniel

2008-01-01

In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Aram and Iani Chaos

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-344, 28 April 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image mosaic was constructed from data acquired by the MOC red wide angle camera. The large, circular feature in the upper left is Aram Chaos, an ancient impact crater filled with layered sedimentary rock that was later disrupted and eroded to form a blocky, 'chaotic' appearance. To the southeast of Aram Chaos, in the lower right of this picture, is Iani Chaos. The light-toned patches amid the large blocks of Iani Chaos are known from higher-resolution MOC images to be layered, sedimentary rock outcrops. The picture center is near 0.5oN, 20oW. Sunlight illuminates the scene from the left/upper left.

Quantum Bio-Informatics II From Quantum Information to Bio-Informatics

NASA Astrophysics Data System (ADS)

Accardi, L.; Freudenberg, Wolfgang; Ohya, Masanori

2009-02-01

The problem of quantum-like representation in economy cognitive science, and genetics / L. Accardi, A. Khrennikov and M. Ohya -- Chaotic behavior observed in linea dynamics / M. Asano, T. Yamamoto and Y. Togawa -- Complete m-level quantum teleportation based on Kossakowski-Ohya scheme / M. Asano, M. Ohya and Y. Tanaka -- Towards quantum cybernetics: optimal feedback control in quantum bio informatics / V. P. Belavkin -- Quantum entanglement and circulant states / D. Chruściński -- The compound Fock space and its application in brain models / K. -H. Fichtner and W. Freudenberg -- Characterisation of beam splitters / L. Fichtner and M. Gäbler -- Application of entropic chaos degree to a combined quantum baker's map / K. Inoue, M. Ohya and I. V. Volovich -- On quantum algorithm for multiple alignment of amino acid sequences / S. Iriyama and M. Ohya --Quantum-like models for decision making in psychology and cognitive science / A. Khrennikov -- On completely positive non-Markovian evolution of a d-level system / A. Kossakowski and R. Rebolledo -- Measures of entanglement - a Hilbert space approach / W. A. Majewski -- Some characterizations of PPT states and their relation / T. Matsuoka -- On the dynamics of entanglement and characterization ofentangling properties of quantum evolutions / M. Michalski -- Perspective from micro-macro duality - towards non-perturbative renormalization scheme / I. Ojima -- A simple symmetric algorithm using a likeness with Introns behavior in RNA sequences / M. Regoli -- Some aspects of quadratic generalized white noise functionals / Si Si and T. Hida -- Analysis of several social mobility data using measure of departure from symmetry / K. Tahata ... [et al.] -- Time in physics and life science / I. V. Volovich -- Note on entropies in quantum processes / N. Watanabe -- Basics of molecular simulation and its application to biomolecules / T. Ando and I. Yamato -- Theory of proton-induced superionic conduction in hydrogen-bonded systems

Chaos and noise.

PubMed

He, Temple; Habib, Salman

2013-09-01

Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.

Chaos in brake squeal noise

NASA Astrophysics Data System (ADS)

Oberst, S.; Lai, J. C. S.

2011-02-01

Brake squeal has become an increasing concern to the automotive industry because of warranty costs and the requirement for continued interior vehicle noise reduction. Most research has been directed to either analytical and experimental studies of brake squeal mechanisms or the prediction of brake squeal propensity using finite element methods. By comparison, there is a lack of systematic analysis of brake squeal data obtained from a noise dynamometer. It is well known that brake squeal is a nonlinear transient phenomenon and a number of studies using analytical and experimental models of brake systems (e.g., pin-on-disc) indicate that it could be treated as a chaotic phenomenon. Data obtained from a full brake system on a noise dynamometer were examined with nonlinear analysis techniques. The application of recurrence plots reveals chaotic structures even in noisy data from the squealing events. By separating the time series into different regimes, lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents. Further analysis of the recurrence plot of squealing events by means of recurrence quantification analysis measures reveals different regimes of laminar and random behaviour, periodicity and chaos-forming recurrent transitions. These results help to classify brake squeal mechanisms and to enhance understanding of friction-related noise phenomena.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

NASA Astrophysics Data System (ADS)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

"Chaos Rules" Revisited

ERIC Educational Resources Information Center

Murphy, David

2011-01-01

About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…

Application of laser chaos control methods to controlling thyroid-catatonic oscillations and burst firing of dopamine neurons

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-11-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang and Bau. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the lasers equations are isomorphic to the Lorenz equations, we use this new method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential lasers controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills and Hunt. This method of control chaos is now extended to various medical and biological systems.

Relations between distributional and Devaney chaos.

PubMed

Oprocha, Piotr

2006-09-01

Recently, it was proven that chaos in the sense of Devaney and weak mixing both imply chaos in the sense of Li and Yorke. In this article we give explicit examples that any of these two implications do not hold for distributional chaos.

Investigation of Supercurrent in the Quantum Hall Regime in Graphene Josephson Junctions

NASA Astrophysics Data System (ADS)

Draelos, Anne W.; Wei, Ming Tso; Seredinski, Andrew; Ke, Chung Ting; Mehta, Yash; Chamberlain, Russell; Watanabe, Kenji; Taniguchi, Takashi; Yamamoto, Michihisa; Tarucha, Seigo; Borzenets, Ivan V.; Amet, François; Finkelstein, Gleb

2018-06-01

In this study, we examine multiple encapsulated graphene Josephson junctions to determine which mechanisms may be responsible for the supercurrent observed in the quantum Hall (QH) regime. Rectangular junctions with various widths and lengths were studied to identify which parameters affect the occurrence of QH supercurrent. We also studied additional samples where the graphene region is extended beyond the contacts on one side, making that edge of the mesa significantly longer than the opposite edge. This is done in order to distinguish two potential mechanisms: (a) supercurrents independently flowing along both non-contacted edges of graphene mesa, and (b) opposite sides of the mesa being coupled by hybrid electron-hole modes flowing along the superconductor/graphene boundary. The supercurrent appears suppressed in extended junctions, suggesting the latter mechanism.

Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.

PubMed

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-05-22

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

3D pulsed chaos lidar system.

PubMed

Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi

2018-04-30

We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

NASA Astrophysics Data System (ADS)

Cook, Robert L.; Riofrío, Carlos A.; Deutsch, Ivan H.

2014-09-01

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a non-negligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem: state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal generalized measurement. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

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.

Finding Order and Direction from Chaos: A Comparison of Chaos Career Counseling and Trait Matching Counseling

ERIC Educational Resources Information Center

McKay, Hannah; Bright, Jim E. H.; Pryor, Robert G. L.

2005-01-01

Chaos career counseling, based on the Chaos Theory of Careers (R. G. L. Pryor & J. E. H. Bright, 2003a, 2003b), was compared with trait matching career counseling and a wait list control. Sixty university students who attended the Careers Research and Assessment Service seeking career advice were randomly assigned to the chaos intervention, the…

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.

Quantum algorithms for quantum field theories.

PubMed

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

Triggered dynamics in a model of different fault creep regimes

PubMed Central

Kostić, Srđan; Franović, Igor; Perc, Matjaž; Vasović, Nebojša; Todorović, Kristina

2014-01-01

The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic- or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale. PMID:24954397

The joy of transient chaos.

PubMed

Tél, Tamás

2015-09-01

We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.

Enhancement of the thermoelectric efficiency in a T-shaped quantum dot system in the linear and nonlinear regimes

NASA Astrophysics Data System (ADS)

Gómez-Silva, G.; Orellana, P. A.; Anda, E. V.

2018-02-01

In the present work, we investigate the thermoelectric properties of a T-shaped double quantum dot system coupled to two metallic leads incorporating the intra-dot Coulomb interaction. We explore the role of the interference effects and Coulomb blockade on the thermoelectric efficiency of the system in the linear and nonlinear regimes. We studied as well the effect of a Van-Hove singularity of the leads density of states (DOS) at the neighborhood of the Fermi energy, a situation that can be obtained using a carbon nanotube, a graphene nano-ribbon or other contacts with one-dimensional properties. The system is studied above the Kondo temperature. The Coulomb blockade of the electronic charges is studied using the Hubbard III approximation, which properly describes the transport properties of this regime. In the linear response, our results show an enhancement of the thermopower and the figure of merit of the system. For a nonlinear situation, we calculate the thermoelectric efficiency and power output, concluding that the T-shaped double quantum dot is an efficient thermoelectric device. Moreover, we demonstrate the great importance of the DOS Van-Hove singularity at the neighborhood of the Fermi energy to obtain a very significant increase in the thermoelectric efficiency of the system.

Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies

PubMed Central

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-01-01

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858

Magnetic field fluctuations analysis for the ion trap implementation of the quantum Rabi model in the deep strong coupling regime

NASA Astrophysics Data System (ADS)

Puebla, Ricardo; Casanova, Jorge; Plenio, Martin B.

2018-03-01

The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.

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.

Efficient quantum transmission in multiple-source networks.

PubMed

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-04-02

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency.

Experimental Induction of Genome Chaos.

PubMed

Ye, Christine J; Liu, Guo; Heng, Henry H

2018-01-01

Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.

Using chaos theory: the implications for nursing.

PubMed

Haigh, Carol

2002-03-01

The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.

Quantum and wave dynamical chaos in superconducting microwave billiards

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

Dietz, B., E-mail: dietz@ikp.tu-darmstadt.de; Richter, A., E-mail: richter@ikp.tu-darmstadt.de

2015-09-15

Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that weremore » performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.« less

Quantum and wave dynamical chaos in superconducting microwave billiards.

PubMed

Dietz, B; Richter, A

2015-09-01

Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.

Nonlinear quantum Rabi model in trapped ions

NASA Astrophysics Data System (ADS)

Cheng, Xiao-Hang; Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas; Chen, Xi; Solano, Enrique

2018-02-01

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.

Dynamical manifestations of quantum chaos

NASA Astrophysics Data System (ADS)

Torres Herrera, Eduardo Jonathan; Santos, Lea

2017-04-01

A main feature of a chaotic quantum system is a rigid spectrum, where the levels do not cross. Dynamical quantities, such as the von Neumann entanglement entropy, Shannon information entropy, and out-of-time correlators can differentiate the ergodic from the nonergodic phase in disordered interacting systems, but not level repulsion from level crossing in the delocalized phase of disordered and clean models. This is in contrast with the long-time evolution of the survival probability of the initial state. The onset of correlated energy levels is manifested by a drop, referred to as correlation hole, below the asymptotic value of the survival probability. The correlation hole is an unambiguous indicator of the presence of level repulsion. EJTH is grateful to VIEP, BUAP for financial support through the VIEP projects program.

Applications of quantum cloning

NASA Astrophysics Data System (ADS)

Pomarico, E.; Sanguinetti, B.; Sekatski, P.; Zbinden, H.; Gisin, N.

2011-10-01

Quantum Cloning Machines (QCMs) allow for the copying of information, within the limits imposed by quantum mechanics. These devices are particularly interesting in the high-gain regime, i.e., when one input qubit generates a state of many output qubits. In this regime, they allow for the study of certain aspects of the quantum to classical transition. The understanding of these aspects is the root of the two recent applications that we will review in this paper: the first one is the Quantum Cloning Radiometer, a device which is able to produce an absolute measure of spectral radiance. This device exploits the fact that in the quantum regime information can be copied with only finite fidelity, whereas when a state becomes macroscopic, this fidelity gradually increases to 1. Measuring the fidelity of the cloning operation then allows to precisely determine the absolute spectral radiance of the input optical source. We will then discuss whether a Quantum Cloning Machine could be used to produce a state visible by the naked human eye, and the possibility of a Bell Experiment with humans playing the role of detectors.

Jeans self gravitational instability of strongly coupled quantum plasma

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

Sharma, Prerana, E-mail: preranaiitd@rediffmail.com; Chhajlani, R. K.

2014-07-15

The Jeans self-gravitational instability is studied for quantum plasma composed of weakly coupled degenerate electron fluid and non-degenerate strongly coupled ion fluid. The formulation for such system is done on the basis of two fluid theory. The dynamics of weakly coupled degenerate electron fluid is governed by inertialess momentum equation. The quantum forces associated with the quantum diffraction effects and the quantum statistical effects act on the degenerate electron fluid. The strong correlation effects of ion are embedded in generalized viscoelastic momentum equation including the viscoelasticity and shear viscosities of ion fluid. The general dispersion relation is obtained using themore » normal mode analysis technique for the two regimes of propagation, i.e., hydrodynamic and kinetic regimes. The Jeans condition of self-gravitational instability is also obtained for both regimes, in the hydrodynamic regime it is observed to be affected by the ion plasma oscillations and quantum parameter while in the kinetic regime in addition to ion plasma oscillations and quantum parameter, it is also affected by the ion velocity which is modified by the viscosity generated compressional effects. The Jeans critical wave number and corresponding critical mass are also obtained for strongly coupled quantum plasma for both regimes.« less

Parameter regimes for a single sequential quantum repeater

NASA Astrophysics Data System (ADS)

Rozpędek, F.; Goodenough, K.; Ribeiro, J.; Kalb, N.; Caprara Vivoli, V.; Reiserer, A.; Hanson, R.; Wehner, S.; Elkouss, D.

