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Sample records for mixed quantum classical

  1. Stereodynamics of chemical reactions: quasi-classical, quantum and mixed quantum-classical theories

    NASA Astrophysics Data System (ADS)

    Xu, Wenwu; Zhao, Guangjiu

    2012-04-01

    In this review, some benchmark works by Han and coworkers on the stereodynamics of typical chemical reactions, triatomic reactions H + D2, Cl + H2 and O + H2 and polyatomic reaction Cl+CH4/CD4, are presented by using the quasi-classical, quantum and mixed quantum-classical methods. The product alignment and orientation in these A+BC model reactions are discussed in detail. We have also compared our theoretical results with experimental measurements and demonstrated that our theoretical results are in good agreement with the experimental results. Quasi-classical trajectory (QCT) method ignores some quantum effects like the tunneling effect and zero-point energy. The quantum method will be very time-consuming. Moreover, the mixed quantum-classical method can take into account some quantum effects and hence is expected to be applicable to large systems and widely used in chemical stereodynamics studies.

  2. Classical-quantum mixing in the random 2-satisfiability problem

    NASA Astrophysics Data System (ADS)

    Potirniche, Ionut-Dragos; Laumann, C. R.; Sondhi, S. L.

    2015-10-01

    Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA, respectively, and they are believed to be intractable for both classical and quantum computers. Statistical ensembles of instances of these problems have been studied previously in an attempt to elucidate their typical, as opposed to worst-case, behavior. In this paper, we introduce a statistical ensemble that interpolates between classical and quantum. For the simplest 2-SAT-2-QSAT ensemble, we find the exact boundary that separates SAT and UNSAT instances. We do so by establishing coincident lower and upper bounds, in the limit of large instances, on the extent of the UNSAT and SAT regions, respectively.

  3. High-NOON states by mixing quantum and classical light.

    PubMed

    Afek, Itai; Ambar, Oron; Silberberg, Yaron

    2010-05-14

    Precision measurements can be brought to their ultimate limit by harnessing the principles of quantum mechanics. In optics, multiphoton entangled states, known as NOON states, can be used to obtain high-precision phase measurements, becoming more and more advantageous as the number of photons grows. We generated "high-NOON" states (N = 5) by multiphoton interference of quantum down-converted light with a classical coherent state in an approach that is inherently scalable. Super-resolving phase measurements with up to five entangled photons were produced with a visibility higher than that obtainable using classical light only.

  4. Mixed quantum-classical dynamics for charge transport in organics.

    PubMed

    Wang, Linjun; Prezhdo, Oleg V; Beljonne, David

    2015-05-21

    Charge transport plays a crucial role in the working principle of most opto-electronic and energy devices. This is especially true for organic materials where the first theoretical models date back to the 1950s and have continuously evolved ever since. Most of these descriptions rely on perturbation theory to treat small interactions in the Hamiltonian. In particular, applying a perturbative treatment to the electron-phonon and electron-electron coupling results in the band and hopping models, respectively, the signature of which is conveyed by a characteristic temperature dependence of mobility. This perspective describes recent progress of studying charge transport in organics using mixed quantum-classical dynamics techniques, including mean field and surface hopping theories. The studies go beyond the perturbation treatments and represent the processes explicitly in the time-domain, as they occur in real life. The challenges, advantages, and disadvantages of both approaches are systematically discussed. Special focus is dedicated to the temperature dependence of mobility, the role of local and nonlocal electron-phonon couplings, as well as the interplay between electronic and electron-phonon interactions.

  5. Classical-to-quantum transition with broadband four-wave mixing.

    PubMed

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

    2015-02-13

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

  6. Mixed quantum-classical versus full quantum dynamics: Coupled quasiparticle-oscillator system

    NASA Astrophysics Data System (ADS)

    Schanz, Holger; Esser, Bernd

    1997-05-01

    The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.

  7. Mixed quantum-classical equilibrium in global flux surface hopping

    SciTech Connect

    Sifain, Andrew E.; Wang, Linjun; Prezhdo, Oleg V.

    2015-06-14

    Global flux surface hopping (GFSH) generalizes fewest switches surface hopping (FSSH)—one of the most popular approaches to nonadiabatic molecular dynamics—for processes exhibiting superexchange. We show that GFSH satisfies detailed balance and leads to thermodynamic equilibrium with accuracy similar to FSSH. This feature is particularly important when studying electron-vibrational relaxation and phonon-assisted transport. By studying the dynamics in a three-level quantum system coupled to a classical atom in contact with a classical bath, we demonstrate that both FSSH and GFSH achieve the Boltzmann state populations. Thermal equilibrium is attained significantly faster with GFSH, since it accurately represents the superexchange process. GFSH converges closer to the Boltzmann averages than FSSH and exhibits significantly smaller statistical errors.

  8. Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach

    SciTech Connect

    Antipov, Sergey V.; Ye, Ziyu; Ananth, Nandini

    2015-05-14

    We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.

  9. Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach.

    PubMed

    Antipov, Sergey V; Ye, Ziyu; Ananth, Nandini

    2015-05-14

    We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors. PMID:25978878

  10. Analysis of the forward-backward trajectory solution for the mixed quantum-classical Liouville equation.

    PubMed

    Hsieh, Chang-Yu; Kapral, Raymond

    2013-04-01

    Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [C.-Y. Hsieh and R. Kapral, J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forward-backward trajectory solution, is analyzed and tested in detail and its various implementations are discussed. PMID:23574211

  11. Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory.

    PubMed

    Semenov, Alexander; Babikov, Dmitri

    2014-01-16

    For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

  12. Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

    NASA Astrophysics Data System (ADS)

    Schubert, Alexander; Falvo, Cyril; Meier, Christoph

    2016-08-01

    We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.

  13. Tunneling dynamics with a mixed quantum-classical method: Quantum corrected propagator combined with frozen Gaussian wave packets

    SciTech Connect

    Gelman, David; Schwartz, Steven D.

    2008-07-14

    The recently developed mixed quantum-classical propagation method is extended to treat tunneling effects in multidimensional systems. Formulated for systems consisting of a quantum primary part and a classical bath of heavier particles, the method employs a frozen Gaussian description for the bath degrees of freedom, while the dynamics of the quantum subsystem is governed by a corrected propagator. The corrections are defined in terms of matrix elements of zeroth-order propagators. The method is applied to a model system of a double-well potential bilinearly coupled to a harmonic oscillator. The extension of the method, which includes nondiagonal elements of the correction propagator, enables an accurate treatment of tunneling in an antisymmetric double-well potential.

  14. Recent Advances in Development and Applications of the Mixed Quantum/Classical Theory for Inelastic Scattering.

    PubMed

    Babikov, Dmitri; Semenov, Alexander

    2016-01-28

    A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies. PMID:26618533

  15. Recent Advances in Development and Applications of the Mixed Quantum/Classical Theory for Inelastic Scattering.

    PubMed

    Babikov, Dmitri; Semenov, Alexander

    2016-01-28

    A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies.

  16. Multipartite quantum and classical correlations in symmetric n-qubit mixed states

    NASA Astrophysics Data System (ADS)

    Giorgi, Gian Luca; Campbell, Steve

    2016-08-01

    We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed n-qubit density matrices. We show that the existence of symmetries greatly reduces the amount of free parameters to be optimized in order to find the optimal measurement that minimizes the conditional entropy in the discord calculation. We apply this approach to the states exhibited dynamically during a thermodynamic protocol to extract maximum work. We also apply the symmetry criterion to a wide class of physically relevant cases of spatially homogeneous noise over multipartite entangled states. Exploiting symmetries we are able to calculate the non-local and genuine quantum features of these states and note some interesting properties.

  17. A mixed quantum-classical description of excitation energy transfer in supramolecular complexes: Förster theory and beyond.

    PubMed

    Megow, Jörg; Röder, Beate; Kulesza, Alexander; Bonačić-Koutecký, Vlasta; May, Volkhard

    2011-02-25

    Electronic excitation energy transfer (EET) is described theoretically for the chromophore complex P(4) formed by a butanediamine dendrimer to which four pheophorbide-a molecules are covalently linked. To achieve a description with atomic resolution, and to account for the effect of an ethanol solvent, a mixed quantum-classical methodology is utilized. Room-temperature molecular dynamics simulations are used to describe the nuclear dynamics, and EET is accounted for in utilizing a mixed quantum-classical formulation of the transition rates. Therefore, the full quantum expression of the EET rates is given and the change to a mixed quantum-classical version is briefly explained. The description results in the calculation of transition rates which coincide rather satisfactory with available experimental data on P(4). It is also shown that different assumptions of classical Förster theory are not valid for P(4). The temporal behavior of EET deduced from the rate equations is confronted with that following from the solution of the time-dependent Schrödinger equation entering the mixed quantum-classical description of EET. From this we can conclude that EET in flexible chromophore complexes such as P(4) can be rather satisfactory estimated by single transition rates. A correct description, however, is only achievable by using a sufficiently large set of rates that correspond to the various possible equilibrium configurations of the complex.

  18. Quantum computing classical physics.

    PubMed

    Meyer, David A

    2002-03-15

    In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.

  19. Rotational quenching of H{sub 2}O by He: Mixed quantum/classical theory and comparison with quantum results

    SciTech Connect

    Ivanov, Mikhail; Dubernet, Marie-Lise; Babikov, Dmitri

    2014-04-07

    The mixed quantum/classical theory (MQCT) formulated in the space-fixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the full-quantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm{sup −1}, while the other shows up at energies above 500 cm{sup −1}. Namely, when the collision energy E is below the state-to-state transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the average-velocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient body-fixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the full-quantum results almost everywhere through four-orders-of-magnitude range of collision energies, except near resonances, where the errors are somewhat larger.

  20. Rotational quenching of H2O by He: mixed quantum/classical theory and comparison with quantum results.

    PubMed

    Ivanov, Mikhail; Dubernet, Marie-Lise; Babikov, Dmitri

    2014-04-01

    The mixed quantum/classical theory (MQCT) formulated in the space-fixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the full-quantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm(-1), while the other shows up at energies above 500 cm(-1). Namely, when the collision energy E is below the state-to-state transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the average-velocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient body-fixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the full-quantum results almost everywhere through four-orders-of-magnitude range of collision energies, except near resonances, where the errors are somewhat larger.

  1. A test of the possibility of calculating absorption spectra by mixed quantum-classical methods

    NASA Astrophysics Data System (ADS)

    Haug, Kenneth; Metiu, Horia

    1992-10-01

    Some of the most efficient methods for studying systems having a large number of degrees of freedom treat a few degrees of freedom quantum mechanically and the remainder classically. Here we examine how these methods fare when used to calculate the cross section for photon absorption by a quantum system imbedded in a medium. To test the method, we study a model which has two degrees of freedom and mimicks the properties of a one-dimensional alkali atom-He dimer. We treat the electron motion quantum mechanically and the distance between the He atom and the alkali ion classically. Light absorption occurs because the electron is coupled to radiation. The calculation of the absorption cross section by quantum-classical methods fails rather dramatically-at certain frequencies, the absorption coefficient is negative. By comparing with exact quantum calculations, we show that this failure takes place because the time evolution of the classical variables influences the dynamics of the quantum degree of freedom through the Hamiltonian only; important information, which a fully quantum treatment would put in the wave function, is missing. To repair this flaw, we experiment with a method which uses a swarm of classical trajectories to generate a ``classical wave function.'' The results are encouraging, but require substantial computer time when the number of classical variables is large. We argue that in the limit of many classical degrees of freedom, accurate calculations can be performed by using the time-dependent Hartree method and treating some degrees of freedom by exact numerical methods (e.g., a fast Fourier transform procedure) and the others by Gaussian wave packets or any other propagation method that is accurate for a very short time. This procedure leads to a simple time domain picture of dephasing and line broadening in the case of a localized quantum system imbedded in a medium with heavy atoms.

  2. On the equivalence between non-factorizable mixed-strategy classical games and quantum games

    PubMed Central

    Iqbal, Azhar; Chappell, James M.; Abbott, Derek

    2016-01-01

    A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a non-factorizable game and determine the limitations of our approach. PMID:26909174

  3. Randomness: Quantum versus classical

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2016-05-01

    Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).

  4. Mixed quantum classical calculation of proton transfer reaction rates: From deep tunneling to over the barrier regimes

    SciTech Connect

    Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang

    2014-05-07

    We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of non-adiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the non-adiabatic transmission coefficients. It is found that the two-surface Landau-Zener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the Landau-Zener formula.

  5. Mixed quantum-classical dynamics with time-dependent external fields: A time-dependent density-functional-theory approach

    SciTech Connect

    Tavernelli, Ivano; Curchod, Basile F. E.; Rothlisberger, Ursula

    2010-05-15

    A mixed quantum-classical method aimed at the study of nonadiabatic dynamics in the presence of external electromagnetic fields is developed within the framework of time-dependent density functional theory. To this end, we use a trajectory-based description of the quantum nature of the nuclear degrees of freedom according to Tully's fewest switches trajectories surface hopping, where both the nonadiabatic coupling elements between the different potential energy surfaces, and the coupling with the external field are given as functionals of the ground-state electron density or, equivalently, of the corresponding Kohn-Sham orbitals. The method is applied to the study of the photodissociation dynamics of some simple molecules in gas phase.

  6. Mixed quantum-classical simulations of charge transport in organic materials: Numerical benchmark of the Su-Schrieffer-Heeger model

    SciTech Connect

    Wang Linjun; Beljonne, David; Chen Liping; Shi Qiang

    2011-06-28

    The electron-phonon coupling is critical in determining the intrinsic charge carrier and exciton transport properties in organic materials. In this study, we consider a Su-Schrieffer-Heeger (SSH) model for molecular crystals, and perform numerical benchmark studies for different strategies of simulating the mixed quantum-classical dynamics. These methods, which differ in the selection of initial conditions and the representation used to solve the time evolution of the quantum carriers, are shown to yield similar equilibrium diffusion properties. A hybrid approach combining molecular dynamics simulations of nuclear motion and quantum-chemical calculations of the electronic Hamiltonian at each geometric configuration appears as an attractive strategy to model charge dynamics in large size systems ''on the fly,'' yet it relies on the assumption that the quantum carriers do not impact the nuclear dynamics. We find that such an approximation systematically results in overestimated charge-carrier mobilities, with the associated error being negligible when the room-temperature mobility exceeds {approx}4.8 cm{sup 2}/Vs ({approx}0.14 cm{sup 2}/Vs) in one-dimensional (two-dimensional) crystals.

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

    SciTech Connect

    Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu

    2014-08-28

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

  8. Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2.

    PubMed

    Semenov, Alexander; Babikov, Dmitri

    2016-06-01

    Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.

  9. The role of solvent structure in the absorption spectrum of solvated electrons: Mixed quantum/classical simulations in tetrahydrofuran

    NASA Astrophysics Data System (ADS)

    Bedard-Hearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.

    2005-04-01

    In polar fluids such as water and methanol, the peak of the solvated electron's absorption spectrum in the red has been assigned as a sum of transitions between an s-like ground state and three nearly degenerate p-like excited states bound in a quasispherical cavity. In contrast, in weakly polar solvents such as tetrahydrofuran (THF), the solvated electron has an absorption spectrum that peaks in the mid-infrared, but no definitive assignment has been offered about the origins of the spectrum or the underlying structure. In this paper, we present the results of adiabatic mixed quantum/classical molecular dynamic simulations of the solvated electron in THF, and provide a detailed explanation of the THF-solvated electron's absorption spectrum and electronic structure. Using a classical solvent model and a fully quantum mechanical excess electron, our simulations show that although the ground and first excited states are bound in a quasispherical cavity, a multitude of other, nearby solvent cavities support numerous, nearly degenerate, bound excited states that have little Franck-Condon overlap with the ground state. We show that these solvent cavities, which are partially polarized so that they act as electron trapping sites, are an inherent property of the way THF molecules pack in the liquid. The absorption spectrum is thus assigned to a sum of bound-to-bound transitions between a localized ground state and multiple disjoint excited states scattered throughout the fluid. Furthermore, we find that the usual spherical harmonic labels (e.g., s-like, p-like) are not good descriptors of the excited-state wave functions of the solvated electron in THF. Our observation of multiple disjoint excited states is consistent with femtosecond pump-probe experiments in the literature that suggest that photoexcitation of solvated electrons in THF causes them to relocalize into solvent cavities far from where they originated.

  10. Computational quantum-classical boundary of noisy commuting quantum circuits.

    PubMed

    Fujii, Keisuke; Tamate, Shuhei

    2016-01-01

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

  11. Computational quantum-classical boundary of noisy commuting quantum circuits

    NASA Astrophysics Data System (ADS)

    Fujii, Keisuke; Tamate, Shuhei

    2016-05-01

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

  12. Computational quantum-classical boundary of noisy commuting quantum circuits

    PubMed Central

    Fujii, Keisuke; Tamate, Shuhei

    2016-01-01

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

  13. Time, classical and quantum

    NASA Astrophysics Data System (ADS)

    Aniello, P.; Ciaglia, F. M.; Di Cosmo, F.; Marmo, G.; Pérez-Pardo, J. M.

    2016-10-01

    We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator T with a suitable real-valued function T on the space of physical states. The proper characterization of the function T relies on a particular relation with the dynamical evolution of the system rather than with the infinitesimal generator of the dynamics (Hamiltonian). We first consider the case of classical hamiltonian mechanics, where observables are functions on phase space and the tools of differential geometry can be applied. The idea is then extended to the case of the unitary evolution of pure states of finite-level quantum systems by means of the geometric formulation of quantum mechanics. It is found that T is a function on the space of pure states which is not associated with any self-adjoint operator. The link between T and the dynamical evolution is interpreted as defining a simultaneity relation for the states of the system with respect to the dynamical evolution itself. It turns out that different dynamical evolutions lead to different notions of simultaneity, i.e., the notion of simultaneity is a dynamical notion.

  14. Quantum Computing's Classical Problem, Classical Computing's Quantum Problem

    NASA Astrophysics Data System (ADS)

    Van Meter, Rodney

    2014-08-01

    Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.

  15. Quantum money with classical verification

    SciTech Connect

    Gavinsky, Dmitry

    2014-12-04

    We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries - this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it.

  16. Ro-vibrational quenching of CO (v = 1) by He impact in a broad range of temperatures: A benchmark study using mixed quantum/classical inelastic scattering theory.

    PubMed

    Semenov, Alexander; Ivanov, Mikhail; Babikov, Dmitri

    2013-08-21

    The mixed quantum/classical approach is applied to the problem of ro-vibrational energy transfer in the inelastic collisions of CO(v = 1) with He atom, in order to predict the quenching rate coefficient in a broad range of temperatures 5 < T < 2500 K. Scattering calculations are done in two different ways: direct calculations of quenching cross sections and, alternatively, calculations of the excitation cross sections plus microscopic reversibility. In addition, a symmetrized average-velocity method of Billing is tried. Combination of these methods allows reproducing experiment in a broad range of temperatures. Excellent agreement with experiment is obtained at 400 < T < 2500 K (within 10%), good agreement in the range 100 < T < 400 K (within 25%), and semi-quantitative agreement at 40 < T < 100 K(within a factor of 2). This study provides a stringent test of the mixed quantum/classical theory, because the vibrational quantum in CO molecule is rather large and the quencher is very light (He atom). For heavier quenchers and closer to dissociation limit of the molecule, the mixed quantum/classical theory is expected to work even better.

  17. Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

    PubMed

    Semenov, Alexander; Babikov, Dmitri

    2015-12-17

    The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

  18. Classical randomness in quantum measurements

    NASA Astrophysics Data System (ADS)

    Mauro D'Ariano, Giacomo; Lo Presti, Paoloplacido; Perinotti, Paolo

    2005-07-01

    Similarly to quantum states, also quantum measurements can be 'mixed', corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies give optimal apparatuses that are indecomposable. Mathematically the problem is posed describing each measuring apparatus by a positive operator-valued measure (POVM), which gives the statistics of the outcomes for any input state. The POVMs form a convex set, and in this language the indecomposable apparatuses are represented by extremal points—the analogous of 'pure states' in the convex set of states. Differently from the case of states, however, indecomposable POVMs are not necessarily rank-one, e.g. von Neumann measurements. In this paper we give a complete classification of indecomposable apparatuses (for discrete spectrum), by providing different necessary and sufficient conditions for extremality of POVMs, along with a simple general algorithm for the decomposition of a POVM into extremals. As an interesting application, 'informationally complete' measurements are analysed in this respect. The convex set of POVMs is fully characterized by determining its border in terms of simple algebraic properties of the corresponding POVMs.

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

    NASA Astrophysics Data System (ADS)

    Kahros, Argyris

    Incorporating quantum mechanics into an atomistic simulation necessarily involves solving the Schrodinger equation. Unfortunately, the computational expense associated with solving this equation scales miserably with the number of included quantum degrees of freedom (DOF). The situation is so dire, in fact, that a molecular dynamics (MD) simulation cannot include more than a small number of quantum DOFs before it becomes computationally intractable. Thus, if one were to simulate a relatively large system, such as one containing several hundred atoms or molecules, it would be unreasonable to attempt to include the effects of all of the electrons associated with all of the components of the system. The mixed quantum/classical (MQC) approach provides a way to circumvent this issue. It involves treating the vast majority of the system classically, which incurs minimal computational expense, and reserves the consideration of quantum mechanical effects for only the few degrees of freedom more directly involved in the chemical phenomenon being studied. For example, if one were to study the bonding of a single diatomic molecule in the gas phase, one could employ a MQC approach by treating the nuclei of the molecule's two atoms classically---including the deeply bound, low-energy electrons that change relatively little---and solving the Schrodinger equation only for the high energy electron(s) directly involved in the bonding of the classical cores. In such a way, one could study the bonding of this molecule in a rigorous fashion while treating only the directly related degrees of freedom quantum mechanically. Pseudopotentials are then responsible for dictating the interactions between the quantum and classical degrees of freedom. As these potentials are the sole link between the quantum and classical DOFs, their proper development is of the utmost importance. This Thesis is concerned primarily with my work on the development of novel, rigorous and dynamical

  20. Non-classical light for quantum information

    NASA Astrophysics Data System (ADS)

    Goldschmidt, Elizabeth Anne

    Non-classical light is both easily encoded with quantum information and robust against decoherence, making it a key resource that enables many quantum information applications including quantum computing, quantum communication, and quantum metrology. We present a wide range of experimental and theoretical research toward the generation, detection, characterization, and storage of non-classical states of light with an eye toward quantum information applications. To provide a basis for the rest of the work, we begin by discussing theoretically the role of photon number statistics in optical quantum information and the use of second-order optical coherence to characterize non-classical light. Building on that, we present an original tool for the difficult problem of reconstructing the underlying mode distribution of multi-mode optical fields using simple measurements of higher-order optical coherence. We then move on to the problem of generating and storing single photons. We do this in a solid-state medium, a rare-earth ion-doped crystal, with a long-lived spin transition ideal for storing quantum information. We experimentally demonstrate the feasibility of this concept by showing correlations between the optical fields that herald storage and retrieval of collective excitations. This scheme can be used for the two important and distinct applications of generating single photons on-demand and storing quantum information and entanglement. The detection of non-classical light is a task as important as its generation. To this end, we study detectors with near unity detection efficiency and photon number resolution for use in quantum-enabled metrology. We use such a detector to experimentally demonstrate compression of spatial fringes and investigate the possibility of improving measurement resolution with classical and non-classical light. Finally, we report a set of experiments using photon number statistics to characterize classical and non-classical light. We

  1. Classical command of quantum systems.

    PubMed

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

    2013-04-25

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

  2. Classical command of quantum systems.

    PubMed

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

    2013-04-25

    Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics. PMID:23619692

  3. Quantum localization of classical mechanics

    NASA Astrophysics Data System (ADS)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-07-01

    Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

  4. Classical communication cost of quantum steering

    NASA Astrophysics Data System (ADS)

    Sainz, Ana Belén; Aolita, Leandro; Brunner, Nicolas; Gallego, Rodrigo; Skrzypczyk, Paul

    2016-07-01

    Quantum steering is observed when performing appropriate local measurements on an entangled state. Here we discuss the possibility of simulating classically this effect, using classical communication instead of entanglement. We show that infinite communication is necessary for exactly simulating steering for any pure entangled state, as well as for a class of mixed entangled states. Moreover, we discuss the communication cost of steering for general entangled states, as well as approximate simulation. Our findings reveal striking differences between Bell nonlocality and steering and provide a natural way of measuring the strength of the latter.

  5. Quantum fields with classical perturbations

    SciTech Connect

    Dereziński, Jan

    2014-07-15

    The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 1/2 fermions, both neutral and charged. Beside free theories, we study their interactions with classical perturbations, called, depending on the context, an external linear source, mass-like term, current or electromagnetic potential. The notes may serve as a first introduction to QFT.

  6. Quantum remnants in the classical limit

    NASA Astrophysics Data System (ADS)

    Kowalski, A. M.; Plastino, A.

    2016-09-01

    We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semi-classic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantum-classic transition. The so-called mutual information is the appropriate quantifier for this task. Additionally, we study the Bandt-Pompe's symbolic patterns that characterize dynamical time series (representative of the semi-classical system under scrutiny) in their evolution towards the classical limit.

  7. Classical Concepts in Quantum Programming

    NASA Astrophysics Data System (ADS)

    Ömer, Bernhard

    2005-07-01

    The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the increasing hardware complexity and fully exploit its potential. This paper investigates, how classical concepts like hardware abstraction, hierarchical programs, data types, memory management, flow of control, and structured programming can be used in quantum computing. The experimental language QCL will be introduced as an example, how elements like irreversible functions, local variables, and conditional branching, which have no direct quantum counterparts, can be implemented, and how nonclassical features like the reversibility of unitary transformation or the nonobservability of quantum states can be accounted for within the framework of a procedural programming language.

  8. Classical analog of quantum phase

    SciTech Connect

    Ord, G.N.

    1992-07-01

    A modified version of the Feynman relativistic chessboard model (FCM) is investigated in which the paths involved are spirals in the space-time. Portions of the paths in which the particle`s proper time is reversed are interpreted in terms of antiparticles. With this intepretation the particle-antiparticle field produced by such trajectories provides a classical analog of the phase associated with particle paths in the unmodified FCM. It is shwon that in the nonrelativistic limit the resulting kernel is the correct Dirac propagator and that particle-antiparticle symmetry is in this case responsible for quantum interference. 7 refs., 3 figs.

  9. Moving solvated electrons with light: Nonadiabatic mixed quantum/classical molecular dynamics simulations of the relocalization of photoexcited solvated electrons in tetrahydrofuran (THF)

    SciTech Connect

    Bedard-Hearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.

    2006-11-21

    Motivated by recent ultrafast spectroscopic experiments [Martini et al., Science 293, 462 (2001)], which suggest that photoexcited solvated electrons in tetrahydrofuran (THF) can relocalize (that is, return to equilibrium in solvent cavities far from where they started), we performed a series of nonequilibrium, nonadiabatic, mixed quantum/classical molecular dynamics simulations that mimic one-photon excitation of the THF-solvated electron. We find that as photoexcited THF-solvated electrons relax to their ground states either by continuous mixing from the excited state or via nonadiabatic transitions, {approx}30% of them relocalize into cavities that can be over 1 nm away from where they originated, in close agreement with the experiments. A detailed investigation shows that the ability of excited THF-solvated electrons to undergo photoinduced relocalization stems from the existence of preexisting cavity traps that are an intrinsic part of the structure of liquid THF. This explains why solvated electrons can undergo photoinduced relocalization in solvents like THF but not in solvents like water, which lack the preexisting traps necessary to stabilize the excited electron in other places in the fluid. We also find that even when they do not ultimately relocalize, photoexcited solvated electrons in THF temporarily visit other sites in the fluid, explaining why the photoexcitation of THF-solvated electrons is so efficient at promoting recombination with nearby scavengers. Overall, our study shows that the defining characteristic of a liquid that permits the photoassisted relocalization of solvated electrons is the existence of nascent cavities that are attractive to an excess electron; we propose that other such liquids can be found from classical computer simulations or neutron diffraction experiments.

  10. Classical Mechanics as Nonlinear Quantum Mechanics

    SciTech Connect

    Nikolic, Hrvoje

    2007-12-03

    All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.

  11. Secure quantum communication using classical correlated channel

    NASA Astrophysics Data System (ADS)

    Costa, D.; de Almeida, N. G.; Villas-Boas, C. J.