2018-07-01

Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during the storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters.

Quantum resource theories in the single-shot regime

NASA Astrophysics Data System (ADS)

Gour, Gilad

2017-06-01

One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions that determine whether one resource can be converted to another by the set of free operations. Here we find such conditions for a large class of quantum resource theories which we call affine resource theories. Affine resource theories include the resource theories of athermality, asymmetry, and coherence, but not entanglement. Remarkably, the necessary and sufficient conditions can be expressed as a family of inequalities between resource monotones (quantifiers) that are given in terms of the conditional min-entropy. The set of free operations is taken to be (1) the maximal set (i.e., consists of all resource nongenerating quantum channels) or (2) the self-dual set of free operations (i.e., consists of all resource nongenerating maps for which the dual map is also resource nongenerating). As an example, we apply our results to quantum thermodynamics with Gibbs preserving operations, and several other affine resource theories. Finally, we discuss the applications of these results to resource theories that are not affine and, along the way, provide the necessary and sufficient conditions that a quantum resource theory consists of a resource destroying map.

One-way quantum repeaters with quantum Reed-Solomon codes

NASA Astrophysics Data System (ADS)

Muralidharan, Sreraman; Zou, Chang-Ling; Li, Linshu; Jiang, Liang

2018-05-01

We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of d -level systems for large dimension d . We study the performance of one-way quantum repeaters with these codes and obtain a significant improvement in key generation rate compared to previously investigated encoding schemes with quantum parity codes and quantum polynomial codes. We also compare the three generations of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.

Fractal Patterns and Chaos Games

ERIC Educational Resources Information Center

Devaney, Robert L.

2004-01-01

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

Reynolds number effects on mixing due to topological chaos

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

Smith, Spencer A.; Warrier, Sangeeta

2016-03-15

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for threemore » different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.« less

Reynolds number effects on mixing due to topological chaos.

PubMed

Smith, Spencer A; Warrier, Sangeeta

2016-03-01

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

Control of Synchronization Regimes in Networks of Mobile Interacting Agents

NASA Astrophysics Data System (ADS)

Perez-Diaz, Fernando; Zillmer, Ruediger; Groß, Roderich

2017-05-01

We investigate synchronization in a population of mobile pulse-coupled agents with a view towards implementations in swarm-robotics systems and mobile sensor networks. Previous theoretical approaches dealt with range and nearest-neighbor interactions. In the latter case, a synchronization-hindering regime for intermediate agent mobility is found. We investigate the robustness of this intermediate regime under practical scenarios. We show that synchronization in the intermediate regime can be predicted by means of a suitable metric of the phase response curve. Furthermore, we study more-realistic K -nearest-neighbor and cone-of-vision interactions, showing that it is possible to control the extent of the synchronization-hindering region by appropriately tuning the size of the neighborhood. To assess the effect of noise, we analyze the propagation of perturbations over the network and draw an analogy between the response in the hindering regime and stable chaos. Our findings reveal the conditions for the control of clock or activity synchronization of agents with intermediate mobility. In addition, the emergence of the intermediate regime is validated experimentally using a swarm of physical robots interacting with cone-of-vision interactions.

Efficient Quantum Transmission in Multiple-Source Networks

PubMed Central

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency. PMID:24691590

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Wiener Chaos and Nonlinear Filtering

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

Lototsky, S.V.

2006-11-15

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. Themore » paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.« less

Survival and weak chaos.

PubMed

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Survival and weak chaos

PubMed Central

2018-01-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as ‘infant mortality’. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality—sensu engineering—without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy. PMID:29892407

Mode Locking of Quantum Cascade Lasers

DTIC Science & Technology

2007-11-09

E. Siegman , Lasers , University Science Books, Mill Valley, CA (1986). [2] A. Yariv, Quantum Electronics, 3rd edition, John Wiley and Sons, New...REPORT Mode Locking of Quantum Cascade Lasers 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: A theoretical and experimental study of multimode operation...regimes in quantum cascade lasers (QCLs) is presented. It is shown that the fast gain recovery of QCLs promotes two multimode regimes in QCLs: One is

Genome chaos: survival strategy during crisis.

PubMed

Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H

2014-01-01

Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.

How to test for partially predictable chaos.

PubMed

Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

2017-04-24

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

Long distance quantum communication with quantum Reed-Solomon codes

NASA Astrophysics Data System (ADS)

Muralidharan, Sreraman; Zou, Chang-Ling; Li, Linshu; Jiang, Liang; Jianggroup Team

We study the construction of quantum Reed Solomon codes from classical Reed Solomon codes and show that they achieve the capacity of quantum erasure channel for multi-level quantum systems. We extend the application of quantum Reed Solomon codes to long distance quantum communication, investigate the local resource overhead needed for the functioning of one-way quantum repeaters with these codes, and numerically identify the parameter regime where these codes perform better than the known quantum polynomial codes and quantum parity codes . Finally, we discuss the implementation of these codes into time-bin photonic states of qubits and qudits respectively, and optimize the performance for one-way quantum repeaters.

Sensitivity to perturbations and quantum phase transitions.

PubMed

Wisniacki, D A; Roncaglia, A J

2013-05-01

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of N two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.

Control of generation regimes of ring chip laser under the action of the stationary magnetic field

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

Aulova, T V; Kravtsov, Nikolai V; Lariontsev, E G

2013-05-31

We consider realisation of different generation regimes in an autonomous ring chip laser, which is a rather complicated problem. We offer and demonstrate a simple and effective method for controlling the radiation dynamics of a ring Nd:YAG chip laser when it is subjected to a stationary magnetic field producing both frequency and substantial amplitude nonreciprocities. The amplitude and frequency nonreciprocities of a ring cavity, arising under the action of this magnetic field, change when the magnet is moved with respect to the active element of the chip laser. Some self-modulation and stationary generation regimes as well as the regime ofmore » beatings and dynamic chaos regime are experimentally realised. Temporal and spectral characteristics of radiation are studied and conditions for the appearance of the generation regime are found. (control of laser radiation parameters)« less

Defect chaos and bursts: hexagonal rotating convection and the complex Ginzburg-Landau equation.

PubMed

Madruga, Santiago; Riecke, Hermann; Pesch, Werner

2006-02-24

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non-Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscillations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Outcrops In Aram Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

16 October 2004 Aram Chaos is the name of an approximately 275 km (171 mi) diameter impact crater near Ares Vallis, roughly half way between the Mars Exploration Rover, Opportunity, site in Meridiani Planum and the easternmost troughs of the Valles Marineris. The Aram Chaos crater is partially filled with a thick accumulation of layered rock. Erosion has exposed light- and dark-toned rock materials in the basin. This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a small area exhibiting some of the rock outcrops in Aram Chaos. The light-toned rocks may be sedimentary in origin. This image is located near 4.0oN, 20.6oW, and covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.

Meaning Finds a Way: Chaos (Theory) and Composition

ERIC Educational Resources Information Center

Kyburz, Bonnie Lenore

2004-01-01

The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.

Testing quantum gravity

NASA Astrophysics Data System (ADS)

Hansson, Johan; Francois, Stephane

The search for a theory of quantum gravity is the most fundamental problem in all of theoretical physics, but there are as yet no experimental results at all to guide this endeavor. What seems to be needed is a pragmatic way to test if gravitation really occurs between quantum objects or not. In this paper, we suggest such a potential way out of this deadlock, utilizing macroscopic quantum systems; superfluid helium, gaseous Bose-Einstein condensates and “macroscopic” molecules. It turns out that true quantum gravity effects — here defined as observable gravitational interactions between truly quantum objects — could and should be seen (if they occur in nature) using existing technology. A falsification of the low-energy limit in the accessible weak-field regime would also falsify the full theory of quantum gravity, making it enter the realm of testable, potentially falsifiable theories, i.e. becoming real physics after almost a century of pure theorizing. If weak-field gravity between quantum objects is shown to be absent (in the regime where the approximation should apply), we know that gravity then is a strictly classical phenomenon absent at the quantum level.

Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Finocchiaro, F.; Guinea, F.; San-Jose, P.

2018-03-01

We consider a two-dimensional electron gas (2DEG) in the quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to a filling factor of ν =1 . We show that, in the presence of spin-orbit coupling, contacting the 2DEG with a narrow strip of an s -wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust π junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a configuration can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Controllable chaos in hybrid electro-optomechanical systems

PubMed Central

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-01-01

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505

Controllable chaos in hybrid electro-optomechanical systems.

PubMed

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-03-07

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.

Quantum cellular automata and free quantum field theory

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro; Perinotti, Paolo

2017-02-01

In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

Negative inductance SQUID qubit operating in a quantum regime

NASA Astrophysics Data System (ADS)

Liu, W. Y.; Su, F. F.; Xu, H. K.; Li, Z. Y.; Tian, Ye; Zhu, X. B.; Lu, Li; Han, Siyuan; Zhao, S. P.

2018-04-01

Two-junction SQUIDs with negative mutual inductance between their two arms, called nSQUIDs, have been proposed for significantly improving quantum information transfer but their quantum nature has not been experimentally demonstrated. We have designed, fabricated, and characterized superconducting nSQUID qubits. Our results provide clear evidence of the quantum coherence of the device, whose properties are well described by theoretical calculations using parameters determined from spectroscopic measurement. In addition to their future application for fast quantum information transfer, the nSQUID qubits exhibit rich characteristics in their tunable two-dimensional (2D) potentials, energy levels, wave function symmetries, and dipole matrix elements, which are essential to the study of a wide variety of macroscopic quantum phenomena such as tunneling in 2D potential landscapes.

Fab Four self-interaction in quantum regime

NASA Astrophysics Data System (ADS)

Arbuzov, A. B.; Latosh, B. N.

2017-10-01

Quantum behavior of the John Lagrangian from the Fab Four class of covariant Galileons is studied. We consider one-loop corrections to the John interaction due to cubic scalar field interaction. Counter terms are calculated, one appears because of massless scalar field theory infrared issues, another one lies in the George class, and the rest of them can be reduced to the initial Lagrangian up to surface terms. The role of quantum corrections in the context of cosmological applications is discussed.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

Bernardini, A. E.; Leal, P.; Bertolami, O.

2018-02-01

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos.

PubMed

Innocenti, Giacomo; Morelli, Alice; Genesio, Roberto; Torcini, Alessandro

2007-12-01

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.

Experimental investigation of different regimes of mode-locking in a high repetition rate passively mode-locked semiconductor quantum-dot laser.

PubMed

Kéfélian, Fabien; O'Donoghue, Shane; Todaro, Maria Teresa; McInerney, John; Huyet, Guillaume

2009-04-13

We report experimental investigations on a two-section 16-GHz repetition rate InAs/GaAs quantum dot passively mode-locked laser. Near the threshold current, pseudo-periodic Q-switching with complex dynamics is exhibited. Mode-locking operation regimes characterized by different repetition rates and timing jitter levels are encountered up to twice the threshold current. Evolution of the RF spectrum and optical spectrum with current is compared. The different mode-locked regimes are shown to be associated with different spectral and temporal shapes, ranging from 1.3 to 6 ps. This point is discussed by introducing the existence of two different supermodes. Repetition rate evolution and timing jitter increase is attributed to the coupling between the dominant and the secondary supermodes.

Household chaos and family sleep during infants' first year.

PubMed

Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M

2018-05-21

Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources

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

Aboussouan, Pierre; Alibart, Olivier; Ostrowsky, Daniel B.

We report on a two-photon interference experiment in a quantum relay configuration using two picosecond regime periodically poled lithium niobate (PPLN) waveguide based sources emitting paired photons at 1550 nm. The results show that the picosecond regime associated with a guided-wave scheme should have important repercussions for quantum relay implementations in real conditions, essential for improving both the working distance and the efficiency of quantum cryptography and networking systems. In contrast to already reported regimes, namely, femtosecond and CW, it allows achieving a 99% net visibility two-photon interference while maintaining a high effective photon pair rate using only standard telecommore » components and detectors.« less

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

Mur-Petit, J; Relaño, A; Molina, R A; Jaksch, D

2018-05-22

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

Counseling Chaos: Techniques for Practitioners

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim E. H.

2006-01-01

The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…

Quantum phase uncertainties in the classical limit

NASA Technical Reports Server (NTRS)

Franson, James D.

1994-01-01

Several sources of phase noise, including spontaneous emission noise and the loss of coherence due to which-path information, are examined in the classical limit of high field intensities. Although the origin of these effects may appear to be quantum-mechanical in nature, it is found that classical analogies for these effects exist in the form of chaos.

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos

NASA Astrophysics Data System (ADS)

Castaño, D.; Navarro, M. C.; Herrero, H.

2016-01-01

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

Continuous quantum measurement and the quantum to classical transition

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

Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

2003-04-01

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities thatmore » describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.« less

Shape and size distribution of chaos areas on Europa

NASA Astrophysics Data System (ADS)

Mikell, T.; Cox, R.