    2016-07-01

    We propose a secure protocol to send quantum information from one part to another without a quantum channel. In our protocol, which resembles quantum teleportation, a sender (Alice) and a receiver (Bob) share classical correlated states instead of EPR ones, with Alice performing measurements in two different bases and then communicating her results to Bob through a classical channel. Our secure quantum communication protocol requires the same amount of classical bits as the standard quantum teleportation protocol. In our scheme, as in the usual quantum teleportation protocol, once the classical channel is established in a secure way, a spy (Eve) will never be able to recover the information of the unknown quantum state, even if she is aware of Alice's measurement results. Security, advantages, and limitations of our protocol are discussed and compared with the standard quantum teleportation protocol.

  12. Secure quantum communication using classical correlated channel

    NASA Astrophysics Data System (ADS)

    Costa, D.; de Almeida, N. G.; Villas-Boas, C. J.

    2016-10-01

    We propose a secure protocol to send quantum information from one part to another without a quantum channel. In our protocol, which resembles quantum teleportation, a sender (Alice) and a receiver (Bob) share classical correlated states instead of EPR ones, with Alice performing measurements in two different bases and then communicating her results to Bob through a classical channel. Our secure quantum communication protocol requires the same amount of classical bits as the standard quantum teleportation protocol. In our scheme, as in the usual quantum teleportation protocol, once the classical channel is established in a secure way, a spy (Eve) will never be able to recover the information of the unknown quantum state, even if she is aware of Alice's measurement results. Security, advantages, and limitations of our protocol are discussed and compared with the standard quantum teleportation protocol.

  13. Open quantum dots—probing the quantum to classical transition

    NASA Astrophysics Data System (ADS)

    Ferry, D. K.; Burke, A. M.; Akis, R.; Brunner, R.; Day, T. E.; Meisels, R.; Kuchar, F.; Bird, J. P.; Bennett, B. R.

    2011-04-01

    Quantum dots provide a natural system in which to study both quantum and classical features of transport. As a closed testbed, they provide a natural system with a very rich set of eigenstates. When coupled to the environment through a pair of quantum point contacts, each of which passes several modes, the original quantum environment evolves into a set of decoherent and coherent states, which classically would compose a mixed phase space. The manner of this breakup is governed strongly by Zurek's decoherence theory, and the remaining coherent states possess all the properties of his pointer states. These states are naturally studied via traditional magnetotransport at low temperatures. More recently, we have used scanning gate (conductance) microscopy to probe the nature of the coherent states, and have shown that families of states exist through the spectrum in a manner consistent with quantum Darwinism. In this review, we discuss the nature of the various states, how they are formed, and the signatures that appear in magnetotransport and general conductance studies.

  14. A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics.

    PubMed

    Yamada, Atsushi; Okazaki, Susumu

    2008-01-28

    We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.

  15. Mixed quantum-classical dynamics of an amide-I vibrational excitation in a protein α -helix

    NASA Astrophysics Data System (ADS)

    Freedman, Holly; Martel, Paulo; Cruzeiro, Leonor

    2010-11-01

    Adenosine triphosphate (ATP) is known to be the main energy currency of the living cell, and is used as a coenzyme to generate energy for many cellular processes through hydrolysis to adenosine diphosphate (ADP), although the mechanism of energy transfer is not well understood. It has been proposed that following hydrolysis of the ATP cofactor bound to a protein, up to two quanta of amide-I vibrational energy are excited and utilized to bring about important structural changes in the protein. To study whether, and how, amide-I vibrational excitations are capable of leading to protein structural changes, we have added components arising from quantum-mechanical amide-I vibrational excitations to the total energy and force terms within a molecular-dynamics simulation. This model is applied to helical deca-alanine as a test case to investigate how its dynamics differs in the presence or absence of an amide-I excitation. We find that the presence of an amide-I excitation can bias the structure toward a more helical state.

  16. Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

    SciTech Connect

    Semenov, Alexander; Babikov, Dmitri

    2013-11-07

    We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

  17. Vibrational energy relaxation of a hydrogen-bonded complex dissolved in a polar liquid via the mixed quantum-classical Liouville method.

    PubMed

    Hanna, Gabriel; Geva, Eitan

    2008-04-01

    The vibrational energy relaxation (VER) of the hydrogen stretch in a linear hydrogen-bonded complex dissolved in a polar solvent is studied. The study is based on the Azzouz-Borgis model [Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361], which is known to account for many important features of real hydrogen-bonded systems, including ionic-to-covalent tautomerism and a broad distribution of hydrogen stretch frequencies. A description of VER in this strongly coupled system is considered, which consists of the following three consecutive steps: (1) solvation on the adiabatic excited vibrational surface; (2) nonadiabatic transition from the excited to the ground adiabatic vibrational surface; and (3) solvation on the adiabatic ground vibrational surface. The relaxation dynamics during those three steps were simulated via the mixed quantum-classical Liouville method, where the hydrogen is treated quantum-mechanically, while the other particles are treated in a classical-like manner. The solvation on the excited-state surface was found to occur rapidly ( approximately 0.5 ps) and to involve energy exchange with both the intramolecular and intermolecular degrees of freedom. It was also found that, while energy is released to the solvent during the solvation of the covalent tautomer, the solvation of the ionic tautomer involves absorption of energy from the solvent. The decrease in the transition frequency during the solvation process also facilitates the nonadiabatic transitions, which occur rapidly ( approximately 0.8 ps) thereafter. The nonadiabatic transitions were shown to be induced by interactions with a large number of solvent molecules and to be relatively insensitive to their location relative to the complex. Finally, solvation on the ground-state surface was seen to occur on a time scale of approximately 1.0 ps and leads to nonequilibrium ionic and covalent subpopulations. Equilibration on the ground-state surface occurs on a significantly slower time scale

  18. From quantum ladder climbing to classical autoresonance

    SciTech Connect

    Marcus, G.; Friedland, L.; Zigler, A.

    2004-01-01

    The autoresonance phenomenon allows excitation of a classical, oscillatory nonlinear system to high energies by using a weak, chirped frequency forcing. Ladder climbing is its counterpart in quantum mechanics. Here, for the first time to our knowledge, conditions for the transition from the quantum to the classical regimes are outlined. The similarities and differences between the two approaches are presented.

  19. Dynamics in the quantum/classical limit based on selective use of the quantum potential

    SciTech Connect

    Garashchuk, Sophya Dell’Angelo, David; Rassolov, Vitaly A.

    2014-12-21

    A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.

  20. Quantum entanglement capacity with classical feedback

    NASA Astrophysics Data System (ADS)

    Leung, Alan W.

    2008-01-01

    For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback (EB) , and we show that this quantity lies between two other well-studied quantities. These two quantities—namely the quantum capacity assisted by two-way classical communication (Q2) and the quantum capacity with classical feedback (QB) —are widely conjectured to be different: There exists a quantum discrete memoryless channel for which Q2>QB . We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly defined quantity of the quantum depolarizing channel, and illustrate with the repetition code and Shor code. We contrast the present notion with entanglement purification protocols by showing that, whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned repetition code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any EB protocols. We then apply this formula to the EB protocols that we discuss to obtain lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel.

  1. A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

    SciTech Connect

    Rekik, Najeh; Freedman, Holly; Hanna, Gabriel; Hsieh, Chang-Yu

    2013-04-14

    We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings

  2. A mixed quantum-classical molecular dynamics study of the hydroxyl stretch in methanol/carbon tetrachloride mixtures III: nonequilibrium hydrogen-bond dynamics and infrared pump-probe spectra.

    PubMed

    Kwac, Kijeong; Geva, Eitan

    2013-06-27

    We present a mixed quantum-classical molecular dynamics study of the nonequilibrium hydrogen-bond dynamics following vibrational energy relaxation of the hydroxyl stretch in a 10 mol % methanol/carbon tetrachloride mixture and pure methanol. The ground and first-excited energy levels and wave functions are identified with the eigenvalues and eigenfunctions of the hydroxyl's adiabatic Hamiltonian and as such depend parametrically on the configuration of the remaining, classically treated, degrees of freedom. The dynamics of the classical degrees of freedom are in turn governed by forces obtained by taking the expectation value of the force with respect to the ground or excited vibrational wave functions. Polarizable force fields and nonlinear mapping relations between the hydroxyl transition frequencies and dipole moments and the electric field along the hydroxyl bond are used, which were previously shown to quantitatively reproduce the experimental infrared steady-state absorption spectra and excited state lifetime [Kwac, K.; Geva, E. J. Phys. Chem. B 2011, 115, 9184; 2012, 116, 2856]. The relaxation from the first-excited state to the ground state is treated as a nonadiabatic transition. Within the mixed quantum-classical treatment, relaxation from the excited state to the ground state is accompanied by a momentum-jump in the classical degrees of freedom, which is in turn dictated by the nonadiabatic coupling vector. We find that the momentum jump leads to breaking of hydrogen bonds involving the relaxing hydroxyl, thereby blue-shifting the transition frequency by more than the Stokes shift between the steady-state emission and absorption spectra. The subsequent nonequilibrium relaxation toward equilibrium on the ground state potential energy surface is thereby accompanied by red shifting of the transition frequency. The signature of this nonequilibrium relaxation process on the pump-probe spectrum is analyzed in detail. The calculated pump-probe spectrum is found

  3. Unraveling Quantum Annealers using Classical Hardness.

    PubMed

    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

  4. Unraveling Quantum Annealers using Classical Hardness.

    PubMed

    Martin-Mayor, Victor; Hen, Itay

    2015-10-20

    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.

  5. Classical Trajectories and Quantum Spectra

    NASA Technical Reports Server (NTRS)

    Mielnik, Bogdan; Reyes, Marco A.

    1996-01-01

    A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

  6. The structure of the hydrated electron. Part 2. A mixed quantum/classical molecular dynamics embedded cluster density functional theory: single-excitation configuration interaction study.

    PubMed

    Shkrob, Ilya A; Glover, William J; Larsen, Ross E; Schwartz, Benjamin J

    2007-06-21

    Adiabatic mixed quantum/classical (MQC) molecular dynamics (MD) simulations were used to generate snapshots of the hydrated electron in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the hydrated electron were extracted from the MQC MD simulations and embedded in a roughly 18 Ax18 Ax18 A matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory (DFT) with the Becke-Lee-Yang-Parr functional and single-excitation configuration interaction (CIS) methods were then applied to these embedded clusters. The salient feature of these hybrid DFT(CIS)/MQC MD calculations is significant transfer (approximately 18%) of the excess electron's charge density into the 2p orbitals of oxygen atoms in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the singly occupied and the lower unoccupied molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfcc) tensors, and the infrared (IR) and Raman spectra of these embedded water cluster anions. The calculated hfcc tensors were used to compute electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectra for the hydrated electron that compared favorably to the experimental spectra of trapped electrons in alkaline ice. The calculated vibrational spectra of the hydrated electron are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. In addition to reproducing the visible/near IR absorption spectrum, the hybrid DFT model also accounts for the hydrated electron's 190-nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, many-electron effects must be accounted for: one-electron models that do not allow for mixing of the excess

  7. Thermodynamic integration from classical to quantum mechanics

    SciTech Connect

    Habershon, Scott; Manolopoulos, David E.

    2011-12-14

    We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.

  8. Decoherence, chaos, the quantum and the classical

    SciTech Connect

    Zurek, W.H.; Paz, J.P.

    1994-04-01

    The key ideas of the environment-induced decoherence approach are reviewed. Application of decoherence to the transition from quantum to classical in open quantum systems with chaotic classical analogs is described. The arrow of time is, in this context, a result of the information loss to the correlations with the environment. The asymptotic rate of entropy production (which is reached quickly, on the dynamical timescale) is independent of the details of the coupling of the quantum system to the environment, and is set by the Lyapunov exponents. We also briefly outline the existential interpretation of quantum mechanics, justifying the slogan ``No information without representation.``

  9. Quantum and Classical Electrostatics Among Atoms

    NASA Astrophysics Data System (ADS)

    Doerr, T. P.; Obolensky, O. I.; Ogurtsov, A. Y.; Yu, Yi-Kuo

    Quantum theory has been unquestionably successful at describing physics at the atomic scale. However, it becomes more difficult to apply as the system size grows. On the other hand, classical physics breaks down at sufficiently short length scales but is clearly correct at larger distances. The purpose of methods such as QM/MM is to gain the advantages of both quantum and classical regimes: quantum theory should provide accuracy at the shortest scales, and classical theory, with its somewhat more tractable computational demands, allows results to be computed for systems that would be inaccessible with a purely quantum approach. This strategy will be most effective when one knows with good accuracy the length scale at which quantum calculations are no longer necessary and classical calculations are sufficient. To this end, we have performed both classical and quantum calculations for systems comprising a small number of atoms for which experimental data is also available. The classical calculations are fully exact; the quantum calculations are at the MP4(SDTQ)/aug-cc-pV5Z and CCSD(T)/aug-cc-pV5Z levels. The precision of both sets of calculations along with the existence of experimental results allows us to draw conclusions about the range of utility of the respective calculations. This research was supported by the Intramural Research Program of the NIH, NLM and utilized the computational resources of the NIH HPC Biowulf cluster.

  10. Classical and Quantum Spreading of Position Probability

    ERIC Educational Resources Information Center

    Farina, J. E. G.

    1977-01-01

    Demonstrates that the standard deviation of the position probability of a particle moving freely in one dimension is a function of the standard deviation of its velocity distribution and time in classical or quantum mechanics. (SL)

  11. Quantum dynamics simulation with classical oscillators

    NASA Astrophysics Data System (ADS)

    Briggs, John S.; Eisfeld, Alexander

    2013-12-01

    In a previous paper [J. S. Briggs and A. Eisfeld, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.052111 85, 052111 (2012)] we showed that the time development of the complex amplitudes of N coupled quantum states can be mapped by the time development of positions and velocities of N coupled classical oscillators. Here we examine to what extent this mapping can be realized to simulate the “quantum,” properties of entanglement and qubit manipulation. By working through specific examples, e.g., of quantum gate operation, we seek to illuminate quantum and classical differences which hitherto have been treated more mathematically. In addition, we show that important quantum coupled phenomena, such as the Landau-Zener transition and the occurrence of Fano resonances can be simulated by classical oscillators.

  12. Understanding singularities — Classical and quantum

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah A.; Helliwell, Thomas M.

    2016-01-01

    The definitions of classical and quantum singularities are reviewed. Examples are given of both as well as their utility in general relativity. In particular, the classical and quantum singularity structure of certain interesting conformally static spherically symmetric spacetimes modeling scalar field collapse are reviewed. The spacetimes include the Roberts spacetime, the Husain-Martinez-Nuñez spacetime and the Fonarev spacetime. The importance of understanding spacetime singularity structure is discussed.

  13. Quantum Backreaction on Classical'' Variables

    SciTech Connect

    Anderson, A. Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2BZ )

    1995-01-30

    A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to compute the backreaction of any quantum system on a quasiclassical one. In particular, it leads to a natural candidate for a theory of gravity coupled to quantized matter in which the gravitational field is not quantized.

  14. Synchronizing quantum and classical clocks made of quantum particles

    NASA Astrophysics Data System (ADS)

    Flores, Philip Caesar M.; Caballar, Roland Cristopher F.; Galapon, Eric A.

    2016-09-01

    We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), 10.1103/PhysRevA.80.030102, can be eliminated up to a given order of ℏ by choosing an appropriate position-dependent phase for the object's wave function. This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock, which tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock by making use of a quantum object with a position-dependent phase imprinted on the object's initial wave function with the use of an impulsive potential.

  15. Unification of quantum theory and classical physics

    SciTech Connect

    Stapp, H.P.

    1985-07-01

    A program is described for unifying quantum theory and classical physics on the basis of the Copenhagen-interpretation idea of external reality and a recently discovered classical part of the electromagnetic field. The program effects an integration of the intuitions of Heisenberg, Bohr, and Einstein.

  16. Classical and Quantum-Mechanical State Reconstruction

    ERIC Educational Resources Information Center

    Khanna, F. C.; Mello, P. A.; Revzen, M.

    2012-01-01

    The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

  17. Quantum Adder of Classical Numbers

    NASA Astrophysics Data System (ADS)

    Cherkas, A. V.; Chivilikhin, S. A.

    2016-08-01

    In this article we show the precise algorithm of functioning of quantum adder on the example of addition of two 2-bit numbers. It consists of the quantum Fourier transformer and conditional rotation gates that let us use the minimum number of qubits to get the addition realization of the sum. Despite the fact that the algorithm uses the minimum amount of operations this accelerates the process of the adder.

  18. Entanglement in the classical limit: Quantum correlations from classical probabilities

    SciTech Connect

    Matzkin, A.

    2011-08-15

    We investigate entanglement for a composite closed system endowed with a scaling property which allows the dynamics to be kept invariant while the effective Planck constant ({Dirac_h}/2{pi}){sub eff} of the system is varied. Entanglement increases as ({Dirac_h}/2{pi}){sub eff}{yields}0. Moreover, for sufficiently low ({Dirac_h}/2{pi}){sub eff} the evolution of the quantum correlations, encapsulated, for example, in the quantum discord, can be obtained from the mutual information of the corresponding classical system. We show this behavior is due to the local suppression of path interferences in the interaction that generates the entanglement.

  19. Quantum and classical dynamics in adiabatic computation

    NASA Astrophysics Data System (ADS)

    Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.

    2014-10-01

    Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.

  20. Classical teleportation of a quantum Bit

    PubMed

    Cerf; Gisin; Massar

    2000-03-13

    Classical teleportation is defined as a scenario where the sender is given the classical description of an arbitrary quantum state while the receiver simulates any measurement on it. This scenario is shown to be achievable by transmitting only a few classical bits if the sender and receiver initially share local hidden variables. Specifically, a communication of 2.19 bits is sufficient on average for the classical teleportation of a qubit, when restricted to von Neumann measurements. The generalization to positive-operator-valued measurements is also discussed.

  1. Trading Classical and Quantum Computational Resources

    NASA Astrophysics Data System (ADS)

    Bravyi, Sergey; Smith, Graeme; Smolin, John A.

    2016-04-01

    We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First, we consider sparse quantum circuits such that each qubit participates in O (1 ) two-qubit gates. It is shown that any sparse circuit on n +k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2O (k )poly (n ) . Second, we study Pauli-based computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n -qubit Pauli operators. The computation begins by initializing each qubit in the so-called magic state. This model is known to be equivalent to the universal quantum computer. We show that any PBC on n +k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2O (k )poly (n ). Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2α npoly (n ) , where α ≈0.94 . This improves upon the brute-force simulation method, which takes time 2npoly (n ). Our algorithm exploits the fact that n -fold tensor products of magic states admit a low-rank decomposition into n -qubit stabilizer states.

  2. Quantum-classical crossover in electrodynamics

    SciTech Connect

    Polonyi, Janos

    2006-09-15

    A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current and the electromagnetic field in the quantum side of the crossover and reproduces standard classical electrodynamics on the other side. The effective action derived in the closed time path formalism and the equations of motion follow from the variational principle. The polarization of the Dirac-sea can be taken into account in the quadratic approximation of the action by the introduction of the deplacement field strengths as in conventional classical electrodynamics. Decoherence appears naturally as a simple one-loop effect in this formalism. It is argued that the radiation time arrow is generated from the quantum boundary conditions in time by decoherence at the quantum-classical crossover and the Abraham-Lorentz force arises from the accelerating charge or from other charges in the macroscopic or the microscopic side, respectively. The functional form of the quantum renormalization group, the generalization of the renormalization group method for the density matrix, is proposed to follow the scale dependence through the quantum-classical crossover in a systematical manner.

  3. Entanglement in Quantum-Classical Hybrid

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2011-01-01

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

  4. Large classical universes emerging from quantum cosmology

    SciTech Connect

    Pinto-Neto, Nelson

    2009-04-15

    It is generally believed that one cannot obtain a large universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the universe after leaving the quantum regime should be around the Planck length, and the standard decelerated classical expansion after that is not sufficient to enlarge the universe in the time available. For instance, in many quantum minisuperspace bouncing models studied in the literature, solutions where the universe leaves the quantum regime in the expanding phase with appropriate size have negligible probability amplitude with respect to solutions leaving this regime around the Planck length. In this paper, I present a general class of moving Gaussian solutions of the Wheeler-DeWitt equation where the velocity of the wave in minisuperspace along the scale factor axis, which is the new large parameter introduced in order to circumvent the above-mentioned problem, induces a large acceleration around the quantum bounce, forcing the universe to leave the quantum regime sufficiently big to increase afterwards to the present size, without needing any classical inflationary phase in between, and with reasonable relative probability amplitudes with respect to models leaving the quantum regime around the Planck scale. Furthermore, linear perturbations around this background model are free of any trans-Planckian problem.

  5. NUCLEAR MIXING METERS FOR CLASSICAL NOVAE

    SciTech Connect

    Kelly, Keegan J.; Iliadis, Christian; Downen, Lori; Champagne, Art; José, Jordi

    2013-11-10

    Classical novae are caused by mass transfer episodes from a main-sequence star onto a white dwarf via Roche lobe overflow. This material possesses angular momentum and forms an accretion disk around the white dwarf. Ultimately, a fraction of this material spirals in and piles up on the white dwarf surface under electron-degenerate conditions. The subsequently occurring thermonuclear runaway reaches hundreds of megakelvin and explosively ejects matter into the interstellar medium. The exact peak temperature strongly depends on the underlying white dwarf mass, the accreted mass and metallicity, and the initial white dwarf luminosity. Observations of elemental abundance enrichments in these classical nova events imply that the ejected matter consists not only of processed solar material from the main-sequence partner but also of material from the outer layers of the underlying white dwarf. This indicates that white dwarf and accreted matter mix prior to the thermonuclear runaway. The processes by which this mixing occurs require further investigation to be understood. In this work, we analyze elemental abundances ejected from hydrodynamic nova models in search of elemental abundance ratios that are useful indicators of the total amount of mixing. We identify the abundance ratios ΣCNO/H, Ne/H, Mg/H, Al/H, and Si/H as useful mixing meters in ONe novae. The impact of thermonuclear reaction rate uncertainties on the mixing meters is investigated using Monte Carlo post-processing network calculations with temperature-density evolutions of all mass zones computed by the hydrodynamic models. We find that the current uncertainties in the {sup 30}P(p, γ){sup 31}S rate influence the Si/H abundance ratio, but overall the mixing meters found here are robust against nuclear physics uncertainties. A comparison of our results with observations of ONe novae provides strong constraints for classical nova models.

  6. Quantum and classical optics-emerging links

    NASA Astrophysics Data System (ADS)

    Eberly, J. H.; Qian, Xiao-Feng; Qasimi, Asma Al; Ali, Hazrat; Alonso, M. A.; Gutiérrez-Cuevas, R.; Little, Bethany J.; Howell, John C.; Malhotra, Tanya; Vamivakas, A. N.

    2016-06-01

    Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum-classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.

  7. Communication capacity of mixed quantum t -designs

    NASA Astrophysics Data System (ADS)

    Brandsen, Sarah; Dall'Arno, Michele; Szymusiak, Anna

    2016-08-01

    We operationally introduce mixed quantum t -designs as the most general arbitrary-rank extension of projective quantum t -designs which preserves indistinguishability from the uniform distribution for t copies. First, we derive upper bounds on the classical communication capacity of any mixed t -design measurement for t ∈[1 ,5 ] . Second, we explicitly compute the classical communication capacity of several mixed t -design measurements, including the depolarized version of any qubit and qutrit symmetric, informationally complete (SIC) measurement and complete mutually unbiased bases, the qubit icosahedral measurement, the Hoggar SIC measurement, any anti-SIC (where each element is proportional to the projector on the subspace orthogonal to one of the elements of the original SIC), and the uniform distribution over pure effects.

  8. Crossover from quantum to classical transport

    NASA Astrophysics Data System (ADS)

    Morr, Dirk K.

    2016-01-01

    Understanding the crossover from quantum to classical transport has become of fundamental importance not only for technological applications due to the creation of sub-10-nm transistors - an important building block of our modern life - but also for elucidating the role played by quantum mechanics in the evolutionary fitness of biological complexes. This article provides a basic introduction into the nature of charge and energy transport in the quantum and classical regimes. It discusses the characteristic transport properties in both limits and demonstrates how they can be connected through the loss of quantum mechanical coherence. The salient features of the crossover physics are identified, and their importance in opening new transport regimes and in understanding efficient and robust energy transport in biological complexes are demonstrated.

  9. Gauge-fields and integrated quantum-classical theory

    SciTech Connect

    Stapp, H.P.

    1986-01-01

    Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs.

  10. Quantum-to-classical transition in cavity quantum electrodynamics.

    PubMed

    Fink, J M; Steffen, L; Studer, P; Bishop, Lev S; Baur, M; Bianchetti, R; Bozyigit, D; Lang, C; Filipp, S; Leek, P J; Wallraff, A

    2010-10-15

    The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation-or effective temperature-is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.

  11. Applying classical geometry intuition to quantum spin

    NASA Astrophysics Data System (ADS)

    Durfee, Dallin S.; Archibald, James L.

    2016-09-01

    Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a mathematically rigorous derivation, the relationships are found by forcing expectation values of the different basis states to have the properties we expect of a classical, geometric coordinate system. The process highlights the correspondence of quantum angular momentum with classical notions of geometric orthogonality, even for the inherently non-classical spin-1/2 system. In the process, differences in and connections between geometrical space and Hilbert space are illustrated.

  12. Born rule in quantum and classical mechanics

    SciTech Connect

    Brumer, Paul; Gong Jiangbin

    2006-05-15

    Considerable effort has been devoted to deriving the Born rule [i.e., that {psi}(x){sup 2}dx is the probability of finding a system, described by {psi}, between x and x+dx] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

  13. Classical Simulated Annealing Using Quantum Analogues

    NASA Astrophysics Data System (ADS)

    La Cour, Brian R.; Troupe, James E.; Mark, Hans M.

    2016-08-01

    In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simultaneous spin flips at each annealing step as an analogue to quantum spin coherence as well as modifications of the Boltzmann acceptance probability to mimic quantum tunneling. We find that the use of multiple spin flips can indeed be advantageous under certain annealing schedules, but only for long anneal times.

  14. Bridging classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.

    2016-10-01

    Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.

  15. Quantum-to-classical crossover near quantum critical point

    PubMed Central

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

    2015-01-01

    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 transition 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) ∈ [0, 1] decreases with the temperature such that Λ(T = 0) = 1 and Λ(T → ∞) = 0. 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. PMID:26688102

  16. Quantum-to-classical crossover near quantum critical point

    SciTech Connect

    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 transition 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.

  17. 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

  18. Multi-time equations, classical and quantum

    PubMed Central

    Petrat, Sören; Tumulka, Roderich

    2014-01-01

    Multi-time equations are evolution equations involving several time variables, one for each particle. Such equations have been considered for the purpose of making theories manifestly Lorentz invariant. We compare their status and significance in classical and quantum physics. PMID:24711721

  19. Classical and quantum Kummer shape algebras

    NASA Astrophysics Data System (ADS)

    Odzijewicz, A.; Wawreniuk, E.

    2016-07-01

    We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.

  20. Comparison of Classical and Quantum Mechanical Uncertainties.

    ERIC Educational Resources Information Center

    Peslak, John, Jr.

    1979-01-01

    Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)

  1. Quantum-classical transitions in complex networks

    NASA Astrophysics Data System (ADS)

    Javarone, Marco Alberto; Armano, Giuliano

    2013-04-01

    The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in terms of phase transitions of quantum gases or representing distances among nodes as if they were particle energies. This paper shows that the emergence of different structures in complex networks, such as the scale-free and the winner-takes-all networks, can be represented in terms of a quantum-classical transition for quantum gases. In particular, we propose a model of fermionic networks that allows us to investigate the network evolution and its dependence on the system temperature. Simulations, performed in accordance with the cited model, clearly highlight the separation between classical random and winner-takes-all networks, in full correspondence with the separation between classical and quantum regions for quantum gases. We deem this model useful for the analysis of synthetic and real complex networks.

  2. Categorical quantum mechanics II: Classical-quantum interaction

    NASA Astrophysics Data System (ADS)

    Coecke, Bob; Kissinger, Aleks

    2016-08-01

    This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part, we focus on classical-quantum interaction. Classical and quantum systems are treated as distinct types, of which the respective behavioral properties are specified in terms of processes and their compositions. In particular, classicality is witnessed by ‘spiders’ which fuse together whenever they connect. We define mixedness and show that pure processes are extremal in the space of all processes, and we define entanglement and show that quantum theory indeed exhibits entanglement. We discuss the classification of tripartite qubit entanglement and show that both the GHZ-state and the W-state come from spider-like families of processes, which differ only in how they behave when they are connected by two or more wires. We define measurements and provide fully comprehensive descriptions of several quantum protocols involving classical data flow. Finally, we give a notion of ‘genuine quantumness’, from which special processes called ‘phase spiders’ arise, and get a first glimpse of quantum nonlocality.