2008-12-01

Chaos terrain is ubiquitous on Europa's surface, but not randomly distributed. The global distribution of chaos areas shows a significant concentration between 30° N and S latitude, decreasing dramatically at higher latitudes. The low-latitude clustering is not an artifact of recognizability, as there is a greater proportion of images with high solar incidence angle (low light) at higher latitudes. Clustering is especially marked in context of the few but vast regional chaos tracts (>15,000 km2) that occupy a substantial proportion of the equatorial region: i.e. the low latitudes have not only greater numbers but much greater areal chaos coverage. Apex-antapex asymmetry is difficult to evaluate because the Galileo longitudinal coverage is so poor; but comparison of the image swaths that follow great circles across the leading and trailing hemispheres respectively shows greater numbers of chaos areas on the leading side. In spite of the equatorial location of a few vast chaos tracts, there is no apparent relationship between chaos area size and latitude. Chaos area outlines vary from smoothly circular to extremely jagged: the irregularity index ranges from 2- 270% (based on the ratio between measured chaos area perimeter and the circumference of a circle of equal area). There is a range of shapes in all size brackets, but smaller chaos areas on average have simpler, more equidimensional shapes, and edge complexity increases for larger chaos areas. Chaos areas of ~10 km equivalent circle diameter (ECD) have outlines that are 4-90% irregular, ones ~50 km ECD are 15-180% and those >100 km ECD are 35-270% irregular. In general, chaos areas with higher irregularity indices also have a higher raft:matrix ratio. These results, while preliminary, are consistent with experimental evidence suggesting an impact origin for some chaos terrain on Europa. In particular, the relationship between shape and size parallels the results of impact experiments into ice over water, in

Chaos Theory and Post Modernism

ERIC Educational Resources Information Center

Snell, Joel

2009-01-01

Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…

Quantum and classical chaos in kicked coupled Jaynes-Cummings cavities

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

Hayward, A. L. C.; Greentree, Andrew D.

2010-06-15

We consider two Jaynes-Cummings cavities coupled periodically with a photon hopping term. The semiclassical phase space is chaotic, with regions of stability over some ranges of the parameters. The quantum case exhibits dynamic localization and dynamic tunneling between classically forbidden regions. We explore the correspondence between the classical and quantum phase space and propose an implementation in a circuit QED system.

!CHAOS: A cloud of controls

NASA Astrophysics Data System (ADS)

Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.

2016-01-01

The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.

Iani Chaos

NASA Technical Reports Server (NTRS)

2005-01-01

[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos

This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed.

Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution.

Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

Iani Chaos

NASA Technical Reports Server (NTRS)

2005-01-01

[figure removed for brevity, see original site] Context image for PIA03046 Iani Chaos

This image shows a small portion of Iani Chaos. The brighter floor material is being covered by sand, probably eroded from the mesas of the Chaos.

Image information: VIS instrument. Latitude 1.7S, Longitude 341.6E. 17 meter/pixel resolution.

Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

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.

Investigation of regime switching from mode locking to Q-switching in a 2 µm InGaSb/AlGaAsSb quantum well laser.

PubMed

Li, Xiang; Wang, Hong; Qiao, Zhongliang; Guo, Xin; Wang, Wanjun; Ng, Geok Ing; Zhang, Yu; Xu, Yingqiang; Niu, Zhichuan; Tong, Cunzhu; Liu, Chongyang

2018-04-02

A two-section InGaSb/AlGaAsSb single quantum well (SQW) laser emitting at 2 μm is presented. By varying the absorber bias voltage with a fixed gain current at 130 mA, passive mode locking at ~18.40 GHz, Q-switched mode locking, and passive Q-switching are observed in this laser. In the Q-switched mode locking regimes, the Q-switched RF signal and mode locked RF signal coexist, and the Q-switched lasing and mode-locked lasing happen at different wavelengths. This is the first observation of these three pulsed working regimes in a GaSb-based diode laser. An analysis of the regime switching mechanism is given based on the interplay between the gain saturation and the saturable absorption.

Household Chaos--Links with Parenting and Child Behaviour

ERIC Educational Resources Information Center

Coldwell, Joanne; Pike, Alison; Dunn, Judy

2006-01-01

Background: The study aimed to confirm previous findings showing links between household chaos and parenting in addition to examining whether household chaos was predictive of children's behaviour over and above parenting. In addition, we investigated whether household chaos acts as a moderator between parenting and children's behaviour. Method:…

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

Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

NASA Astrophysics Data System (ADS)

Li, Jun; Fan, Ruihua; Wang, Hengyan; Ye, Bingtian; Zeng, Bei; Zhai, Hui; Peng, Xinhua; Du, Jiangfeng

2017-07-01

The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, it also diagnoses the chaotic behavior of many-body quantum systems and characterizes information scrambling. Based on OTOCs, three different concepts—quantum chaos, holographic duality, and information scrambling—are found to be intimately related to each other. Despite its theoretical importance, the experimental measurement of the OTOC is quite challenging, and thus far there is no experimental measurement of the OTOC for local operators. Here, we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and nonintegrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for nonintgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.

Decrease of cardiac chaos in congestive heart failure

NASA Astrophysics Data System (ADS)

Poon, Chi-Sang; Merrill, Christopher K.

1997-10-01

The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.

Exploiting chaos for applications.

PubMed

Ditto, William L; Sinha, Sudeshna

2015-09-01

We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.

Chaos, Chaos Control and Synchronization of a Gyrostat System

NASA Astrophysics Data System (ADS)

GE, Z.-M.; LIN, T.-N.

2002-03-01

The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.

Applied Chaos: From Oxymoron to Reality.

NASA Astrophysics Data System (ADS)

Ditto, William

1996-11-01

The rapidly emerging field of chaotic dynamics has presented the applied scientist with intriguing new tools to understand and manipulate systems that behave chaotically. An overview will be presented which will answer the questions: What is Chaos? and What can you do with Chaos? Examples of recent applications of chaos theory to the physical and biological sciences will be presented covering applications that range from encryption in communications to control of chaotically beating human hearts. Part A of program listing

The Capabilities of Chaos and Complexity

PubMed Central

Abel, David L.

2009-01-01

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? PMID:19333445

The microwave induced resistance response of a high mobility 2DEG from the quasi-classical limit to the quantum Hall regime

NASA Astrophysics Data System (ADS)

Studenikin, S. A.; Byszewski, M.; Maude, D. K.; Potemski, M.; Sachrajda, A.; Wasilewski, Z. R.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

2006-08-01

Microwave induced resistance oscillations (MIROs) were studied experimentally over a very wide range of frequencies ranging from ∼20 GHz up to ∼4 THz, and from the quasi-classical regime to the quantum Hall effect regime. At low frequencies regular MIROs were observed, with a periodicity determined by the ratio of the microwave to cyclotron frequencies. For frequencies below 150 GHz the magnetic field dependence of MIROs waveform is well described by a simplified version of an existing theoretical model, where the damping is controlled by the width of the Landau levels. In the THz frequency range MIROs vanish and only pronounced resistance changes are observed at the cyclotron resonance. The evolution of MIROs with frequency is presented and discussed.

Adventures in order and chaos : a scientific autobiography

NASA Astrophysics Data System (ADS)

Contopoulos, George

The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and Astrophysics. In recent years the theory of chaos has been extended to new areas, like relativity, cosmology and quantum mechanics and it continues expanding in almost all branches of physics. The book describes many important ideas in this field in a simple way. It refers also to problems of more general interest, like writing papers and giving lectures and the interaction of authors and referees. Finally it gives some useful prospects for the future of dynamical astronomy and related fields. George Contopoulos, PhD U.Athens1953; Professor of Astronomy U.Thessaloniki 1957-75; U.Athens 1975-96; Emeritus 1996-; Member, Academy of Athens 1997-. Visiting Professor Yale U., Harvard U., MIT, Cornell U., U.Chicago, U.Maryland, U. Florida, Florida State U., U. Milan; Res. Associate, Yerkes Obs., Inst.Adv.Study Princeton, Inst.Space Studies, Goddard Flight Center, Columbia U., ESO. Author or Editor of 15 books, and about 250 papers on Galactic Dynamics, Relativity and Celestial Mechanics. Positions held: Gen.Secretary of the IAU; Director General Nat.Obs.of Greece, Pres.Hellenic Astron.Soc.; Nat.Representative of Greece in NATO, etc. Distinctions: Amer. Astron.Soc. Brouwer Prize; U.Chicago, Honorary Doctor's Degree; IAU, Pres. Commission 33 (Galaxy); Member Academia Europaea; Associate Royal Astron. Soc.; Chairman of the European Journal "Astronomy and Astrophysics"; Assoc. Editor of

Three Temperature Regimes in Superconducting Photon Detectors: Quantum, Thermal and Multiple Phase-Slips as Generators of Dark Counts

PubMed Central

Murphy, Andrew; Semenov, Alexander; Korneev, Alexander; Korneeva, Yulia; Gol’tsman, Gregory; Bezryadin, Alexey

2015-01-01

We perform measurements of the switching current distributions of three w ≈ 120 nm wide, 4 nm thick NbN superconducting strips which are used for single-photon detectors. These strips are much wider than the diameter of the vortex cores, so they are classified as quasi-two-dimensional (quasi-2D). We discover evidence of macroscopic quantum tunneling by observing the saturation of the standard deviation of the switching distributions at temperatures around 2 K. We analyze our results using the Kurkijärvi-Garg model and find that the escape temperature also saturates at low temperatures, confirming that at sufficiently low temperatures, macroscopic quantum tunneling is possible in quasi-2D strips and can contribute to dark counts observed in single photon detectors. At the highest temperatures the system enters a multiple phase-slip regime. In this range single phase-slips are unable to produce dark counts and the fluctuations in the switching current are reduced. PMID:25988591

Three temperature regimes in superconducting photon detectors: quantum, thermal and multiple phase-slips as generators of dark counts.

PubMed

Murphy, Andrew; Semenov, Alexander; Korneev, Alexander; Korneeva, Yulia; Gol'tsman, Gregory; Bezryadin, Alexey

2015-05-19

We perform measurements of the switching current distributions of three w ≈ 120 nm wide, 4 nm thick NbN superconducting strips which are used for single-photon detectors. These strips are much wider than the diameter of the vortex cores, so they are classified as quasi-two-dimensional (quasi-2D). We discover evidence of macroscopic quantum tunneling by observing the saturation of the standard deviation of the switching distributions at temperatures around 2 K. We analyze our results using the Kurkijärvi-Garg model and find that the escape temperature also saturates at low temperatures, confirming that at sufficiently low temperatures, macroscopic quantum tunneling is possible in quasi-2D strips and can contribute to dark counts observed in single photon detectors. At the highest temperatures the system enters a multiple phase-slip regime. In this range single phase-slips are unable to produce dark counts and the fluctuations in the switching current are reduced.

On the motion of classical three-body system with consideration of quantum fluctuations

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

Public-channel cryptography based on mutual chaos pass filters.

PubMed

Klein, Einat; Gross, Noam; Kopelowitz, Evi; Rosenbluh, Michael; Khaykovich, Lev; Kinzel, Wolfgang; Kanter, Ido

2006-10-01

We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker, however, fails to recover an errorless message even if he amplifies the coupling signal.

Detecting nonlinearity and chaos in epidemic data

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

Ellner, S.; Gallant, A.R.; Theiler, J.

1993-08-01

Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude ofmore » epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.« less

Contractility of glycerinated Amoeba proteus and Chaos-chaos.

PubMed

Rinaldi, R; Opas, M; Hrebenda, B

1975-05-01

Immediate contact with large volumes of cold 50% (v/v) buffered glycerol preserved typical ameboid shape of Chaos chaos and Amoeba proteus with no visible distortions. These technics allowed determination of the contraction sites in these glycerinated models upon applications of ATP-Ca-Mg-solutions. The ectoplasmic tube was the main site of contraction. Preliminary EM investigations revealed thick and thin filaments, associated with the ectoplasmic tube near the plasma-lemma, which appeared to be the basis for the contractility of the ectoplasmic tube. There was no predominant contraction of the pseudopodial tips or the endoplasm in these models. The changes of volume were as much as 50%, and in some cases were not accompanied by any change in the length of the ameba; however, lengthwise contractions of the ectoplasmic tube in some amebae occurred to as much as 25%. The data substantiate a basic requirement of the ectoplasmic tube contraction theory of ameboid locomotion.

Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

Polarization State of Light Scattered from Quantum Plasmonic Dimer Antennas.

PubMed

Yang, Longkun; Wang, Hancong; Fang, Yan; Li, Zhipeng

2016-01-26

Plasmonic antennas are able to concentrate and re-emit light in a controllable manner through strong coupling between metallic nanostructures. Only recently has it found that quantum mechanical effects can drastically change the coupling strength as the feature size approaches atomic scales. Here, we present a comprehensive experimental and theoretical study of the evolution of the resonance peak and its polarization state as the dimer-antenna gap narrows to subnanometer scale. We clearly can identify the classical plasmonic regime, a crossover regime where nonlocal screening plays an important role, and the quantum regime where a charge transfer plasmon appears due to interparticle electron tunneling. Moreover, as the gap decreases from tens of to a few nanometers, the bonding dipole mode tends to emit photons with increasing polarizability. When the gap narrows to quantum regime, a significant depolarization of the mode emission is observed due to the reduction of the charge density of coupled quantum plasmons. These results would be beneficial for the understanding of quantum effects on emitting-polarization of nanoantennas and the development of quantum-based photonic nanodevices.