  3. A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solution based upon a mixed quantum-classical approximation. II. Proton transfer reaction in non-polar solvent.

    PubMed

    Kojima, H; Yamada, A; Okazaki, S

    2015-05-01

    The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantum-classical molecular dynamics (QCMD) calculations and fully classical molecular dynamics (FCMD) calculations. Comparing these calculated results with those for malonaldehyde in water reported in Part I [A. Yamada, H. Kojima, and S. Okazaki, J. Chem. Phys. 141, 084509 (2014)], the solvent dependence of the reaction rate, the reaction mechanism involved, and the quantum effect therein have been investigated. With FCMD, the reaction rate in weakly interacting neon is lower than that in strongly interacting water. However, with QCMD, the order of the reaction rates is reversed. To investigate the mechanisms in detail, the reactions were categorized into three mechanisms: tunneling, thermal activation, and barrier vanishing. Then, the quantum and solvent effects were analyzed from the viewpoint of the reaction mechanism focusing on the shape of potential energy curve and its fluctuations. The higher reaction rate that was found for neon in QCMD compared with that found for water solvent arises from the tunneling reactions because of the nearly symmetric double-well shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zero-point energy. The number of reactions based on these two mechanisms in water was greater than that in neon in both QCMD and FCMD because these reactions are dominated by the strength of solute-solvent interactions.

  4. A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solution based upon a mixed quantum-classical approximation. II. Proton transfer reaction in non-polar solvent.

    PubMed

    Kojima, H; Yamada, A; Okazaki, S

    2015-05-01

    The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantum-classical molecular dynamics (QCMD) calculations and fully classical molecular dynamics (FCMD) calculations. Comparing these calculated results with those for malonaldehyde in water reported in Part I [A. Yamada, H. Kojima, and S. Okazaki, J. Chem. Phys. 141, 084509 (2014)], the solvent dependence of the reaction rate, the reaction mechanism involved, and the quantum effect therein have been investigated. With FCMD, the reaction rate in weakly interacting neon is lower than that in strongly interacting water. However, with QCMD, the order of the reaction rates is reversed. To investigate the mechanisms in detail, the reactions were categorized into three mechanisms: tunneling, thermal activation, and barrier vanishing. Then, the quantum and solvent effects were analyzed from the viewpoint of the reaction mechanism focusing on the shape of potential energy curve and its fluctuations. The higher reaction rate that was found for neon in QCMD compared with that found for water solvent arises from the tunneling reactions because of the nearly symmetric double-well shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zero-point energy. The number of reactions based on these two mechanisms in water was greater than that in neon in both QCMD and FCMD because these reactions are dominated by the strength of solute-solvent interactions. PMID:25956108

  5. Quantum and classical dissipation of charged particles

    SciTech Connect

    Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.; Hernández-Saldaña, H.; Kunold, A.; Roa-Neri, J.A.E.

    2013-08-15

    A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge.

  6. Monodisperse cluster crystals: Classical and quantum dynamics.

    PubMed

    Díaz-Méndez, Rogelio; Mezzacapo, Fabio; Cinti, Fabio; Lechner, Wolfgang; Pupillo, Guido

    2015-11-01

    We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquidlike long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: Zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics. PMID:26651695

  7. Mapping quantum-classical Liouville equation: projectors and trajectories.

    PubMed

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

    2012-02-28

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

  8. Time in classical and in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Elçi, A.

    2010-07-01

    This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac-Heisenberg-von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac-Heisenberg-von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.

  9. New variables for classical and quantum gravity

    NASA Technical Reports Server (NTRS)

    Ashtekar, Abhay

    1986-01-01

    A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.

  10. Quantum cryptography approaching the classical limit.

    PubMed

    Weedbrook, Christian; Pirandola, Stefano; Lloyd, Seth; Ralph, Timothy C

    2010-09-10

    We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave.

  11. Quantum cryptography approaching the classical limit.

    PubMed

    Weedbrook, Christian; Pirandola, Stefano; Lloyd, Seth; Ralph, Timothy C

    2010-09-10

    We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave. PMID:20867556

  12. Classical system boundaries cannot be determined within quantum Darwinism

    NASA Astrophysics Data System (ADS)

    Fields, Chris

    Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.

  13. Sharing the Quantum State and the Classical Information Simultaneously

    NASA Astrophysics Data System (ADS)

    Qin, Huawang; Dai, Yuewei

    2016-08-01

    An efficient quantum secret sharing scheme is proposed, in which the quantum state and the classical information can be shared simultaneously through only one distribution. The dealer uses the operations of quantum-controlled-not and Hadamard gate to encode the secret quantum state and classical information, and the participants use the single-particle measurements to recover the original quantum state and classical information. Compared to the existing schemes, our scheme is more efficient when the quantum state and the classical information need to be shared simultaneously.

  14. How quantum are classical spin ices?

    NASA Astrophysics Data System (ADS)

    Gingras, Michel J. P.; Rau, Jeffrey G.

    The pyrochlore spin ice compounds Dy2TiO7 and Ho2Ti2O7 are well described by classical Ising models down to low temperatures. Given the empirical success of this description, the question of the importance of quantum effects in these materials has been mostly ignored. We argue that the common wisdom that the strictly Ising moments of non-interacting Dy3+ and Ho3+ ions imply Ising interactions is too naive and that a more complex argument is needed to explain the close agreement between the classical Ising model theory and experiments. By considering a microscopic picture of the interactions in rare-earth oxides, we show that the high-rank multipolar interactions needed to induce quantum effects in these two materials are generated only very weakly by superexchange. Using this framework, we formulate an estimate of the scale of quantum effects in Dy2Ti2O7 and Ho2Ti2O7, finding it to be well below experimentally relevant temperatures. Published as: PHYSICAL REVIEW B 92, 144417 (2015).

  15. Quantum-classical dynamics of wave fields.

    PubMed

    Sergi, Alessandro

    2007-02-21

    An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.

  16. Classical and Quantum Probability for Biologists - Introduction

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei.

    2010-01-01

    The aim of this review (oriented to biologists looking for applications of QM) is to provide a detailed comparative analysis of classical (Kolmogorovian) and quantum (Dirac-von Neumann) models. We will stress differences in the definition of conditional probability and as a consequence in the structures of matrices of transition probabilities, especially the condition of double stochasticity which arises naturally in QM. One of the most fundamental differences between two models is deformation of the classical formula of total probability (FTP) which plays an important role in statistics and decision making. An additional term appears in the QM-version of FTP - so called interference term. Finally, we discuss Bell's inequality and show that the common viewpoint that its violation induces either nonlocality or "death of realism" has not been completely justified. For us it is merely a sign of non-Kolmogorovianity of probabilistic data collected in a few experiments with incompatible setups of measurement devices.

  17. Classical and quantum physics of hydrogen clusters.

    PubMed

    Mezzacapo, Fabio; Boninsegni, Massimo

    2009-04-22

    We present results of a comprehensive theoretical investigation of the low temperature (T) properties of clusters of para-hydrogen (p-H(2)), both pristine as well as doped with isotopic impurities (i.e., ortho-deuterium, o-D(2)). We study clusters comprising up to N = 40 molecules, by means of quantum simulations based on the continuous-space Worm algorithm. Pristine p-H(2) clusters are liquid-like and superfluid in the [Formula: see text] limit. The superfluid signal is uniform throughout these clusters; it is underlain by long cycles of permutation of molecules. Clusters with more than 22 molecules display solid-like, essentially classical behavior at temperatures down to T∼1 K; some of them are seen to turn liquid-like at sufficiently low T (quantum melting).

  18. Probing quantum entanglement, quantum discord, classical correlation, and the quantum state without disturbing them

    SciTech Connect

    Li Zhenni; Jin Jiasen; Yu Changshui

    2011-01-15

    We present schemes for a type of one-parameter bipartite quantum state to probe quantum entanglement, quantum discord, the classical correlation, and the quantum state based on cavity QED. It is shown that our detection does not influence all these measured quantities. We also discuss how the spontaneous emission introduced by our probe atom influences our detection.

  19. Classical Information Storage in an n-Level Quantum System

    NASA Astrophysics Data System (ADS)

    Frenkel, Péter E.; Weiner, Mihály

    2015-12-01

    A game is played by a team of two—say Alice and Bob—in which the value of a random variable x is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is given a quantum n-level system, respectively a classical n-state system, which she can put in possession of Bob in any state she wishes. We evaluate how successfully they managed to store and recover the value of x by requiring Bob to specify a value z and giving a reward of value f ( x, z) to the team. We show that whatever the probability distribution of x and the reward function f are, when using a quantum n-level system, the maximum expected reward obtainable with the best possible team strategy is equal to that obtainable with the use of a classical n-state system. The proof relies on mixed discriminants of positive matrices and—perhaps surprisingly—an application of the Supply-Demand Theorem for bipartite graphs. As a corollary, we get an infinite set of new, dimension dependent inequalities regarding positive operator valued measures and density operators on complex n-space. As a further corollary, we see that the greatest value, with respect to a given distribution of x, of the mutual information I ( x; z) that is obtainable using an n-level quantum system equals the analogous maximum for a classical n-state system.

  20. Tomographic quantum cryptography: equivalence of quantum and classical key distillation.

    PubMed

    Bruss, Dagmar; Christandl, Matthias; Ekert, Artur; Englert, Berthold-Georg; Kaszlikowski, Dagomir; Macchiavello, Chiara

    2003-08-29

    The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.

  1. Collectibility for mixed quantum states

    NASA Astrophysics Data System (ADS)

    Rudnicki, Łukasz; Puchała, Zbigniew; Horodecki, Paweł; Życzkowski, Karol

    2012-12-01

    Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.150502 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.

  2. Arbiter as the Third Man in Classical and Quantum Games

    NASA Astrophysics Data System (ADS)

    Pykacz, Jarosław; FraÇkiewicz, Piotr

    2010-12-01

    We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.

  3. Selected Studies in Classical and Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Saotome, Ryo

    This thesis is composed of two parts, one corresponding to classical and the other to quantum gravitational phenomena. In the classical part, we focus on the behavior of various classical scalar fields in the presence of black holes. New fundamental results discussed include the first confirmation of the Belinskii, Khalatnikov, and Lifschitz (BKL) conjecture for an asymptotically flat spacetime, where we find that the dynamics of a canonical test scalar field near a black hole singularity are dominated by terms with time derivatives. We also perform a numerical simulation of the gravitational collapse of a non-canonical scalar field showing that signals can escape black holes in the k-essence dark energy model and find numerical confirmation that the accretion of various scalar fields onto a black hole from generic initial conditions is stationary. In the second part, we focus on the long distance behavior of perturbative quantum gravity. New results discussed include a proof of the cancellation of collinear divergences to all orders in the amplitudes of the theory as well as a characterization of all infrared divergent diagrams. In particular, we find that the only diagrams that can have soft divergences are ladder and crossed ladder diagrams, and that the only collinearly divergent diagrams are those with only three point vertices and no internal jet loops. Also presented is a construction of a double copy relation between gravity and gauge theory amplitudes similar to that conjectured by Bern, Carrasco, and Johansson for the case where there is no hard momentum exchange in the scattering, which we find implies a squaring relation between the classical shockwave solutions of the two theories as well. Finally, the first calculation of a gravitational scattering amplitude through the next-to-leading eikonal order is performed. We find that this correction to the scattering amplitude exponentiates, and that these power corrections probe smaller impact parameters

  4. A mixed quantum-classical molecular dynamics study of anti-tetrol and syn-tetrol dissolved in liquid chloroform II: infrared emission spectra, vibrational excited-state lifetimes, and nonequilibrium hydrogen-bond dynamics.

    PubMed

    Kwac, Kijeong; Geva, Eitan

    2013-11-21

    The effect of vibrational excitation and relaxation of the hydroxyl stretch on the hydrogen-bond structure and dynamics of stereoselectively synthesized syn-tetrol and anti-tetrol dissolved in deuterated chloroform are investigated via a mixed quantum-classical molecular dynamics simulation. Emphasis is placed on the changes in hydrogen-bond structure upon photoexcitation and the nonequilibrium hydrogen-bond dynamics that follows the subsequent relaxation from the excited to the ground vibrational state. The propensity to form hydrogen bonds is shown to increase upon photoexcitation of the hydroxyl stretch, thereby leading to a sizable red-shift of the infrared emission spectra relative to the corresponding absorption spectra. The vibrational excited state lifetimes are calculated within the framework of Fermi's golden rule and the harmonic-Schofield quantum correction factor, and found to be sensitive reporters of the underlying hydrogen-bond structure. The energy released during the relaxation from the excited to the ground state is shown to break hydrogen bonds involving the relaxing hydroxyl. The spectral signature of this nonequilibrium relaxation process is analyzed in detail.

  5. Quantum information theory: classical communication over quantum channels

    NASA Astrophysics Data System (ADS)

    Cortese, John Anthony

    This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.

  6. The scalable implementation of quantum walks using classical light

    NASA Astrophysics Data System (ADS)

    Goyal, Sandeep K.; Roux, F. S.; Forbes, Andrew; Konrad, Thomas

    2014-02-01

    A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.

  7. Emergence of a classical Universe from quantum gravity and cosmology.

    PubMed

    Kiefer, Claus

    2012-09-28

    I describe how we can understand the classical appearance of our world from a universal quantum theory. The essential ingredient is the process of decoherence. I start with a general discussion in ordinary quantum theory and then turn to quantum gravity and quantum cosmology. There is a whole hierarchy of classicality from the global gravitational field to the fluctuations in the cosmic microwave background, which serve as the seeds for the structure in the Universe.