Anisotropy-Induced Quantum Interference and Population Trapping between Orthogonal Quantum Dot Exciton States in Semiconductor Cavity Systems

NASA Astrophysics Data System (ADS)

Hughes, Stephen; Agarwal, Girish S.

2017-02-01

We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate how the dipole-dipole coupling can control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a double-field pumping scenario can completely eliminate the decay of coherent Rabi oscillations and lead to population trapping. In the Mollow triplet regime, we explore the emitted spectra from the driven dipoles and show how a nonpumped dipole can take on the form of a spectral triplet, quintuplet, or a singlet, which has applications for producing subnatural linewidth single photons and more easily accessing regimes of high-field quantum optics and cavity-QED.

Anisotropy-Induced Quantum Interference and Population Trapping between Orthogonal Quantum Dot Exciton States in Semiconductor Cavity Systems.

PubMed

Hughes, Stephen; Agarwal, Girish S

2017-02-10

We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate how the dipole-dipole coupling can control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a double-field pumping scenario can completely eliminate the decay of coherent Rabi oscillations and lead to population trapping. In the Mollow triplet regime, we explore the emitted spectra from the driven dipoles and show how a nonpumped dipole can take on the form of a spectral triplet, quintuplet, or a singlet, which has applications for producing subnatural linewidth single photons and more easily accessing regimes of high-field quantum optics and cavity-QED.

Non-equilibrium many-body dynamics following a quantum quench

NASA Astrophysics Data System (ADS)

Vyas, Manan

2017-12-01

We study analytically and numerically the non-equilibrium dynamics of an isolated interacting many-body quantum system following a random quench. We model the system Hamiltonian by Embedded Gaussian Orthogonal Ensemble (EGOE) of random matrices with one plus few-body interactions for fermions. EGOE are paradigmatic models to study the crossover from integrability to chaos in interacting many-body quantum systems. We obtain a generic formulation, based on spectral variances, for describing relaxation dynamics of survival probabilities as a function of rank of interactions. Our analytical results are in good agreement with numerics.

Unraveling Quantum Annealers using Classical Hardness

PubMed Central

Martin-Mayor, Victor; Hen, Itay

2015-01-01

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257

'Chaos is come again': Nothingness in Shakespeare's metadramatic time and space

NASA Astrophysics Data System (ADS)

Oswald, John David

The extraordinary advances of twentieth-century science, which overlay, and in some cases overturn, the Newtonian precepts upon which physics was founded, have captured a share of the popular imagination. Quantum mechanics, relativity theory, and chaos theory are the stuff of science fact and science fiction, of technological innovation and artistic invention. Intricate ``fractal'' images adorn poster art, and science fiction fantasy (long a niche market for popular fiction) is the genre of the blockbuster film and the television franchise. Astronomers and physicists are writing pop-science bestsellers for the layman, making theory accessible to those who cannot do the math. This work focuses on Shakespearean notions of time and space in selected metadramatic passages from three plays that feature embattled monarchs: Richard II, King Lear, and The Winter's Tale. Shakespeare's employment of metaphors that are also ``cardinal metaphors'' of science is examined to determine how his dramatic works fare under a post-deterministic paradigm. A chaos-theory model is advanced for theatrical performance, and analogies are drawn from scientific theory to discuss dramatic language and action (e.g., ``nothingness'' in different contexts is compared variously with black holes, dark matter, vacuum genesis in a spatial void roiling with virtual particles, the empty space within matter, etc.). Of primary importance are the notions of quantum observership (the impossibility of separating observation from participation in scientific experimentation) and complementarity (Bohr's theory to account for the dual behavior of radiation as both waves and particles). Shakespeare's persistent metadramatic emphasis is seen as an effort to draw his audience (observers) into conscious participation in the imaginative act of bringing his plays into being. Complementarity relates to the promotion of multiple perspectives in all three plays and to the dramaturgical structure of The Winter's Tale.

Chaos based encryption system for encrypting electroencephalogram signals.

PubMed

Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

2014-05-01

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

Investigating a link between large and small-scale chaos features on Europa

NASA Astrophysics Data System (ADS)

Tognetti, L.; Rhoden, A.; Nelson, D. M.

2017-12-01

Chaos is one of the most recognizable, and studied, features on Europa's surface. Most models of chaos formation invoke liquid water at shallow depths within the ice shell; the liquid destabilizes the overlying ice layer, breaking it into mobile rafts and destroying pre-existing terrain. This class of model has been applied to both large-scale chaos like Conamara and small-scale features (i.e. microchaos), which are typically <10 km in diameter. Currently unknown, however, is whether both large-scale and small-scale features are produced together, e.g. through a network of smaller sills linked to a larger liquid water pocket. If microchaos features do form as satellites of large-scale chaos features, we would expect a drop off in the number density of microchaos with increasing distance from the large chaos feature; the trend should not be observed in regions without large-scale chaos features. Here, we test the hypothesis that large chaos features create "satellite" systems of smaller chaos features. Either outcome will help us better understand the relationship between large-scale chaos and microchaos. We focus first on regions surrounding the large chaos features Conamara and Murias (e.g. the Mitten). We map all chaos features within 90,000 sq km of the main chaos feature and assign each one a ranking (High Confidence, Probable, or Low Confidence) based on the observed characteristics of each feature. In particular, we look for a distinct boundary, loss of preexisting terrain, the existence of rafts or blocks, and the overall smoothness of the feature. We also note features that are chaos-like but lack sufficient characteristics to be classified as chaos. We then apply the same criteria to map microchaos features in regions of similar area ( 90,000 sq km) that lack large chaos features. By plotting the distribution of microchaos with distance from the center point of the large chaos feature or the mapping region (for the cases without a large feature), we

Making a molecular gas in the quantum regime

NASA Astrophysics Data System (ADS)

Ni, Kang-Kuen

2017-04-01

Ultracold molecules are exciting systems for a large range of scientific explorations including studies of novel phases of matter and precision measurement. In this talk, I will present a brief story of the first quantum gas of molecules, KRb, created under my PhD advisor, Deborah Jin, in 2008. A complete surprise was finding ultracold chemistry in such a system through measurements of reactant losses. In particular, long-range physics that determines KRb reactant collision rates, including van der Waals interactions, quantum statistics, and dipolar interactions, were studied extensively. However, the short-range behavior of these chemical reactions remains unknown. A legacy of her work is carried out in my lab at Harvard, where we are integrating physical chemistry tools with cold atom techniques to study ultracold chemistry with KRb molecules. In particular, we aim to elucidate the four-center reaction 2 KRb ->K2 + Rb2 by detecting the reaction products through ionization - both identify the product species and mapping out their complete quantum states.

Experimental evidence of quantum radiation reaction in aligned crystals.

PubMed

Wistisen, Tobias N; Di Piazza, Antonino; Knudsen, Helge V; Uggerhøj, Ulrik I

2018-02-23

Quantum radiation reaction is the influence of multiple photon emissions from a charged particle on the particle's dynamics, characterized by a significant energy-momentum loss per emission. Here we report experimental radiation emission spectra from ultrarelativistic positrons in silicon in a regime where quantum radiation reaction effects dominate the positron's dynamics. Our analysis shows that while the widely used quantum approach is overall the best model, it does not completely describe all the data in this regime. Thus, these experimental findings may prompt seeking more generally valid methods to describe quantum radiation reaction. This experiment is a fundamental test of quantum electrodynamics in a regime where the dynamics of charged particles is strongly influenced not only by the external electromagnetic fields but also by the radiation field generated by the charges themselves and where each photon emission may significantly reduce the energy of the charge.

Chaos in the Solar System

NASA Technical Reports Server (NTRS)

Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.

2001-01-01

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

Distribution of electron density and magnetocapacitance in the regime of the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Pikus, F. G.; Efros, A. L.

1993-06-01

A two-dimensional electron liquid (TDEL), subjected to a smooth random potential, is studied in the regime of the fractional quantum Hall effect. An analytical theory of the nonlinear screening is presented for the case when the fractional gap is much less than the magnitude of the unscreened random potential. In this ``narrow-gap approximation'' (NGA), we calculate the electron density distribution function, the fraction of the TDEL which is in the incompressible state, and the thermodynamic density of states. The magnetocapacitance is calculated to compare with the recent experiments. The NGA is found to be not accurate enough to describe the data. The results for larger fractional gaps are obtained by computer modeling. To fit the recent experimental data we have also taken into account the anyon-anyon interaction in the vicinity of a fractional singularity.

Brain Neurons as Quantum Computers:

NASA Astrophysics Data System (ADS)

Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.

The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.

Energy spectra of quantum rings.

PubMed

Fuhrer, A; Lüscher, S; Ihn, T; Heinzel, T; Ensslin, K; Wegscheider, W; Bichler, M

2001-10-25

Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov-Bohm effect, one of the best examples of quantum mechanical phase coherence. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated. The energy spectra of closed rings have only recently been studied by optical spectroscopy. The prediction that they allow persistent current has been explored in various experiments. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Effortful control and school adjustment: The moderating role of classroom chaos.

PubMed

Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

2017-11-01

Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

Analog quantum simulation of generalized Dicke models in trapped ions

NASA Astrophysics Data System (ADS)

Aedo, Ibai; Lamata, Lucas

2018-04-01

We propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behavior arises, and the ultrastrong coupling (USC) regime, where a rotating-wave approximation cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes and the two-qubit anisotropic Dicke model in the USC regime and the deep-strong coupling regime. The agreement between the mathematical models and the ion system convinces us that these quantum simulations can be implemented in the laboratory with current or near-future technology. This formalism establishes an avenue for the quantum simulation of many-spin Dicke models in trapped ions.

Chaos as a Social Determinant of Child Health: Reciprocal Associations?

PubMed Central

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250

Chaos: Choto delat?

NASA Astrophysics Data System (ADS)

Campbell, David

1987-11-01

I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.

Origins of Chaos in Autonomous Boolean Networks

NASA Astrophysics Data System (ADS)

Socolar, Joshua; Cavalcante, Hugo; Gauthier, Daniel; Zhang, Rui

2010-03-01

Networks with nodes consisting of ideal Boolean logic gates are known to display either steady states, periodic behavior, or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power-law. In an experiment, non-ideal behavior of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and the asymmetry between the logic states tends to engender periodic behavior. On the other hand, a memory effect termed ``degradation'' can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra. The non-ideal effects identified here also have implications for the statistics of attractors in large complex networks.

Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems

PubMed Central

Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2015-01-01

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems. PMID:25758591

Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.

PubMed

Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2015-03-11

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

The Six Fundamental Characteristics of Chaos and Their Clinical Relevance to Psychiatry: a New Hypothesis for the Origin of Psychosis

NASA Astrophysics Data System (ADS)

Schmid, Gary Bruno

, characteristics and examples) and to the idea of "psychological disturbance as dynamical illness". On the one hand, it is argued that the developmental course of psychosis is chaotic. On the other hand, we propose the hypothesis that the mental state of psychosis may be a linear information processing pathology. (2) The second aspect under discussion is the Assessment of Chaos / Diagnosis of Illness. In order to better understand how POPSY research treats this aspect, we take a look at the 3 different classes of (non-quantum) motion as models of 3 different possible courses of illness and outline present-day methods available for the quantitative assessment of chaotic (fractal) motion. (3) The third aspect, namely. Prediction of Chaos / Prognosis of Illness considers how each of these 3 classes of motion implies a different way of looking into the future: linear-causal, statistical and nonlinear-fractal, respectively (4) The fourth aspect of the relationship between chaos theory and POPSY, Control of Chaos / Treatment of Illness, is shown to have certain implications to complementary medicine. This paper completes with a short summary, conclusion and a closing remark.

Quantum correction to classical gravitational interaction between two polarizable objects

NASA Astrophysics Data System (ADS)

Wu, Puxun; Hu, Jiawei; Yu, Hongwei

2016-12-01

When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like r-11 in the retarded regime and r-10 in the near regime. Our result agrees with what were recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.

Weyl corrections to diffusion and chaos in holography

NASA Astrophysics Data System (ADS)

Li, Wei-Jia; Liu, Peng; Wu, Jian-Pin

2018-04-01

Using holographic methods in the Einstein-Maxwell-dilaton-axion (EMDA) theory, it was conjectured that the thermal diffusion in a strongly coupled metal without quasi-particles saturates an universal lower bound that is associated with the chaotic property of the system at infrared (IR) fixed points [1]. In this paper, we investigate the thermal transport and quantum chaos in the EMDA theory with a small Weyl coupling term. It is found that the Weyl coupling correct the thermal diffusion constant D Q and butterfly velocity v B in different ways, hence resulting in a modified relation between the two at IR fixed points. Unlike that in the EMDA case, our results show that the ratio D Q /( v B 2 τ L ) always contains a non-universal Weyl correction which depends also on the bulk fields as long as the U(1) current is marginally relevant in the IR.