  8. Classical Physics and the Bounds of Quantum Correlations.

    PubMed

    Frustaglia, Diego; Baltanás, José P; Velázquez-Ahumada, María C; Fernández-Prieto, Armando; Lujambio, Aintzane; Losada, Vicente; Freire, Manuel J; Cabello, Adán

    2016-06-24

    A unifying principle explaining the numerical bounds of quantum correlations remains elusive, despite the efforts devoted to identifying it. Here, we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along meter-size transmission-line circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed. PMID:27391707

  9. Classical Physics and the Bounds of Quantum Correlations.

    PubMed

    Frustaglia, Diego; Baltanás, José P; Velázquez-Ahumada, María C; Fernández-Prieto, Armando; Lujambio, Aintzane; Losada, Vicente; Freire, Manuel J; Cabello, Adán

    2016-06-24

    A unifying principle explaining the numerical bounds of quantum correlations remains elusive, despite the efforts devoted to identifying it. Here, we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along meter-size transmission-line circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed.

  10. Quantum-Classical Hybrid for Information Processing

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2011-01-01

    Based upon quantum-inspired entanglement in quantum-classical hybrids, a simple algorithm for instantaneous transmissions of non-intentional messages (chosen at random) to remote distances is proposed. The idea is to implement instantaneous transmission of conditional information on remote distances via a quantum-classical hybrid that preserves superposition of random solutions, while allowing one to measure its state variables using classical methods. Such a hybrid system reinforces the advantages, and minimizes the limitations, of both quantum and classical characteristics. Consider n observers, and assume that each of them gets a copy of the system and runs it separately. Although they run identical systems, the outcomes of even synchronized runs may be different because the solutions of these systems are random. However, the global constrain must be satisfied. Therefore, if the observer #1 (the sender) made a measurement of the acceleration v(sub 1) at t =T, then the receiver, by measuring the corresponding acceleration v(sub 1) at t =T, may get a wrong value because the accelerations are random, and only their ratios are deterministic. Obviously, the transmission of this knowledge is instantaneous as soon as the measurements have been performed. In addition to that, the distance between the observers is irrelevant because the x-coordinate does not enter the governing equations. However, the Shannon information transmitted is zero. None of the senders can control the outcomes of their measurements because they are random. The senders cannot transmit intentional messages. Nevertheless, based on the transmitted knowledge, they can coordinate their actions based on conditional information. If the observer #1 knows his own measurements, the measurements of the others can be fully determined. It is important to emphasize that the origin of entanglement of all the observers is the joint probability density that couples their actions. There is no centralized source

  11. Nonlinear quantum equations: Classical field theory

    SciTech Connect

    Rego-Monteiro, M. A.; Nobre, F. D.

    2013-10-15

    An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

  12. Comparisons of classical and quantum dynamics for initially localized states

    SciTech Connect

    Davis, M.J.; Heller, E.J.

    1984-05-15

    We compare the dynamics of quantum wave packets with the dynamics of classical trajectory ensembles. The wave packets are Gaussian with expectation values of position and momenta which centers them in phase space. The classical trajectory ensembles are generated directly from the quantum wave packets via the Wigner transform. Quantum and classical dynamics are then compared using several quantum measures and the analogous classical ones derived from the Wigner equivalent formalism. Comparisons are made for several model potentials and it is found that there is generally excellent classical--quantum correspondence except for certain specific cases of tunneling and interference. In general, this correspondence is also very good in regions of phase space where there is classical chaos.

  13. Fate of classical solitons in one-dimensional quantum systems.

    SciTech Connect

    Pustilnik, M.; Matveev, K. A.

    2015-11-23

    We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.

  14. Ergodicity and mixing in quantum dynamics

    NASA Astrophysics Data System (ADS)

    Zhang, Dongliang; Quan, H. T.; Wu, Biao

    2016-08-01

    After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.

  15. Ergodicity and mixing in quantum dynamics.

    PubMed

    Zhang, Dongliang; Quan, H T; Wu, Biao

    2016-08-01

    After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy. PMID:27627289

  16. Beyond quantum-classical analogies: high time for agreement?

    NASA Astrophysics Data System (ADS)

    Marrocco, Michele

    Lately, many quantum-classical analogies have been investigated and published in many acknowledged journals. Such a surge of research on conceptual connections between quantum and classical physics forces us to ask whether the correspondence between the quantum and classical interpretation of the reality is deeper than the correspondence principle stated by Bohr. Here, after a short introduction to quantum-classical analogies from the recent literature, we try to examine the question from the perspective of a possible agreement between quantum and classical laws. A paradigmatic example is given in the striking equivalence between the classical Mie theory of electromagnetic scattering from spherical scatterers and the corresponding quantum-mechanical wave scattering analyzed in terms of partial waves. The key features that make the correspondence possible are examined and finally employed to deal with the fundamental blackbody problem that marks the initial separation between classical and quantum physics. The procedure allows us to recover the blackbody spectrum in classical terms and the proof is rich in consequences. Among them, the strong analogy between the quantum vacuum and its classical counterpart.

  17. Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. I. Theory.

    PubMed

    Bousquet, David; Hughes, Keith H; Micha, David A; Burghardt, Irene

    2011-02-14

    A mixed quantum-classical formulation is developed for a quantum subsystem in strong interaction with an N-particle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the N-particle distribution and the corresponding reduced single-particle distribution, exact quantum hydrodynamic equations are obtained for the momentum moments of the single-particle distribution coupled to a discretized quantum subsystem. The quantum-classical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a Grad-Hermite-type closure, (ii) a Gaussian closure at the level of a quantum-classical local Maxwellian distribution, and (iii) a dynamical density functional theory approximation by which the hydrodynamic pressure term is replaced by a free energy functional derivative. The latter limit yields a mixed quantum-classical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys. 134, 343 (2006).

  18. Quantum Particles from Classical Probabilities in Phase Space

    NASA Astrophysics Data System (ADS)

    Wetterich, C.

    2012-10-01

    Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow, including interference or tunneling. The appropriate quantum observables for position and momentum contain a statistical part which reflects the roughness of the probability distribution. "Zwitters" realize a continuous interpolation between quantum and classical particles. Such objects may provide for an effective one-particle description of classical or quantum collective states as droplets of a liquid, macromolecules or a Bose-Einstein condensate. They may also be used for quantitative fundamental tests of quantum mechanics. We show that the ground state for zwitters has no longer a sharp energy. This feature permits to put quantitative experimental bounds on a small parameter for possible deviations from quantum mechanics.

  19. Complementarity of quantum discord and classically accessible information

    SciTech Connect

    Zwolak, Michael P.; Zurek, Wojciech H.

    2013-05-20

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.

  20. Complementarity of quantum discord and classically accessible information

    DOE PAGES

    Zwolak, Michael P.; Zurek, Wojciech H.

    2013-05-20

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an anti-symmetry property relating accessible information and discord. Itmore » shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.« less

  1. Complementarity of quantum discord and classically accessible information

    PubMed Central

    Zwolak, Michael; Zurek, Wojciech H.

    2013-01-01

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. We also prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.

  2. Mixed quantum/classical theory for inelastic scattering of asymmetric-top-rotor + atom in the body-fixed reference frame and application to the H{sub 2}O + He system

    SciTech Connect

    Semenov, Alexander; Dubernet, Marie-Lise; Babikov, Dmitri

    2014-09-21

    The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H{sub 2}O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm{sup −1} the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm{sup −1} the errors are consistently in the range of 1%–2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n{sup 2}, where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n{sup 3}. Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.

  3. Heterotic quantum and classical computing on convergence spaces

    NASA Astrophysics Data System (ADS)

    Patten, D. R.; Jakel, D. W.; Irwin, R. J.; Blair, H. A.

    2015-05-01

    Category-theoretic characterizations of heterotic models of computation, introduced by Stepney et al., combine computational models such as classical/quantum, digital/analog, synchronous/asynchronous, etc. to obtain increased computational power. A highly informative classical/quantum heterotic model of computation is represented by Abramsky's simple sequential imperative quantum programming language which extends the classical simple imperative programming language to encompass quantum computation. The mathematical (denotational) semantics of this classical language serves as a basic foundation upon which formal verification methods can be developed. We present a more comprehensive heterotic classical/quantum model of computation based on heterotic dynamical systems on convergence spaces. Convergence spaces subsume topological spaces but admit finer structure from which, in prior work, we obtained differential calculi in the cartesian closed category of convergence spaces allowing us to define heterotic dynamical systems, given by coupled systems of first order differential equations whose variables are functions from the reals to convergence spaces.

  4. On the correspondence between quantum and classical variational principles

    SciTech Connect

    Ruiz, D. E.; Dodin, I. Y.

    2015-06-10

    Here, classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein-Gordon particles.

  5. INCLINATION MIXING IN THE CLASSICAL KUIPER BELT

    SciTech Connect

    Volk, Kathryn; Malhotra, Renu

    2011-07-20

    We investigate the long-term evolution of the inclinations of the known classical and resonant Kuiper Belt objects (KBOs). This is partially motivated by the observed bimodal inclination distribution and by the putative physical differences between the low- and high-inclination populations. We find that some classical KBOs undergo large changes in inclination over gigayear timescales, which means that a current member of the low-inclination population may have been in the high-inclination population in the past, and vice versa. The dynamical mechanisms responsible for the time variability of inclinations are predominantly distant encounters with Neptune and chaotic diffusion near the boundaries of mean motion resonances. We reassess the correlations between inclination and physical properties including inclination time variability. We find that the size-inclination and color-inclination correlations are less statistically significant than previously reported (mostly due to the increased size of the data set since previous works with some contribution from inclination variability). The time variability of inclinations does not change the previous finding that binary classical KBOs have lower inclinations than non-binary objects. Our study of resonant objects in the classical Kuiper Belt region includes objects in the 3:2, 7:4, 2:1, and eight higher-order mean motion resonances. We find that these objects (some of which were previously classified as non-resonant) undergo larger changes in inclination compared to the non-resonant population, indicating that their current inclinations are not generally representative of their original inclinations. They are also less stable on gigayear timescales.

  6. Hybrid Quantum-Classical Approach to Correlated Materials

    NASA Astrophysics Data System (ADS)

    Bauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, Matthias

    2016-07-01

    Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.

  7. Quasi-superactivation for the classical capacity of quantum channels

    SciTech Connect

    Gyongyosi, Laszlo; Imre, Sandor

    2014-12-04

    The superactivation effect has its roots in the extreme violation of additivity of the channel capacity and enables to reliably transmit quantum information over zero-capacity quantum channels. In this work we demonstrate a similar effect for the classical capacity of a quantum channel which previously was thought to be impossible.

  8. Hybrid quantum-classical approach to correlated materials

    NASA Astrophysics Data System (ADS)

    Bauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, Matthias

    Recent improvements in control of quantum systems make it seem feasible to finally build a programmable general-purpose quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

  9. Classical and quantum superintegrability with applications

    NASA Astrophysics Data System (ADS)

    Miller, Willard, Jr.; Post, Sarah; Winternitz, Pavel

    2013-10-01

    A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta. We present a classification of second-order superintegrable systems in two-dimensional Riemannian and pseudo-Riemannian spaces. It is based on the study of the quadratic algebras of the integrals of motion and on the equivalence of different systems under coupling constant metamorphosis. The determining equations for the existence of integrals of motion of arbitrary order in real Euclidean space E2 are presented and partially solved for the case of third-order integrals. A systematic exposition is given of systems in two and higher dimensional space that allow integrals of arbitrary order. The algebras of integrals of motions are not necessarily quadratic but close polynomially or rationally. The relation between superintegrability and the classification of orthogonal polynomials is analyzed.

  10. Embedding Quantum into Classical: Contextualization vs Conditionalization

    PubMed Central

    Dzhafarov, Ehtibar N.; Kujala, Janne V.

    2014-01-01

    We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions. PMID:24681665

  11. Interpretation neutrality in the classical domain of quantum theory

    NASA Astrophysics Data System (ADS)

    Rosaler, Joshua

    2016-02-01

    I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.

  12. Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades.

    PubMed

    Yepez, Jeffrey; Vahala, George; Vahala, Linda; Soe, Min

    2009-08-21

    The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a Bose-Einstein condensate superfluid described by the Gross-Pitaevskii equation on grids up to 5760(3). For the first time, an accurate power-law scaling for the quantum Kelvin wave cascade is determined: k(-3). The incompressible kinetic energy spectrum exhibits very distinct power-law spectra in 3 ranges of k space: a classical Kolmogorov k(-(5/3)) spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum k(-3) on scales smaller than the inner radius of the quantum vortex core. The k(-3) quantum Kelvin wave spectrum due to phonon radiation is robust, while the k(-(5/3)) classical Kolmogorov spectrum becomes robust on large grids.

  13. Quantum and classical simulations of molecular clusters

    NASA Astrophysics Data System (ADS)

    Dong, Xiao

    to a fast discovery of accessible topological paths towards the global minimum. The ATMC can be readily linked to systems described by classical model potentials or systems described quantum mechanically. Serial and parallel versions of the ATMC have been implemented and applied for the structural optimization of classical Lennard-Jones nanoclusters and Morse nanoclusters, and tight-binding calcium nanoclusters, crystallization of infinite Lennard-Jones liquid, and optimization of the folding process leading to the native state of a polypeptide chain.

  14. Arbitrated quantum signature of classical messages without using authenticated classical channels

    NASA Astrophysics Data System (ADS)

    Luo, Yi-Ping; Hwang, Tzonelih

    2014-01-01

    This paper points out design confusion existing in all the arbitrated quantum signatures (AQS) that require public discussions over authenticated classical channels. Instead, an AQS scheme of classical messages without using authenticated classical channels is proposed here. A cryptographic hash function is used in combine with quantum mechanics to check the existence of an eavesdropping or to verify a signature. In addition, by using only single photons, this scheme provides higher efficiency both in quantum transmissions and generations. The proposed AQS scheme is shown to be immune to several well-known attacks, i.e., the Trojan-horse attacks and the existential forgery attack.

  15. Hybrid quantum/classical approaches for proton transfer in condensed phase systems

    NASA Astrophysics Data System (ADS)

    Kim, Soo Young

    Nuclear quantum effects such as tunneling and zero point energy play an important role in proton transfer reactions. Since a fully quantum mechanical treatment of condensed phase systems is not practical, mixed quantum/classical methods have been developed to simulate proton transfer reactions in solution. In this work the molecular dynamics with quantum transitions (MDQT) method, which incorporates nonadiabatic transitions among the vibrational states, was extended to treat the donor-acceptor vibrational motion as well as the hydrogen motion quantum mechanically for proton transfer reactions. This approach was applied to a model system representing intramolecular proton transfer within a phenol-amine complex in liquid methyl chloride. In addition, a hybrid quantum/classical molecular dynamics approach was applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-limited regime, which is most relevant for proton transfer in proteins. In these two studies, the fundamental issues such as the nuclear quantum effects of the proton and donor-acceptor motions and the dissipation effects in the hybrid quantum/classical approach were explored. These results have important implications for applications to hydrogen transfer reactions in solution and proteins.