Comparison Between Terrestrial Explosion Crater Morphology in Floating Ice and Europan Chaos

NASA Technical Reports Server (NTRS)

Billings, S. E.; Kattenhorn, S. A.

2003-01-01

Craters created by explosives have been found to serve as valuable analogs to impact craters, within limits. Explosion craters have been created in floating terrestrial ice in experiments related to clearing ice from waterways. Features called chaos occur on the surface of Europa s floating ice shell. Chaos is defined as a region in which the background plains have been disrupted. Common features of chaos include rafted blocks of pre-existing terrain suspended in a matrix of smooth or hummocky material; low surface albedo; and structural control on chaos outline shape by pre-existing lineaments. All published models of chaos formation call on endogenic processes whereby chaos forms through thermal processes. Nonetheless, we note morphological similarities between terrestrial explosion craters and Europan chaos at a range of scales and consider whether some chaos may have formed by impact. We explore these similarities through geologic and morphologic mapping.

Pulsed quantum optomechanics

PubMed Central

Vanner, M. R.; Pikovski, I.; Cole, G. D.; Kim, M. S.; Brukner, Č.; Hammerer, K.; Milburn, G. J.; Aspelmeyer, M.

2011-01-01

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing, and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions. PMID:21900608

Gullies of Gorgonus Chaos

NASA Technical Reports Server (NTRS)

2002-01-01

(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the

Velocity-dependent quantum phase slips in 1D atomic superfluids.

PubMed

Tanzi, Luca; Scaffidi Abbate, Simona; Cataldini, Federica; Gori, Lorenzo; Lucioni, Eleonora; Inguscio, Massimo; Modugno, Giovanni; D'Errico, Chiara

2016-05-18

Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures but their existence in ultracold quantum gases has not been demonstrated yet. We now study experimentally the nucleation rate of phase slips in one-dimensional superfluids realized with ultracold quantum gases, flowing along a periodic potential. We observe a crossover between a regime of temperature-dependent dissipation at small velocity and interaction and a second regime of velocity-dependent dissipation at larger velocity and interaction. This behavior is consistent with the predicted crossover from thermally-assisted quantum phase slips to purely quantum phase slips.

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

Photon mirror acceleration in the quantum regime

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Fedele, R.

2014-12-01

Reflection of an electron beam by an intense laser pulse is considered. This is the so-called photon mirror configuration for laser acceleration in vacuum, where the energy of the incident electron beam is nearly double-Doppler shifted due to reflection on the laser pulse front. A wave-electron optical description for electron reflection and resonant backscattering, due to both linear electric field force and quadratic ponderomotive force, is provided beyond the paraxial approximation. This is done by assuming that the single electron of the beam is spin-less and therefore its motion can be described by a quantum scalar field whose spatiotemporal evolution is governed by the Klein-Gordon equation (Klein-Gordon field). Our present model, not only confirms the classical results but also shows the occurrence of purely quantum effects, such as partial reflection of the incident electron beam and enhanced backscattering due to Bragg resonance.

The path integral on the Poincaré upper half plane and for Liouville quantum mechanics

NASA Astrophysics Data System (ADS)

Grosche, C.; Steiner, F.

1987-08-01

We present a rigorous path integral treatment of free motion on the Poincaré upper half plane. The Poincaré upper half plane, as a riemannian manifold, has recently become important in string theory and in the theory of quantum chaos. The calculation is done by a time-transformation and the use of the canonical method for determining quantum corrections to the classical lagrangian. Furthermore, we shall show that the same method also works for Liouville quantum mechanics. In both cases, the energy spectrum and the normalized wavefunctions are determined.

Polynomiography and Chaos

NASA Astrophysics Data System (ADS)

Kalantari, Bahman

Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.

Quantum memristors

DOE PAGES

Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; ...

2016-07-06

Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantummore » regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. As a result, the proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.« less

Hybrid quantum-classical modeling of quantum dot devices

NASA Astrophysics Data System (ADS)

Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

2017-11-01

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

Collision analysis of one kind of chaos-based hash function

NASA Astrophysics Data System (ADS)

Xiao, Di; Peng, Wenbing; Liao, Xiaofeng; Xiang, Tao

2010-02-01

In the last decade, various chaos-based hash functions have been proposed. Nevertheless, the corresponding analyses of them lag far behind. In this Letter, we firstly take a chaos-based hash function proposed very recently in Amin, Faragallah and Abd El-Latif (2009) [11] as a sample to analyze its computational collision problem, and then generalize the construction method of one kind of chaos-based hash function and summarize some attentions to avoid the collision problem. It is beneficial to the hash function design based on chaos in the future.

Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

PubMed

Adin, Mehmet Emin

2017-10-01

Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.

Low-dimensional chaos in turbulence

NASA Technical Reports Server (NTRS)

Vastano, John A.

1989-01-01

Direct numerical simulations are being performed on two different fluid flows in an attempt to discover the mechanism underlying the transition to turbulence in each. The first system is Taylor-Couette flow; the second, two-dimensional flow over an airfoil. Both flows exhibit a gradual transition to high-dimensional turbulence through low-dimensional chaos. The hope is that the instabilities leading to chaos will be easier to relate to physical processes in this case, and that the understanding of these mechanisms can then be applied to a wider array of turbulent systems.

Anisoplanatic image propagation along a slanted path under lower atmosphere phase turbulence in the presence of encrypted chaos

NASA Astrophysics Data System (ADS)

Chatterjee, Monish R.; Mohamed, Ali A.

2017-05-01

In recent research, anisoplanatic electromagnetic (EM) wave propagation along a slanted path in the presence of low atmosphere phase turbulence (modified von Karman spectrum or MVKS) has been investigated assuming a Hufnagel-Valley (HV) type structure parameter. Preliminary results indicate a strong dependence on the slant angle especially for long range transmission and relatively strong turbulence. The investigation was further divided into two regimes, viz. (a) one where the EM source consisted of a plane wave modulated with a digitized image, which is propagated along the turbulent path and recovered via demodulation at the receiver; and (b) transmit the plane wave without modulation along the turbulent path through an image transparency and a thin lens designed to gather the received image in the focal plane. In this paper, we reexamine the same problem (part (a) only) in the presence of a chaotic optical carrier where the chaos is generated in the feedback loop of an acousto-optic Bragg cell. The image information is encrypted within the chaos wave, and subsequently propagated along a similar slant path and identical turbulence conditions. The recovered image extracted via heterodyning from the received chaos is compared quantitatively (through image cross-correlations and mean-squared error measures) for the non-chaotic versus the chaotic approaches. Generally, "packaging" the information in chaos improves performance through turbulent propagation, and results are discussed from this perspective. Concurrently, we will also examine the effect of a non-encrypted plane EM wave propagation through a transparency-lens combination. These results are also presented with appropriate comparisons with the cases involving lensless transmission of imagery through corresponding turbulent and non-turbulent layers.

Chaos in plasma simulation and experiment

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

Watts, C.; Newman, D.E.; Sprott, J.C.

1993-09-01

We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFPmore » dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

Criticality and Chaos in Systems of Communities

NASA Astrophysics Data System (ADS)

Ostilli, Massimo; Figueiredo, Wagner

2016-01-01

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

The Nature (and Nurture) of Children's Perceptions of Family Chaos

ERIC Educational Resources Information Center

Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert

2010-01-01

Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…

Chaos Theory as a Model for Managing Issues and Crises.

ERIC Educational Resources Information Center

Murphy, Priscilla

1996-01-01

Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…

God's Stuff: The Constructive Powers of Chaos for Teaching Religion

ERIC Educational Resources Information Center

Willhauck, Susan

2010-01-01

Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…

Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

NASA Astrophysics Data System (ADS)

Gover, Avraham; Pan, Yiming

2018-06-01

In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value - the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle-wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.

Superfluidity and Chaos in low dimensional circuits

PubMed Central

Arwas, Geva; Vardi, Amichay; Cohen, Doron

2015-01-01

The hallmark of superfluidity is the appearance of “vortex states” carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states. PMID:26315272

Free-Space Quantum Communication with a Portable Quantum Memory

NASA Astrophysics Data System (ADS)

Namazi, Mehdi; Vallone, Giuseppe; Jordaan, Bertus; Goham, Connor; Shahrokhshahi, Reihaneh; Villoresi, Paolo; Figueroa, Eden

2017-12-01

The realization of an elementary quantum network that is intrinsically secure and operates over long distances requires the interconnection of several quantum modules performing different tasks. In this work, we report the realization of a communication network functioning in a quantum regime, consisting of four different quantum modules: (i) a random polarization qubit generator, (ii) a free-space quantum-communication channel, (iii) an ultralow-noise portable quantum memory, and (iv) a qubit decoder, in a functional elementary quantum network possessing all capabilities needed for quantum-information distribution protocols. We create weak coherent pulses at the single-photon level encoding polarization states |H ⟩ , |V ⟩, |D ⟩, and |A ⟩ in a randomized sequence. The random qubits are sent over a free-space link and coupled into a dual-rail room-temperature quantum memory and after storage and retrieval are analyzed in a four-detector polarization analysis akin to the requirements of the BB84 protocol. We also show ultralow noise and fully portable operation, paving the way towards memory-assisted all-environment free-space quantum cryptographic networks.

The relation between the quantum discord and quantum teleportation: The physical interpretation of the transition point between different quantum discord decay regimes

NASA Astrophysics Data System (ADS)

Roszak, K.; Cywiński, Ł.

2015-10-01

We study quantum teleportation via Bell-diagonal mixed states of two qubits in the context of the intrinsic properties of the quantum discord. We show that when the quantum-correlated state of the two qubits is used for quantum teleportation, the character of the teleportation efficiency changes substantially depending on the Bell-diagonal-state parameters, which can be seen when the worst-case-scenario or best-case-scenario fidelity is studied. Depending on the parameter range, one of two types of single-qubit states is hardest/easiest to teleport. The transition between these two parameter ranges coincides exactly with the transition between the range of classical correlation decay and quantum correlation decay characteristic for the evolution of the quantum discord. The correspondence provides a physical interpretation for the prominent feature of the decay of the quantum discord.

Quasiperiodicity route to chaos in cardiac conduction model

NASA Astrophysics Data System (ADS)

Quiroz-Juárez, M. A.; Vázquez-Medina, R.; Ryzhii, E.; Ryzhii, M.; Aragón, J. L.

2017-01-01

It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system proposed in Ref. [Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. Comput Meth Prog Bio 2014;117(1):40-49. doi:10.1016/j.cmpb.2014.04.009.], by including an ectopic pacemaker that stimulates the ventricular muscle to model arrhythmias. With this modification, the transition from normal rhythm to ventricular fibrillation is controlled by a single parameter. We show that this transition follows the so-called torus of quasi-periodic route to chaos, as verified by using numerical tools such as power spectrum and largest Lyapunov exponent.

The Importance of Chaos and Lenticulae on Europa for the JIMO Mission

NASA Technical Reports Server (NTRS)

Spaun, Nicole A.

2003-01-01

The Galileo Solid State Imaging (SSI) experiment provided high-resolution images of Europa's surface allowing identification of surface features barely distinguishable at Voyager's resolution. SSI revealed the visible pitting on Europa's surface to be due to large disrupted features, chaos, and smaller sub-circular patches, lenticulae. Chaos features contain a hummocky matrix material and commonly contain dislocated blocks of ridged plains. Lenticulae are morphologically interrelated and can be divided into three classes: domes, spots, and micro-chaos. Domes are broad, upwarped features that generally do not disrupt the texture of the ridged plains. Spots are areas of low albedo that are generally smooth in texture compared to other units. Micro-chaos are disrupted features with a hummocky matrix material, resembling that observed within chaos regions. Chaos and lenticulae are ubiquitous in the SSI regional map observations, which average approximately 200 meters per pixel (m/pxl) in resolution, and appear in several of the ultra-high resolution, i.e., better than 50 m/pxl, images of Europa as well. SSI also provided a number of multi-spectral observations of chaos and lenticulae. Using this dataset we have undertaken a thorough study of the morphology, size, spacing, stratigraphy, and color of chaos and lenticulae to determine their properties and evaluate models of their formation. Geological mapping indicates that chaos and micro-chaos have a similar internal morphology of in-situ degradation suggesting that a similar process was operating during their formation. The size distribution denotes a dominant size of 4-8 km in diameter for features containing hummocky material (i.e., chaos and micro-chaos). Results indicate a dominant spacing of 15 - 36 km apart. Chaos and lenticulae are generally among the youngest features stratigraphically observed on the surface, suggesting a recent change in resurfacing style. Also, the reddish non-icy materials on Europa

Effects of quantum coherence on work statistics

NASA Astrophysics Data System (ADS)

Xu, Bao-Ming; Zou, Jian; Guo, Li-Sha; Kong, Xiang-Mu

2018-05-01

In the conventional two-point measurement scheme of quantum thermodynamics, quantum coherence is destroyed by the first measurement. But as we know the coherence really plays an important role in the quantum thermodynamics process, and how to describe the work statistics for a quantum coherent process is still an open question. In this paper, we use the full counting statistics method to investigate the effects of quantum coherence on work statistics. First, we give a general discussion and show that for a quantum coherent process, work statistics is very different from that of the two-point measurement scheme, specifically the average work is increased or decreased and the work fluctuation can be decreased by quantum coherence, which strongly depends on the relative phase, the energy level structure, and the external protocol. Then, we concretely consider a quenched one-dimensional transverse Ising model and show that quantum coherence has a more significant influence on work statistics in the ferromagnetism regime compared with that in the paramagnetism regime, so that due to the presence of quantum coherence the work statistics can exhibit the critical phenomenon even at high temperature.

Chaos: A Topic for Interdisciplinary Education in Physics

ERIC Educational Resources Information Center

Bae, Saebyok

2009-01-01

Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…

Controlling chaos faster.

PubMed

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

Quantum optics, cavity QED, and quantum optomechanics

NASA Astrophysics Data System (ADS)

Meystre, Pierre

2013-05-01

Quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion. It does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from 10-20 g to several kilos. Its underlying ideas can be traced back to the study of gravitational wave antennas, quantum optics, cavity QED and laser cooling which, when combined with the recent availability of advanced micromechanical and nanomechanical devices, opens a path to the realization of macroscopic mechanical systems that operate deep in the quantum regime. At the fundamental level this development paves the way to experiments that will lead to a more profound understanding of quantum mechanics; and from the point of view of applications, quantum optomechanical techniques will provide motion and force sensing near the fundamental limit imposed by quantum mechanics (quantum metrology) and significantly expand the toolbox of quantum information science. After a brief summary of key historical developments, the talk will give a broad overview of the current state of the art of quantum optomechanics, and comment on future prospects both in applied and in fundamental science. Work supported by NSF, ARO and the DARPA QuASAR and ORCHID programs.

Chaos and the (un)predictability of evolution in a changing environment

PubMed Central

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-01-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. PMID:29235104

Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

PubMed

Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram

2015-04-01

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Temporal dynamics of soil microbial communities under different moisture regimes: high-throughput sequencing and bioinformatics analysis

NASA Astrophysics Data System (ADS)

Semenov, Mikhail; Zhuravleva, Anna; Semenov, Vyacheslav; Yevdokimov, Ilya; Larionova, Alla

2017-04-01

Recent climate scenarios predict not only continued global warming but also an increased frequency and intensity of extreme climatic events such as strong changes in temperature and precipitation regimes. Microorganisms are well known to be more sensitive to changes in environmental conditions than to other soil chemical and physical parameters. In this study, we determined the shifts in soil microbial community structure as well as indicative taxa in soils under three moisture regimes using high-throughput Illumina sequencing and range of bioinformatics approaches for the assessment of sequence data. Incubation experiments were performed in soil-filled (Greyic Phaeozems Albic) rhizoboxes with maize and without plants. Three contrasting moisture regimes were being simulated: 1) optimal wetting (OW), a watering 2-3 times per week to maintain soil moisture of 20-25% by weight; 2) periodic wetting (PW), with alternating periods of wetting and drought; and 3) constant insufficient wetting (IW), while soil moisture of 12% by weight was permanently maintained. Sampled fresh soils were homogenized, and the total DNA of three replicates was extracted using the FastDNA® SPIN kit for Soil. DNA replicates were combined in a pooled sample and the DNA was used for PCR with specific primers for the 16S V3 and V4 regions. In order to compare variability between different samples and replicates within a single sample, some DNA replicates treated separately. The products were purified and submitted to Illumina MiSeq sequencing. Sequence data were evaluated by alpha-diversity (Chao1 and Shannon H' diversity indexes), beta-diversity (UniFrac and Bray-Curtis dissimilarity), heatmap, tagcloud, and plot-bar analyses using the MiSeq Reporter Metagenomics Workflow and R packages (phyloseq, vegan, tagcloud). Shannon index varied in a rather narrow range (4.4-4.9) with the lowest values for microbial communities under PW treatment. Chao1 index varied from 385 to 480, being a more flexible

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Scrambling in the quantum Lifshitz model

NASA Astrophysics Data System (ADS)

Plamadeala, Eugeniu; Fradkin, Eduardo

2018-06-01

We study signatures of chaos in the quantum Lifshitz model through out-of-time ordered correlators (OTOC) of current operators. This model is a free scalar field theory with dynamical critical exponent z  =  2. It describes the quantum phase transition in 2D systems, such as quantum dimer models, between a phase with a uniform ground state to another one with spontaneously broken translation invariance. At the lowest temperatures the chaotic dynamics are dominated by a marginally irrelevant operator which induces a temperature dependent stiffness term. The numerical computations of OTOC exhibit a non-zero Lyapunov exponent (LE) in a wide range of temperatures and interaction strengths. The LE (in units of temperature) is a weakly temperature-dependent function; it vanishes at weak interaction and saturates for strong interaction. The Butterfly velocity increases monotonically with interaction strength in the studied region while remaining smaller than the interaction-induced velocity/stiffness.

Chaos in learning a simple two-person game

PubMed Central

Sato, Yuzuru; Akiyama, Eizo; Farmer, J. Doyne

2002-01-01

We investigate the problem of learning to play the game of rock–paper–scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy. PMID:11930020

Does chaos theory have major implications for philosophy of medicine?

PubMed

Holm, S

2002-12-01

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.

Dynamics of Topological Excitations in a Model Quantum Spin Ice

NASA Astrophysics Data System (ADS)

Huang, Chun-Jiong; Deng, Youjin; Wan, Yuan; Meng, Zi Yang

2018-04-01

We study the quantum spin dynamics of a frustrated X X Z model on a pyrochlore lattice by using large-scale quantum Monte Carlo simulation and stochastic analytic continuation. In the low-temperature quantum spin ice regime, we observe signatures of coherent photon and spinon excitations in the dynamic spin structure factor. As the temperature rises to the classical spin ice regime, the photon disappears from the dynamic spin structure factor, whereas the dynamics of the spinon remain coherent in a broad temperature window. Our results provide experimentally relevant, quantitative information for the ongoing pursuit of quantum spin ice materials.

Biologically inspired rate control of chaos.

PubMed

Olde Scheper, Tjeerd V

2017-10-01

The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

Optical scheme for simulating post-quantum nonlocality distillation.

PubMed

Chu, Wen-Jing; Yang, Ming; Pan, Guo-Zhu; Yang, Qing; Cao, Zhuo-Liang

2016-11-28

An optical scheme for simulating nonlocality distillation is proposed in post-quantum regime. The nonlocal boxes are simulated by measurements on appropriately pre- and post-selected polarization entangled photon pairs, i.e. post-quantum nonlocality is simulated by exploiting fair-sampling loophole in a Bell test. Mod 2 addition on the outputs of two nonlocal boxes combined with pre- and post-selection operations constitutes the key operation of simulating nonlocality distillation. This scheme provides a possible tool for the experimental study on the nonlocality in post-quantum regime and the exact physical principle precisely distinguishing physically realizable correlations from nonphysical ones.

Chaos in charged AdS black hole extended phase space

NASA Astrophysics Data System (ADS)

Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

2018-06-01

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

A universal order underlying the pseudogap regime of the underdoped high Tc cuprates

NASA Astrophysics Data System (ADS)

Harrison, Neil

2014-03-01

A major achievement in condensed matter physics in the last quarter century has been a step towards the understanding of the unconventional d-wave superconducting state in the copper-oxide materials. Surprisingly, the normal state out of which the superconducting state emerges remains a mystery at low charge carrier densities, i.e., in the underdoped regime. This regime is of particular interest because it is characterised by an unusual momentum dependent energy pseudogap in the excitation spectrum that has defied explanation and is key to a full understanding of the unconventional d-wave superconducting state. I will present new quantum oscillation experimental results within the pseudogap regime of the high Tc superconductors YBa2Cu3O6+x and YBa2Cu4O8 which now extend up to the optimally-doped regime. These data reveal the evolution of the Fermi surface approaching the putative quantum critical point under the superconducting dome. A comprehensive angle-resolved study of the Fermi surface enables us to unambiguously identify a specific form of order that accounts for the observed quantum oscillations as well as other spectroscopic, transport and thermodynamic probes within the pseudogap regime. The author would like to thank B. Ramshaw, S. Sebastian, F. Balakirev, C. Mielke, M. Altarawneh, P. Goddard, S. Sabok, B. Babrowski, D. Bonn, W. Hardy, R. Liang and G. Lonzarich. This work was supported by the DOE BES ``Science of 100 tesla'' project and by the NSF and Florida State.

Non-equilibrium quantum phase transition via entanglement decoherence dynamics.

PubMed

Lin, Yu-Chen; Yang, Pei-Yun; Zhang, Wei-Min

2016-10-07

We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained.

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

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

NASA Astrophysics Data System (ADS)

Vojta, Günter; Vojta, Matthias

Classical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner- Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument i with = Vo/kT.Translated AbstractQuantenstatistik des Toda-Oszillators im Formalismus der Wigner-FunktionKlassische und quantenmechanische Toda-Systeme (Toda-Moleküle, Toda-Gitter, Toda-Quantenfelder) haben als nichtlineare Systeme mit Solitonen und Chaos in jüngster Zeit zunehmend an Interesse gewonnen. Wir untersuchen die statistische Thermodynamik eines Systems quantenmechanischer Toda-Oszillatoren, die durch eine potentielle Energie der Form V(q) = Vo cos h q charakterisiert sind, im Formalismus der Wigner-Funktion (Phasenraum-Formalismus der Quantenstatistik). Die Zustandssumme wird als Wigner-Kirkwood-Reihe nach Potenzen von h2 (semiklassische Entwicklung) dargestellt, und aus ihr werden die thermodynamischen Funktionen berechnet. Sämtliche Funktionen sind durch einfache geschlossene Formeln allein mit den modifizierten Hankel-Funktionen Ko und K1 des rein imaginären Arguments i mit = Vo/kT mit großer Genauigkeit darzustellen.

Chaos and Christianity: A Response to Butz and a Biblical Alternative.

ERIC Educational Resources Information Center

Watts, Richard E.; Trusty, Jerry

1997-01-01

M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

Convergent chaos

NASA Astrophysics Data System (ADS)

Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael

2017-07-01

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

Effect of smoothing on robust chaos.

PubMed

Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

2010-08-01

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

Dynamic Ice-Water Interactions Form Europa's Chaos Terrains

NASA Astrophysics Data System (ADS)

Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.

2011-12-01

Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

NASA Astrophysics Data System (ADS)

González-Tudela, A.; Cirac, J. I.

2017-10-01

We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which cannot be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band, we predict an exponential relaxation at a rate different from that predicted by Fermi's golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.

Chaos and the (un)predictability of evolution in a changing environment.

PubMed

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-02-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Remnants of semiclassical bistability in the few-photon regime of cavity QED.

PubMed

Kerckhoff, Joseph; Armen, Michael A; Mabuchi, Hideo

2011-11-21

Broadband homodyne detection of the light transmitted by a Fabry-Perot cavity containing a strongly-coupled (133)Cs atom is used to probe the dynamic optical response in a regime where semiclassical theory predicts bistability but strong quantum corrections should apply. While quantum fluctuations destabilize true equilibrium bistability, our observations confirm the existence of metastable states with finite lifetimes and a hysteretic response is apparent when the optical drive is modulated on comparable timescales. Our experiment elucidates remnant semiclassical behavior in the attojoule (~10 photon) regime of single-atom cavity QED, of potential significance for ultra-low power photonic signal processing. © 2011 Optical Society of America

Li-Yorke Chaos in Hybrid Systems on a Time Scale

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2015-12-01

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

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.

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

PubMed

Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur

2014-12-01

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

"I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

ERIC Educational Resources Information Center

Pryor, Robert; Bright, Jim

2004-01-01

This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…

Thermoelectric energy harvesting with quantum dots

NASA Astrophysics Data System (ADS)

Sothmann, Björn; Sánchez, Rafael; Jordan, Andrew N.

2015-01-01

We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.

Applying Chaos Theory to Lesson Planning and Delivery

ERIC Educational Resources Information Center

Cvetek, Slavko

2008-01-01

In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…

Planning in Higher Education and Chaos Theory: A Model, a Method.

ERIC Educational Resources Information Center

Cutright, Marc

This paper proposes a model, based on chaos theory, that explores strategic planning in higher education. It notes that chaos theory was first developed in the physical sciences to explain how apparently random activity was, in fact, complexity patterned. The paper goes on to describe how chaos theory has subsequently been applied to the social…

Quantum jumps on Anderson attractors

NASA Astrophysics Data System (ADS)

Yusipov, I. I.; Laptyeva, T. V.; Ivanchenko, M. V.

2018-01-01

In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In a diffusive regime, statistics of quantum jumps is non-Poissonian and has a power-law interval, a footprint of intermittent locking in Anderson modes. Ballistic propagation reflects dispersion of an ordered lattice and introduces the second timescale for jumps, resulting in non-nonmonotonous probability distribution. Hermitian dephasing dissipation makes localization features vanish, and Poissonian jump statistics along with normal diffusion are recovered.