  16. Generic emergence of classical features in quantum Darwinism

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  17. Generic emergence of classical features in quantum Darwinism.

    PubMed

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

    2015-01-01

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

  18. Controlling the dynamics of classical and quantum information in spin systems

    NASA Astrophysics Data System (ADS)

    Dalal, Parin B.

    The precise, human control of quantum systems, by its definition, must combine models of the classical and the quantum world into a calculus that supports both. Open, irreversible quantum systems must interact with closed, reversible quantum systems to predict evolutions that are partially open and closed. Inevitably, the problems of quantum measurement, the assumptions of scattering, and the role of spacetime comes under scrutiny. Such considerations have extraordinary practical value: the precise control of a quantum information is the cornerstone of scalable quantum computing. Traditionally, quantum control theory as well as a formalism of redundancy and partial measurements, known as quantum error correction, attempt to remedy systematic quantum-noise and random quantum-noise respectively, but have had mixed success. This dissertation examines how the imprecision of control in quantum and classical spin systems affects the flow of select information to a receiver and how such systems may be optimized against the imprecise scattering of control fields and spins. To this end, this dissertation intertwines the physics of state evolution with the physics of information control in classical and quantum systems. First in classical systems, a method for encoding and decoding classical spin-processing information provides an example of information flow. Then an analytic calculation of a semi-conductor spin channel's information capacity is performed. The results limit the rate of information processing and inform the design of materials for optimal spintronic information-processing in semiconductors. Next, noisy quantum interactions are described, so that the complexities of correcting small, random phase errors using traditional control theory and quantum error correction may be explained. How these noisy processes affect the relevant information flow of a quantum algorithm (derivatives of the Quantum Fourier Transform and Grover Search) is considered, several novel

  19. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.

  20. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened. PMID:26124246

  1. Inverse Problems in Classical and Quantum Physics

    NASA Astrophysics Data System (ADS)

    Almasy, Andrea A.

    2009-12-01

    The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. In this thesis, also two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

  2. Two-slit experiment: quantum and classical probabilities

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2015-06-01

    Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum-classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).

  3. Entanglement, the quantum formalism and the classical world

    SciTech Connect

    Matzkin, A.

    2011-09-23

    75 years after the term 'entanglement' was coined to a peculiar feature inherent to quantum systems, the connection between quantum and classical mechanics remains an open problem. Drawing on recent results obtained in semiclassical systems, we discuss here the fate of entanglement in a closed system as Planck's constant becomes vanishingly small. In that case the generation of entanglement in a quantum system is perfectly reproduced by properly defined correlations of the corresponding classical system. We speculate on what these results could imply regarding the status of entanglement and of the ensuing quantum correlations.

  4. Quantum-classical correspondence in steady states of nonadiabatic systems

    SciTech Connect

    Fujii, Mikiya; Yamashita, Koichi

    2015-12-31

    We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels.

  5. Sharing of classical and quantum correlations via XY interaction

    SciTech Connect

    Wang, Jieci; Silva, Jaime; Lanceros-Mendez, Senentxu

    2014-09-15

    The sharing of classical and quantum correlations via XY interaction is investigated. The model includes two identical networks consisting of n nodes, the ith node of one network sharing a correlated state with the jth node of the other network, while all other nodes are initially unconnected. It is shown that classical correlation, quantum discord as well as entanglement can be shared between any two nodes of the network via XY interaction and that quantum information can be transferred effectively between them. It is found that there is no simple dominating relation between the quantum correlation and entanglement in inertial system.

  6. Is classical flat Kasner spacetime flat in quantum gravity?

    NASA Astrophysics Data System (ADS)

    Singh, Parampreet

    2016-05-01

    Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.

  7. Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods.

    PubMed

    Agostini, Federica; Min, Seung Kyu; Abedi, Ali; Gross, E K U

    2016-05-10

    Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods. PMID:27030209

  8. Classical and quantum dynamics of the impulsively driven hydrogen atom

    SciTech Connect

    Melles, M.; Reinhold, C.O.; Burgdoerfer, J. |

    1992-12-01

    We investigate the classical and quantum dynamics of the hydrogen atom in a Rydberg state subject to a sequence of periodic and random pulses. One goal of this study is to test the validity of classical electron transport theories. We analyze the critical momentum transfer for which 10% of the Rydberg atoms are ionized after a large number of pulses as a function of the frequency of the perturbation. The quantum mechanical results for a periodic sequence of pulses exhibit clear structures which are not present in a classical simulation. These structures are shown to vanish for the case of stochastic pulses for which agreement is obtained between the classical and quantum mechanical results. The dynamics of the quantum mechanical periodic system is analyzed in terms of quasi-eigenstates of the period-one time evolution operator.

  9. Strong-field ionization in classical and quantum dynamics

    SciTech Connect

    Ritchie, B. ); Bowden, C.M.; Sung, C.C.; Li, Y.Q. )

    1990-06-01

    Classical and quantum results for the strong-electromagnetic-field ionization of the ground state of a generic model are compared. Quantum results are also presented for the strong-field ionization of the hydrogen atom. These results demonstrate that ionization depends strongly on the phase of the field in such a way that the interaction potential acts as a barrier or well at large distances from the binding region, producing effectively a closed or open gate'' to the region of space outside the atom. The open gate is analogous to a strong, static electric field applied to an atom such that the atom ionizes classically. Quantum and classical ensemble results for the ionization probability are found to show close qualitative agreement. Other comparisons are made for classical versus quantum wave-packet trajectories.

  10. Classical and quantum dynamics of the impulsively driven hydrogen atom

    SciTech Connect

    Melles, M.; Reinhold, C.O.; Burgdoerfer, J. Oak Ridge National Lab., TN )

    1992-01-01

    We investigate the classical and quantum dynamics of the hydrogen atom in a Rydberg state subject to a sequence of periodic and random pulses. One goal of this study is to test the validity of classical electron transport theories. We analyze the critical momentum transfer for which 10% of the Rydberg atoms are ionized after a large number of pulses as a function of the frequency of the perturbation. The quantum mechanical results for a periodic sequence of pulses exhibit clear structures which are not present in a classical simulation. These structures are shown to vanish for the case of stochastic pulses for which agreement is obtained between the classical and quantum mechanical results. The dynamics of the quantum mechanical periodic system is analyzed in terms of quasi-eigenstates of the period-one time evolution operator.

  11. Entropies and correlations in classical and quantum systems

    NASA Astrophysics Data System (ADS)

    Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe

    2016-09-01

    We present a review of entropy properties for classical and quantum systems including Shannon entropy, von Neumann entropy, Rényi entropy, and Tsallis entropy. We discuss known and new entropic and information inequalities for classical and quantum systems, both composite and noncomposite. We demonstrate matrix inequalities associated with the entropic subadditivity and strong subadditivity conditions and give a new inequality for matrix elements of unitary matrices.

  12. The roles of electronic exchange and correlation in charge-transfer- to-solvent dynamics: Many-electron nonadiabatic mixed quantum/classical simulations of photoexcited sodium anions in the condensed phase

    SciTech Connect

    Glover, William J.; Larsen, Ross E.; Schwartz, Benjamin J.

    2008-10-28

    The charge-transfer-to-solvent (CTTS) reactions of solvated atomic anions serve as ideal models for studying the dynamics of electron transfer: The fact that atomic anions have no internal degrees of freedom provides one of the most direct routes to understanding how the motions of solvent molecules influence charge transfer, and the relative simplicity of atomic electronic structure allows for direct contact between theory and experiment. To date, molecular dynamics simulations of the CTTS process have relied on a single-electron description of the atomic anion--only the electron involved in the charge transfer has been treated quantum mechanically, and the electronic structure of the atomic solute has been treated via pseudopotentials. In this paper, we examine the severity of approximating the electronic structure of CTTS anions with a one-electron model and address the role of electronic exchange and correlation in both CTTS electronic structure and dynamics. To do this, we perform many-electron mixed quantum/classical molecular dynamics simulations of the ground- and excited-state properties of the aqueous sodium anion (sodide). We treat both of the sodide valence electrons quantum mechanically and solve the Schroedinger equation using configuration interaction with singles and doubles (CISD), which provides an exact solution for two electrons. We find that our multielectron simulations give excellent general agreement with experimental results on the CTTS spectroscopy and dynamics of sodide in related solvents. We also compare the results of our multielectron simulations to those from one-electron simulations on the same system [C. J. Smallwood et al., J. Chem. Phys. 119, 11263 (2003)] and find substantial differences in the equilibrium CTTS properties and the nonadiabatic relaxation dynamics of one- and two-electron aqueous sodide. For example, the one-electron model substantially underpredicts the size of sodide, which in turn results in a dramatically

  13. Experimental characterization of Gaussian quantum discord generated by four-wave mixing

    NASA Astrophysics Data System (ADS)

    Vogl, Ulrich; Glasser, Ryan T.; Glorieux, Quentin; Clark, Jeremy B.; Corzo, Neil V.; Lett, Paul D.

    2013-01-01

    We experimentally determine the Gaussian quantum discord present in two-mode squeezed vacuum generated by a four-wave mixing process in hot rubidium vapor. The frequency spectra of the discord as well as the quantum and classical mutual information are also measured. In addition, the effects of symmetric attenuation introduced into both modes of the squeezed vacuum on the Gaussian quantum discord, and the quantum mutual information and the classical correlations are examined experimentally. Finally, we show that due to the multi-spatial-mode nature of the four-wave mixing process, the Gaussian quantum discord may exhibit sub- or superadditivity depending on which spatial channels are selected.

  14. Playing with functions of positive type, classical and quantum

    NASA Astrophysics Data System (ADS)

    Aniello, Paolo

    2015-06-01

    A function of positive type can be defined as a positive functional on a convolution algebra of a locally compact group. In the case where the group is abelian, by Bochner’s theorem a function of positive type is, up to normalization, the Fourier transform of a probability measure. Therefore, considering the group of translations on phase space, a suitably normalized phase-space function of positive type can be regarded as a realization of a classical state. Thus, it may be called a function of classical positive type. Replacing the ordinary convolution on phase space with the twisted convolution, one obtains a noncommutative algebra of functions whose positive functionals we may call functions of quantum positive type. In fact, by a quantum version of Bochner’s theorem, a continuous function of quantum positive type is, up to normalization, the (symplectic) Fourier transform of a Wigner quasi-probability distribution; hence, it can be regarded as a phase-space realization of a quantum state. Playing with functions of positive type—classical and quantum—one is led in a natural way to consider a class of semigroups of operators, the classical-quantum semigroups. The physical meaning of these mathematical objects is unveiled via quantization, so obtaining a class of quantum dynamical semigroups that, borrowing terminology from quantum information science, may be called classical-noise semigroups.

  15. Experimental detection of nonclassical correlations in mixed-state quantum computation

    SciTech Connect

    Passante, G.; Moussa, O.; Trottier, D. A.; Laflamme, R.

    2011-10-15

    We report on an experiment to detect nonclassical correlations in a highly mixed state. The correlations are characterized by the quantum discord and are observed using four qubits in a liquid-state nuclear magnetic resonance quantum information processor. The state analyzed is the output of a DQC1 computation, whose input is a single quantum bit accompanied by n maximally mixed qubits. This model of computation outperforms the best known classical algorithms and, although it contains vanishing entanglement, it is known to have quantum correlations characterized by the quantum discord. This experiment detects nonvanishing quantum discord, ensuring the existence of nonclassical correlations as measured by the quantum discord.

  16. Classical and quantum communication without a shared reference frame.

    PubMed

    Bartlett, Stephen D; Rudolph, Terry; Spekkens, Robert W

    2003-07-11

    We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.

  17. Comparison of quantum and classical relaxation in spin dynamics.

    PubMed

    Wieser, R

    2013-04-01

    The classical Landau-Lifshitz equation with a damping term has been derived from the time evolution of a quantum mechanical wave function under the assumption of a non-Hermitian Hamilton operator. Further, the trajectory of a classical spin (S) has been compared with the expectation value of the spin operator (Ŝ). A good agreement between classical and quantum mechanical trajectories can be found for Hamiltonians linear in Ŝ or S, respectively. Quadratic or higher order terms in the Hamiltonian result in a disagreement.

  18. Statistical mechanics based on fractional classical and quantum mechanics

    SciTech Connect

    Korichi, Z.; Meftah, M. T.

    2014-03-15

    The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

  19. Nonmonotonicity in the quantum-classical transition: chaos induced by quantum effects.

    PubMed

    Kapulkin, Arie; Pattanayak, Arjendu K

    2008-08-15

    The classical-quantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is nonmonotonic in variant Planck's over 2pi. PMID:18764537

  20. PREFACE: Particles and Fields: Classical and Quantum

    NASA Astrophysics Data System (ADS)

    Asorey, M.; Clemente-Gallardo, J.; Marmo, G.

    2007-07-01

    This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his life-long activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J Clemente-Gallardo and G Marmo The Local Organizing Committee George Sudarshan George Sudarshan

    International Advisory Committee

    A. Ashtekhar (Pennsylvania State University, USA)
    L. J. Boya (Universidad de Zaragoza, Spain)
    I. Cirac (Max Planck Institute, Garching

    1. Communication Tasks with Infinite Quantum-Classical Separation.

      PubMed

      Perry, Christopher; Jain, Rahul; Oppenheim, Jonathan

      2015-07-17

      Quantum resources can be more powerful than classical resources-a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two parties' inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than their classical counterpart. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n. Next, we consider a version of the task where the parties may have access to entanglement. With this assistance, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n. The task is related to the Pusey-Barrett-Rudolph theorem which arises in the context of the foundations of quantum theory. PMID:26230777

    2. Communication Tasks with Infinite Quantum-Classical Separation.

      PubMed

      Perry, Christopher; Jain, Rahul; Oppenheim, Jonathan

      2015-07-17

      Quantum resources can be more powerful than classical resources-a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two parties' inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than their classical counterpart. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n. Next, we consider a version of the task where the parties may have access to entanglement. With this assistance, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n. The task is related to the Pusey-Barrett-Rudolph theorem which arises in the context of the foundations of quantum theory.