Path Entanglement of Continuous-Variable Quantum Microwaves

NASA Astrophysics Data System (ADS)

Menzel, E. P.; Deppe, F.; Eder, P.; Zhong, L.; Haeberlein, M.; Baust, A.; Hoffmann, E.; Marx, A.; Gross, R.; di Candia, R.; Solano, E.; Ballester, D.; Ihmig, M.; Inomata, K.; Yamamoto, T.; Nakamura, Y.

2013-03-01

Entanglement is a quantum mechanical phenomenon playing a key role in quantum communication and information processing protocols. Here, we report on frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two separated paths. In our experiment, we combine a squeezed and a vacuum state via a beam splitter. Overcoming the challenges imposed by the low photon energies in the microwave regime, we reconstruct the squeezed state and, independently from this, detect and quantify the produced entanglement via correlation measurements (E. P. Menzel et al., arXiv:1210.4413). Our work paves the way towards quantum communication and teleportation with continuous variables in the microwave regime. This work is supported by SFB 631, German Excellence Initiative via NIM, EU projects SOLID, CCQED and PROMISCE, MEXT Kakenhi ``Quantum Cybernetics'', JSPS FIRST Program, the NICT Commissioned Research, EPSRC EP/H050434/1, Basque Government IT472-10, and Spanish MICINN FIS2009-12773-C02-01.

Chaos in the classical mechanics of bound and quasi-bound HX-4He complexes with X = F, Cl, Br, CN.

PubMed

Gamboa, Antonio; Hernández, Henar; Ramilowski, Jordan A; Losada, J C; Benito, R M; Borondo, F; Farrelly, David

2009-10-01

The classical dynamics of weakly bound floppy van der Waals complexes have been extensively studied in the past except for the weakest of all, i.e., those involving He atoms. These complexes are of considerable current interest in light of recent experimental work focussed on the study of molecules trapped in small droplets of the quantum solvent (4)He. Despite a number of quantum investigations, details on the dynamics of how quantum solvation occurs remain unclear. In this paper, the classical rotational dynamics of a series of van der Waals complexes, HX-(4)He with X = F, Cl, Br, CN, are studied. In all cases, the ground state dynamics are found to be almost entirely chaotic, in sharp contrast to other floppy complexes, such as HCl-Ar, for which chaos sets in only at relatively high energies. The consequences of this result for quantum solvation are discussed. We also investigate rotationally excited states with J = 1 which, except for HCN-(4)He, are actually resonances that decay by rotational pre-dissociation.

Conduct problems, IQ, and household chaos: a longitudinal multi-informant study

PubMed Central

Deater-Deckard, Kirby; Mullineaux, Paula Y.; Beekman, Charles; Petrill, Stephen A.; Schatschneider, Chris; Thompson, Lee A.

2010-01-01

Background We tested the hypothesis that household chaos would be associated with lower child IQ and more child conduct problems concurrently and longitudinally over two years while controlling for housing conditions, parent education/IQ, literacy environment, parental warmth/negativity, and stressful events. Methods The sample included 302 families with same-sex twins (58% female) in Kindergarten/1st grade at the first assessment. Parents’ and observers’ ratings were gathered, with some collected over a two-year period. Results Chaos varied widely. There was substantial mother–father agreement and longitudinal stability. Chaos covaried with poorer housing conditions, lower parental education/IQ, poorer home literacy environment, higher stress, higher negativity and lower warmth. Chaos statistically predicted lower IQ and more conduct problems, beyond the effects of other home environment factors. Conclusions Even with other home environment factors controlled, higher levels of chaos were linked concurrently with lower child IQ, and concurrently and longitudinally with more child conduct problems. Parent self-reported chaos represents an important aspect of housing and family functioning, with respect to children’s cognitive and behavioral functioning. PMID:19527431

Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

PubMed

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

NASA Astrophysics Data System (ADS)

Liu, Hui; Jin, Cong

2017-03-01

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

The Butterfly and the Photon:. New Perspectives on Unpredictability, and the Notion of Casual Reality, in Quantum Physics

NASA Astrophysics Data System (ADS)

Palmer, T. N.

2012-12-01

This essay discusses a proposal that draws together the three great revolutionary theories of 20th Century physics: quantum theory, relativity theory and chaos theory. Motivated by the Bohmian notion of implicate order, and what in chaos theory would be described as a strange attractor, the proposal attributes special ontological significance to certain non-computable, dynamically invariant state-space geometries for the universe as a whole. Studying the phenomenon of quantum interference, it is proposed to understand quantum wave-particle duality, and indeed classical electromagnetism, in terms of particles in space time and waves on this state space geometry. Studying the EPR experiment, the acausal constraints that this invariant geometry provides on spatially distant degrees of freedom, provides a way for the underlying dynamics to be consistent with the Bell theorem, yet be relativistically covariant ("nonlocality without nonlocality"). It is suggested that the physical basis for such non-computable geometries lies in properties of gravity with the information irreversibility implied by black hole no-hair theorems being crucial. In conclusion it is proposed that quantum theory may be emergent from an extended theory of gravity which is geometric not only in space time, but also in state space. Such a notion would undermine most current attempts to "quantise gravity".

Changes in discharge dynamics under the constraints of local and global changes in the Chao Lake basin (China)

NASA Astrophysics Data System (ADS)

Chu, Y.; Salles, C.; Rodier, C.; Crès, F.-N.; Huang, L.; Tournoud, M.-G.

2012-04-01

Located on the Yangtze basin, the Chao Lake is the fifth largest freshwater lake in China and of great importance in terms of water resources and aquaculture. Its catchment (9130 km2) includes the city of Hefei and large extends of agricultural and rural areas. Fast changes are expected in land uses and agricultural practices for the future, due to the touristic appeal of the Chao Lake shore and the growth of the city of Hefei. Climate changes are also expected in this region, with a high impact on rainfall regime. The consequences of these changes on the sustainability of the water inflows into the lake are a major issue for the economical development of the Chao Lake area even though they are little-known. Our study aims to give tools for estimating such consequences, accounting for uncertainties in scenario data and model parameters. The dynamics of rivers flowing into the Chao Lake is not very well-known, except for the Fengle River. The Fengle catchment (1480 km2) is mainly rural. River discharges are recorded at Taoxi station, upstream its outlet into the lake. 20-year records of daily discharges are available. Nine rain gauges, with daily data, daily temperature and evapotranspiration data are also available. The current dynamics of the Fengle River is characterized in terms of flood frequencies on discharge-duration-frequency curves. The ATHYS freely available hydrological tool (www.athys-soft.org) is used to calibrate and validate a distributed model of the Fengle catchment. Four calibration runs are done on four independent 5-year discharge records. Four different sets of model parameters are discussed. The model is then run for validation. The uncertainties in model predictions are evaluated in terms of errors in the simulated discharges during the validation period, with regards to the 5-year period used for calibration. The model is then applied on scenarios of changes in land uses and climate. Uncertainties in scenarios of changes are estimated

The Chaos Theory of Careers: A User's Guide

ERIC Educational Resources Information Center

Bright, Jim E. H.; Pryor, Robert G. L.

2005-01-01

The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…

Filamentation instability in a quantum magnetized plasma

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

Bret, A.; and Instituto de Investigaciones Energeticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real

2008-02-15

The filamentation instability occurring when a nonrelativistic electron beam passes through a quantum magnetized plasma is investigated by means of a cold quantum magnetohydrodynamic model. It is proved that the instability can be completely suppressed by quantum effects if and only if a finite magnetic field is present. A dimensionless parameter is identified that measures the strength of quantum effects. Strong quantum effects allow for a much smaller magnetic field to suppress the instability than in the classical regime.

Jarzynski equality in PT-symmetric quantum mechanics

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-04-13

We show that the quantum Jarzynski equality generalizes to PT -symmetric quantum mechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

Order parameter fluctuations at a buried quantum critical point

PubMed Central

Feng, Yejun; Wang, Jiyang; Jaramillo, R.; van Wezel, Jasper; Haravifard, S.; Srajer, G.; Liu, Y.; Xu, Z.-A.; Littlewood, P. B.; Rosenbaum, T. F.

2012-01-01

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe2 at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface. PMID:22529348

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

NASA Technical Reports Server (NTRS)

Konkov, L. E.; Prants, S. V.

1996-01-01

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems

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

Akhmet, Marat, E-mail: marat@metu.edu.tr; Fen, Mehmet Onur; Rafatov, Ismail

2014-12-15

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases themore » potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].« less

Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences.

PubMed

Gärttner, Martin; Hauke, Philipp; Rey, Ana Maria

2018-01-26

Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimentally. In this work, we formally demonstrate that the multiple-quantum coherence spectra, a specific family of OTOCs well known in NMR, can be used as an entanglement witness and as a direct probe of multiparticle entanglement. Our results open a path to experimentally testing the fascinating idea that entanglement is the underlying glue that links thermodynamics, statistical mechanics, and quantum gravity.

Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences

NASA Astrophysics Data System (ADS)

Gärttner, Martin; Hauke, Philipp; Rey, Ana Maria

2018-01-01

Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimentally. In this work, we formally demonstrate that the multiple-quantum coherence spectra, a specific family of OTOCs well known in NMR, can be used as an entanglement witness and as a direct probe of multiparticle entanglement. Our results open a path to experimentally testing the fascinating idea that entanglement is the underlying glue that links thermodynamics, statistical mechanics, and quantum gravity.

Non-equilibrium quantum phase transition via entanglement decoherence dynamics

PubMed Central

Lin, Yu-Chen; Yang, Pei-Yun; Zhang, Wei-Min

2016-01-01

We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained. PMID:27713556

Home Chaos: Sociodemographic, Parenting, Interactional, and Child Correlates

ERIC Educational Resources Information Center

Dumas, Jean E.; Nissley, Jenelle; Nordstrom, Alicia; Smith, Emilie Phillips; Prinz, Ronald J.; Levine, Douglas W.

2005-01-01

We conducted 2 studies to (a) establish the usefulness of the construct of home chaos, (b) investigate its correlates, and (c) determine the validity of the Confusion, Hubbub, and Order Scale (CHAOS) used to measure the construct in each study. Study 1 relied on a sample of European American preschoolers and their mothers and Study 2 on a sample…

Broken selection rule in the quantum Rabi model

PubMed Central

Forn-Díaz, P.; Romero, G.; Harmans, C. J. P. M.; Solano, E.; Mooij, J. E.

2016-01-01

Understanding the interaction between light and matter is very relevant for fundamental studies of quantum electrodynamics and for the development of quantum technologies. The quantum Rabi model captures the physics of a single atom interacting with a single photon at all regimes of coupling strength. We report the spectroscopic observation of a resonant transition that breaks a selection rule in the quantum Rabi model, implemented using an LC resonator and an artificial atom, a superconducting qubit. The eigenstates of the system consist of a superposition of bare qubit-resonator states with a relative sign. When the qubit-resonator coupling strength is negligible compared to their own frequencies, the matrix element between excited eigenstates of different sign is very small in presence of a resonator drive, establishing a sign-preserving selection rule. Here, our qubit-resonator system operates in the ultrastrong coupling regime, where the coupling strength is 10% of the resonator frequency, allowing sign-changing transitions to be activated and, therefore, detected. This work shows that sign-changing transitions are an unambiguous, distinctive signature of systems operating in the ultrastrong coupling regime of the quantum Rabi model. These results pave the way to further studies of sign-preserving selection rules in multiqubit and multiphoton models. PMID:27273346

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Technical Reports Server (NTRS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Astrophysics Data System (ADS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-08-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Carr et al., 1998; Greenberg et al., 1999], or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 2000]. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Manifestation of resonance-related chaos in coupled Josephson junctions

NASA Astrophysics Data System (ADS)

Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.

2012-11-01

Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

Chaotic quantum ratchets and filters with cold atoms in optical lattices: Properties of Floquet states

NASA Astrophysics Data System (ADS)

Hur, Gwang-Ok

The -kicked rotor is a paradigm of quantum chaos. Its realisation with clouds of cold atoms in pulsed optical lattices demonstrated the well-known quantum chaos phenomenon of 'dynamical localisation'. In those experi ments by several groups world-wide, the £-kicks were applied at equal time intervals. However, recent theoretical and experimental work by the cold atom group at UCL Monteiro et al 2002, Jonckheere et al 2003, Jones et al 2004 showed that novel quantum and classical dynamics arises if the atomic cloud is pulsed with repeating sequences of unequally spaced kicks. In Mon teiro et al 2002 it was found that the energy absorption rates depend on the momentum of the atoms relative to the optical lattice hence a type of chaotic ratchet was proposed. In Jonckheere et al and Jones et al, a possible mechanism for selecting atoms according to their momenta (velocity filter) was investigated. The aim of this thesis was to study the properties of the underlying eigen values and eigenstates. Despite the unequally-spaced kicks, these systems are still time-periodic, so we in fact investigated the Floquet states, which are eigenstates of U(T), the one-period time evolution operator. The Floquet states and corresponding eigenvalues were obtained by diagonalising a ma trix representation of the operator U(T). It was found that the form of the eigenstates enables us to analyse qual itatively the atomic momentum probability distributions, N(p) measured experimentally. In particular, the momentum width of the individual eigen states varies strongly with < p > as expected from the theoretical and ex- perimental results obtained previously. In addition, at specific < p > close to values which in the experiment yield directed motion (ratchet transport), the probability distribution of the individual Floquet states is asymmetric, mirroring the asymmetric N(p) measured in clouds of cesium atoms. In the penultimate chapter, the spectral fluctuations (eigenvalue statis tics) are

Controlling Mackey-Glass chaos.

PubMed

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Controlling Mackey-Glass chaos

NASA Astrophysics Data System (ADS)

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Quantum synchronization of quantum van der Pol oscillators with trapped ions.

PubMed

Lee, Tony E; Sadeghpour, H R

2013-12-06

The van der Pol oscillator is the prototypical self-sustained oscillator and has been used to model nonlinear behavior in biological and other classical processes. We investigate how quantum fluctuations affect phase locking of one or many van der Pol oscillators. We find that phase locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for 171Yb+ achievable with current technology.

A Chaos MIMO-OFDM Scheme for Mobile Communication with Physical-Layer Security

NASA Astrophysics Data System (ADS)

Okamoto, Eiji

Chaos communications enable a physical-layer security, which can enhance the transmission security in combining with upper-layer encryption techniques, or can omit the upper-layer secure protocol and enlarges the transmission efficiency. However, the chaos communication usually degrades the error rate performance compared to unencrypted digital modulations. To achieve both physical-layer security and channel coding gain, we have proposed a chaos multiple-input multiple-output (MIMO) scheme in which a rate-one chaos convolution is applied to MIMO multiplexing. However, in the conventional study only flat fading is considered. To apply this scheme to practical mobile environments, i.e., multipath fading channels, we propose a chaos MIMO-orthogonal frequency division multi-plexing (OFDM) scheme and show its effectiveness through computer simulations.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Atlantis Chaos - False Color

NASA Image and Video Library

2014-12-23

The THEMIS VIS camera contains 5 filters. The data from different filters can be combined in multiple ways to create a false color image. This false color image from NASA 2001 Mars Odyssey spacecraft shows part of Atlantis Chaos.

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Developing Quality Preschool Movement Programs: CHAOS and KinderPlay

ERIC Educational Resources Information Center

Robert, Darren L.; Yongue, Bill

2004-01-01

This article presents two models for creating new developmentally appropriate preschool movement programs: CHAOS (Children Helping Adults Open Senses) at Eastern Connecticut State University and "KinderPlay" at Florida International University. CHAOS and KinderPlay utilize skill themes and movement concepts as their focus and incorporate…

Universality and Quantum Criticality of the One-Dimensional Spinor Bose Gas

NASA Astrophysics Data System (ADS)

PâÅ£u, Ovidiu I.; Klümper, Andreas; Foerster, Angela

2018-06-01

We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime, the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.

Single photon sources with single semiconductor quantum dots

NASA Astrophysics Data System (ADS)

Shan, Guang-Cun; Yin, Zhang-Qi; Shek, Chan Hung; Huang, Wei

2014-04-01

In this contribution, we briefly recall the basic concepts of quantum optics and properties of semiconductor quantum dot (QD) which are necessary to the understanding of the physics of single-photon generation with single QDs. Firstly, we address the theory of quantum emitter-cavity system, the fluorescence and optical properties of semiconductor QDs, and the photon statistics as well as optical properties of the QDs. We then review the localization of single semiconductor QDs in quantum confined optical microcavity systems to achieve their overall optical properties and performances in terms of strong coupling regime, efficiency, directionality, and polarization control. Furthermore, we will discuss the recent progress on the fabrication of single photon sources, and various approaches for embedding single QDs into microcavities or photonic crystal nanocavities and show how to extend the wavelength range. We focus in particular on new generations of electrically driven QD single photon source leading to high repetition rates, strong coupling regime, and high collection efficiencies at elevated temperature operation. Besides, new developments of room temperature single photon emission in the strong coupling regime are reviewed. The generation of indistinguishable photons and remaining challenges for practical single-photon sources are also discussed.

Quantum effects in energy and charge transfer in an artificial photosynthetic complex

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

Ghosh, Pulak Kumar; Smirnov, Anatoly Yu.; Nori, Franco

2011-06-28

We investigate the quantum dynamics of energy and charge transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex. This complex consists of six light-harvesting chromophores and an electron-acceptor fullerene. To describe quantum effects on a femtosecond time scale, we derive the set of exact non-Markovian equations for the Heisenberg operators of this photosynthetic complex in contact with a Gaussian heat bath. With these equations we can analyze the regime of strong system-bath interactions, where reorganization energies are of the order of the intersite exciton couplings. We show that the energy of the initially excited antenna chromophores is efficiently funneled tomore » the porphyrin-fullerene reaction center, where a charge-separated state is set up in a few picoseconds, with a quantum yield of the order of 95%. In the single-exciton regime, with one antenna chromophore being initially excited, we observe quantum beatings of energy between two resonant antenna chromophores with a decoherence time of {approx}100 fs. We also analyze the double-exciton regime, when two porphyrin molecules involved in the reaction center are initially excited. In this regime we obtain pronounced quantum oscillations of the charge on the fullerene molecule with a decoherence time of about 20 fs (at liquid nitrogen temperatures). These results show a way to directly detect quantum effects in artificial photosynthetic systems.« less

Gaussian private quantum channel with squeezed coherent states.

PubMed

Jeong, Kabgyun; Kim, Jaewan; Lee, Su-Yong

2015-09-14

While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime.

Specifying the Links Between Household Chaos and Preschool Children’s Development

PubMed Central

Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne

2011-01-01

Household chaos has been linked to poorer cognitive, behavioral, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120

Quantum simulation of transverse Ising models with Rydberg atoms

NASA Astrophysics Data System (ADS)

Schauss, Peter

2018-04-01

Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

[Chaos theory: a fascinating concept for oncologists].

PubMed

Denis, F; Letellier, C

2012-05-01

The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

Fractals and Chaos

DTIC Science & Technology

1991-06-01

22 C. AFFINE TRANSFORMATIONS OF THE PLANE ........................... 25 D. CONTRACTION MAPPINGS OF THE SPACE gi(X...Henri Poincare (1854-1912) knew about chaos in dynamical systems in the late nineteenth century. Additionally, the French mathematicians Pierre Fatou...portion) are presented in the Euclidean plane , with a brief mention of more abstract spaces where applicable. Mathematical proofs that can be

Quantum resonances in a single plaquette of Josephson junctions: excitations of Rabi oscillations

NASA Astrophysics Data System (ADS)

Fistul, M. V.

2002-03-01

We present a theoretical study of a quantum regime of the resistive (whirling) state of dc driven anisotropic single plaquette containing small Josephson junctions. The current-voltage characteristics of such systems display resonant steps that are due to the resonant interaction between the time dependent Josephson current and the excited electromagnetic oscillations (EOs). The voltage positions of the resonances are determined by the quantum interband transitions of EOs. We show that in the quantum regime as the system is driven on the resonance, coherent Rabi oscillations between the quantum levels of EOs occur. At variance with the classical regime the magnitude and the width of resonances are determined by the frequency of Rabi oscillations that in turn, depends in a peculiar manner on an externally applied magnetic field and the parameters of the system.

Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case

ERIC Educational Resources Information Center

Akmansoy, Vesile; Kartal, Sadik

2014-01-01

Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…

Error function attack of chaos synchronization based encryption schemes.

PubMed

Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

2004-03-01

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

PubMed Central

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

2015-01-01

Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

Single-molecule quantum dot as a Kondo simulator

NASA Astrophysics Data System (ADS)

Hiraoka, R.; Minamitani, E.; Arafune, R.; Tsukahara, N.; Watanabe, S.; Kawai, M.; Takagi, N.

2017-06-01

Structural flexibility of molecule-based systems is key to realizing the novel functionalities. Tuning the structure in the atomic scale enables us to manipulate the quantum state in the molecule-based system. Here we present the reversible Hamiltonian manipulation in a single-molecule quantum dot consisting of an iron phthalocyanine molecule attached to an Au electrode and a scanning tunnelling microscope tip. We precisely controlled the position of Fe2+ ion in the molecular cage by using the tip, and tuned the Kondo coupling between the molecular spins and the Au electrode. Then, we realized the crossover between the strong-coupling Kondo regime and the weak-coupling regime governed by spin-orbit interaction in the molecule. The results open an avenue to simulate low-energy quantum many-body physics and quantum phase transition through the molecular flexibility.

Generalized Entanglement Entropies of Quantum Designs.

PubMed

Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun

2018-03-30

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.

Generalized Entanglement Entropies of Quantum Designs

NASA Astrophysics Data System (ADS)

Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun

2018-03-01

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.

Quantum Gibbs ensemble Monte Carlo

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

Fantoni, Riccardo, E-mail: rfantoni@ts.infn.it; Moroni, Saverio, E-mail: moroni@democritos.it

We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.

The Application of Chaos Theory to the Career-Plateaued Worker.

ERIC Educational Resources Information Center

Duffy, Jean Ann

2000-01-01

Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)

A linear triple quantum dot system in isolated configuration

NASA Astrophysics Data System (ADS)

Flentje, Hanno; Bertrand, Benoit; Mortemousque, Pierre-André; Thiney, Vivien; Ludwig, Arne; Wieck, Andreas D.; Bäuerle, Christopher; Meunier, Tristan

2017-06-01

The scaling up of electron spin qubit based nanocircuits has remained challenging up till date and involves the development of efficient charge control strategies. Here, we report on the experimental realization of a linear triple quantum dot in a regime isolated from the reservoir. We show how this regime can be reached with a fixed number of electrons. Charge stability diagrams of the one, two, and three electron configurations where only electron exchange between the dots is allowed are observed. They are modeled with the established theory based on a capacitive model of the dot systems. The advantages of the isolated regime with respect to experimental realizations of quantum simulators and qubits are discussed. We envision that the results presented here will make more manipulation schemes for existing qubit implementations possible and will ultimately allow to increase the number of tunnel coupled quantum dots which can be simultaneously controlled.

Enhanced quantum spin fluctuations in a binary Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Bisset, R. N.; Kevrekidis, P. G.; Ticknor, C.

2018-02-01

For quantum fluids, the role of quantum fluctuations may be significant in several regimes such as when the dimensionality is low, the density is high, the interactions are strong, or for low particle numbers. In this paper, we propose a fundamentally different regime for enhanced quantum fluctuations without being restricted by any of the above conditions. Instead, our scheme relies on the engineering of an effective attractive interaction in a dilute, two-component Bose-Einstein condensate (BEC) consisting of thousands of atoms. In such a regime, the quantum spin fluctuations are significantly enhanced (atom bunching with respect to the noninteracting limit) since they act to reduce the interaction energy, a remarkable property given that spin fluctuations are normally suppressed (antibunching) at zero temperature. In contrast to the case of true attractive interactions, our approach is not vulnerable to BEC collapse. We numerically demonstrate that these quantum fluctuations are experimentally accessible by either spin or single-component Bragg spectroscopy, offering a useful platform on which to test beyond-mean-field theories. We also develop a variational model and use it to analytically predict the shift of the immiscibility critical point, finding good agreement with our numerics.

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

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

Sun Wei, E-mail: wsun@mathstat.concordia.ca; Zeng Yong, E-mail: zengy@umkc.edu; Zhang Shu, E-mail: zhangshuisme@hotmail.com

2013-06-15

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical schememore » based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.« less

Experimental characterization of pairwise correlations from triple quantum correlated beams generated by cascaded four-wave mixing processes

NASA Astrophysics Data System (ADS)

Wang, Wei; Cao, Leiming; Lou, Yanbo; Du, Jinjian; Jing, Jietai

2018-01-01

We theoretically and experimentally characterize the performance of the pairwise correlations from triple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The pairwise correlations between any two of the beams are theoretically calculated and experimentally measured. The experimental and theoretical results are in good agreement. We find that two of the three pairwise correlations can be in the quantum regime. The other pairwise correlation is always in the classical regime. In addition, we also measure the triple-beam correlation which is always in the quantum regime. Such unbalanced and controllable pairwise correlation structures may be taken as advantages in practical quantum communications, for example, hierarchical quantum secret sharing. Our results also open the way for the classification and application of quantum states generated from the cascaded FWM processes.

Predicting transport regime and local electrostatic environment from Coulomb blockade diamond sizes

NASA Astrophysics Data System (ADS)

Olsen, Stine T.; Hansen, Thorsten; Mikkelsen, Kurt V.

2017-03-01

Electron transport through a molecule is often described in one of the two regimes: the coherent tunnelling regime or the Coulomb blockade regime. The twilight zone of the two regimes still possesses many unsolved questions. A theoretical analysis of the oligophenylenevinylene OPV3 experiments by Bjørnholm and co-workers is performed. The experiments showed how two OPV3 derivatives performed very differently despite the strong similarity of the molecular structure, hence the experimental data showed two different transport mechanisms. The different transport mechanisms of the two OPV3 derivatives are explained from quantum mechanical calculations of the molecular redox energies and from the experimentally accessible window size.