    3. Classical and quantum proton vibration in a nonharmonic strongly coupled system

      NASA Astrophysics Data System (ADS)

      McDonald, K. M.; Thorson, W. R.; Choi, J. H.

      1993-09-01

      Classical and quantum descriptions of proton vibration are compared for a coupled nonharmonic model based on an ab initio potential for the bifluoride ion, [FHF]-. Accurate quantum calculations and exact classical dynamics are compared with quantum and classical versions of the self-consistent-field (SCF) approximation. Semiclassical and quantum SCF eigenvalues agree within JWKB-type errors. The SCF scheme closely approximates exact quantum states for the lowest 4-5 vibrational levels of each symmetry, except at avoided crossings where strong CI mixing of SCF levels occurs. True classical motion, however, is mainly irregular except at very low energies, and even where it remains regular it may be strongly reorganized by a 1:1 periodic resonance associated with major potential surface features. Strongly mixed CI states at systematic avoided crossings of SCF levels at higher energies do have classical analogs in the reorganized classical motions seen at low energies; stabilized CI components correspond to a stable periodic 1:1 orbit, destabilized components to an unstable periodic 1:1 elliptical orbit. Canonical perturbation theory is used to study further the sense in which the exactly separable classical SCF Hamiltonian is ``close'' to the true Hamiltonian. Where true motion is modal or SCF-like, first-order perturbed trajectories and second-order perturbed energies describe it very accurately. However since the dynamics can be strongly disturbed even at very low energies, correlation effects are obviously not ``small'' in the sense usually meant in classical dynamics, i.e., that regular trajectories mostly remain regular in the nonseparable perturbed system.

    4. Maximal Parrondo's Paradox for Classical and Quantum Markov Chains

      NASA Astrophysics Data System (ADS)

      Grünbaum, F. Alberto; Pejic, Michael

      2016-02-01

      Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. In this paper, we will analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox. The game we have utilized is simpler than games for which this behavior has been previously noted in the classical and quantum cases. We will show that in certain situations the paradox can occur to a greater degree in the quantum version than is possible in the classical versions.

    5. Steering Quantum States Towards Classical Bohr-Like Orbits

      SciTech Connect

      Dunning, F. B.; Reinhold, Carlos O; Yoshida, S.; Burgdorfer, J.

      2010-01-01

      This article furnishes an introduction to the properties of time-dependent electronic wavefunctions in atoms and to physics at the interface between the quantum and classical worlds. We describe how, almost 100 years after the introduction of the Bohr model of the atom, it is now possible using pulsed electric fields to create in the laboratory localized wavepackets in high-n (n ~ 300) Rydberg atoms that travel in near-circular Bohr-like orbits mimicking the behavior of a classical electron. The control protocols employed are explained with the aid of quantum and classical dynamics. Remarkably, while many aspects of the underlying behavior can be described using classical arguments, even at n ~ 300 purely quantum effects such as revivals can be seen.

    6. Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

      NASA Astrophysics Data System (ADS)

      Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor

      2016-06-01

      Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.

    7. Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations.

      PubMed

      Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor

      2016-06-17

      Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states. PMID:27367395

    8. A wave equation interpolating between classical and quantum mechanics

      NASA Astrophysics Data System (ADS)

      Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

      2015-10-01

      We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

    9. Planck's radiation law: is a quantum-classical perspective possible?

      NASA Astrophysics Data System (ADS)

      Marrocco, Michele

      2016-05-01

      Planck's radiation law provides the solution to the blackbody problem that marks the decline of classical physics and the rise of the quantum theory of the radiation field. Here, we venture to suggest the possibility that classical physics might be equally suitable to deal with the blackbody problem. A classical version of the Planck's radiation law seems to be achievable if we learn from the quantum-classical correspondence between classical Mie theory and quantum-mechanical wave scattering from spherical scatterers (partial wave analysis). This correspondence designs a procedure for countable energy levels of the radiation trapped within the blackbody treated within the multipole approach of classical electrodynamics (in place of the customary and problematic expansion in terms of plane waves that give rise to the ultraviolet catastrophe). In turn, introducing the Boltzmann discretization of energy levels, the tools of classical thermodynamics and statistical theory become available for the task. On the other hand, the final result depends on a free parameter whose physical units are those of an action. Tuning this parameter on the value given by the Planck constant makes the classical result agree with the canonical Planck's radiation law.

    10. Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates

      NASA Astrophysics Data System (ADS)

      Bravyi, Sergey; Gosset, David

      2016-06-01

      We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates. The first demonstrations of fault-tolerant quantum circuits based on 2D topological codes are likely to be dominated by Clifford gates due to a high implementation cost associated with logical T gates. Thus our algorithm may serve as a verification tool for near-term quantum computers which cannot in practice be simulated by other means. To demonstrate the power of the new method, we performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T gates.

    11. Quantum stochastic walks: A generalization of classical random walks and quantum walks

      NASA Astrophysics Data System (ADS)

      Whitfield, James D.; Rodríguez-Rosario, César A.; Aspuru-Guzik, Alán

      2010-02-01

      We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

    12. Quantum stochastic walks: A generalization of classical random walks and quantum walks

      SciTech Connect

      Whitfield, James D.; Rodriguez-Rosario, Cesar A.; Aspuru-Guzik, Alan

      2010-02-15

      We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

    13. Quantum stochastic walks: A generalization of classical random walks and quantum walks

      SciTech Connect

      Rodriguez-Rosario, Cesar A.; Aspuru-Guzik, Alan; Whitfield, James D.

      2010-02-23

      We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

    14. Entangling distant quantum dots using classical interference

      NASA Astrophysics Data System (ADS)

      Busch, Jonathan; Kyoseva, Elica S.; Trupke, Michael; Beige, Almut

      2008-10-01

      We show that it is possible to employ reservoir engineering to turn two distant and relatively bad cavities into one good cavity with a tunable spontaneous decay rate. As a result, quantum computing schemes, which would otherwise require the shuttling of atomic qubits in and out of an optical resonator, can now be applied to distant quantum dots. To illustrate this we transform a recent proposal to entangle two qubits via the observation of macroscopic fluorescence signals [J. Metz , Phys. Rev. Lett. 97, 040503 (2006)] to the electron-spin states of two semiconductor quantum dots. Our scheme requires neither the coherent control of qubit-qubit interactions nor the detection of single photons. Moreover, the scheme is relatively robust against spin-bath couplings, parameter fluctuations, and the spontaneous emission of photons.

    15. Quantum Plasma Effects in the Classical Regime

      SciTech Connect

      Brodin, G.; Marklund, M.; Manfredi, G.

      2008-05-02

      For quantum effects to be significant in plasmas it is often assumed that the temperature over density ratio must be small. In this paper we challenge this assumption by considering the contribution to the dynamics from the electron spin properties. As a starting point we consider a multicomponent plasma model, where electrons with spin-up and spin-down are regarded as different fluids. By studying the propagation of Alfven wave solitons we demonstrate that quantum effects can survive in a relatively high-temperature plasma. The consequences of our results are discussed.

    16. Implementing Quantum Walks Using Orbital Angular Momentum of Classical Light

      NASA Astrophysics Data System (ADS)

      Goyal, Sandeep K.; Roux, Filippus S.; Forbes, Andrew; Konrad, Thomas

      2013-06-01

      We present an implementation scheme for a quantum walk in the orbital angular momentum space of a laser beam. The scheme makes use of a ring interferometer, containing a quarter-wave plate and a q plate. This setup enables one to perform an arbitrary number of quantum walk steps. In addition, the classical nature of the implementation scheme makes it possible to observe the quantum walk evolution in real time. We use nonquantum entanglement of the laser beam’s polarization with its orbital angular momentum to implement the quantum walk.

    17. Observation of Quantum Fingerprinting Beating the Classical Limit

      NASA Astrophysics Data System (ADS)

      Guan, Jian-Yu; Xu, Feihu; Yin, Hua-Lei; Li, Yuan; Zhang, Wei-Jun; Chen, Si-Jing; Yang, Xiao-Yan; Li, Li; You, Li-Xing; Chen, Teng-Yun; Wang, Zhen; Zhang, Qiang; Pan, Jian-Wei

      2016-06-01

      Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantum-mechanical properties of physical systems for practical applications. In the field of communication complexity, quantum communication allows the advantage of an exponential reduction in the transmitted information over classical communication to accomplish distributed computational tasks. However, to date, demonstrating this advantage in a practical setting continues to be a central challenge. Here, we report a proof-of-principle experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting single-photon detectors and a stable fiber-based Sagnac interferometer are used to implement a quantum fingerprinting system that is capable of transmitting less information than the classical proven lower bound over 20 km standard telecom fiber for input sizes of up to 2 Gbits. The results pave the way for experimentally exploring the advanced features of quantum communication and open a new window of opportunity for research in communication complexity and testing the foundations of physics.

    18. Observation of Quantum Fingerprinting Beating the Classical Limit.

      PubMed

      Guan, Jian-Yu; Xu, Feihu; Yin, Hua-Lei; Li, Yuan; Zhang, Wei-Jun; Chen, Si-Jing; Yang, Xiao-Yan; Li, Li; You, Li-Xing; Chen, Teng-Yun; Wang, Zhen; Zhang, Qiang; Pan, Jian-Wei

      2016-06-17

      Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantum-mechanical properties of physical systems for practical applications. In the field of communication complexity, quantum communication allows the advantage of an exponential reduction in the transmitted information over classical communication to accomplish distributed computational tasks. However, to date, demonstrating this advantage in a practical setting continues to be a central challenge. Here, we report a proof-of-principle experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting single-photon detectors and a stable fiber-based Sagnac interferometer are used to implement a quantum fingerprinting system that is capable of transmitting less information than the classical proven lower bound over 20 km standard telecom fiber for input sizes of up to 2 Gbits. The results pave the way for experimentally exploring the advanced features of quantum communication and open a new window of opportunity for research in communication complexity and testing the foundations of physics. PMID:27367371

    19. Observation of Quantum Fingerprinting Beating the Classical Limit.

      PubMed

      Guan, Jian-Yu; Xu, Feihu; Yin, Hua-Lei; Li, Yuan; Zhang, Wei-Jun; Chen, Si-Jing; Yang, Xiao-Yan; Li, Li; You, Li-Xing; Chen, Teng-Yun; Wang, Zhen; Zhang, Qiang; Pan, Jian-Wei

      2016-06-17

      Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantum-mechanical properties of physical systems for practical applications. In the field of communication complexity, quantum communication allows the advantage of an exponential reduction in the transmitted information over classical communication to accomplish distributed computational tasks. However, to date, demonstrating this advantage in a practical setting continues to be a central challenge. Here, we report a proof-of-principle experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting single-photon detectors and a stable fiber-based Sagnac interferometer are used to implement a quantum fingerprinting system that is capable of transmitting less information than the classical proven lower bound over 20 km standard telecom fiber for input sizes of up to 2 Gbits. The results pave the way for experimentally exploring the advanced features of quantum communication and open a new window of opportunity for research in communication complexity and testing the foundations of physics.

    20. Classical-driving-assisted quantum speed-up

      NASA Astrophysics Data System (ADS)

      Zhang, Ying-Jie; Han, Wei; Xia, Yun-Jie; Cao, Jun-Peng; Fan, Heng

      2015-03-01

      We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.

    1. A generalization of Fermat's principle for classical and quantum systems

      NASA Astrophysics Data System (ADS)

      Elsayed, Tarek A.

      2014-09-01

      The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substantiate this conjecture for time-independent quantum systems and for a classical system consisting of coupled harmonic oscillators. An exception to this principle is the configuration space of a charged particle in a constant magnetic field; in this case the principle is valid in a frame rotating by half the Larmor frequency, not the stationary lab frame.

    2. A quantum-classical bracket that satisfies the Jacobi identity

      SciTech Connect

      Prezhdo, Oleg V.

      2006-05-28

      A quantum-classical bracket is proposed and is shown to satisfy the Jacobi identity, in contrast to previous definitions that obey this property only up to higher order terms in the Planck constant ({Dirac_h}/2{pi}). The Jacobi identity is required of a true Lie bracket and ensures that the Lie bracket of constants of motion is also a constant of motion. An explicit calculation of the Jacobi identity highlights the difference between the proposed and traditional definitions. A further example illustrates that the proposed bracket generates a more consistent quantum-classical dynamics than the traditional bracket. The traditional quantum-classical dynamics in the Henon-Heiles system diverges due to higher order ({Dirac_h}/2{pi}) terms. The divergence is eliminated with the proposed bracket.

    3. PREFACE: Particles and Fields: Classical and Quantum

      NASA Astrophysics Data System (ADS)

      Asorey, M.; Clemente-Gallardo, J.; Marmo, G.

      2007-07-01

      This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his life-long activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J Clemente-Gallardo and G Marmo The Local Organizing Committee George Sudarshan George Sudarshan

      International Advisory Committee

      A. Ashtekhar (Pennsylvania State University, USA)
      L. J. Boya (Universidad de Zaragoza, Spain)
      I. Cirac (Max Planck Institute, Garching

    4. One-Shot Classical-Quantum Capacity and Hypothesis Testing

      NASA Astrophysics Data System (ADS)

      Wang, Ligong; Renner, Renato

      2012-05-01

      The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein’s lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.

    5. Classical and quantum cosmology of minimal massive bigravity

      NASA Astrophysics Data System (ADS)

      Darabi, F.; Mousavi, M.

      2016-10-01

      In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.

    6. Bandt-Pompe-Tsallis quantifier and quantum-classical transition

      NASA Astrophysics Data System (ADS)

      Kowalski, A. M.; Plastino, A.

      2009-10-01

      We concern ourselves with statistical quantifiers of semiclassical time-evolutions and their classical limit. The system of interest represents the interaction between matter and a given field. Our tool here is the so-called Permutation Entropy, evaluated by recourse to the so-called Bandt-Pompe technique, within a Tsallis scenario. We encounter that the most salient details of the quantum-classical transition are well-described, indeed, in a better fashion than that of previous approaches.

    7. Quantum chaos of a mixed open system of kicked cold atoms

      SciTech Connect

      Krivolapov, Yevgeny; Fishman, Shmuel; Ott, Edward; Antonsen, Thomas M.

      2011-01-15

      The quantum and classical dynamics of particles kicked by a Gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The fidelity (Loschmidt echo) is found to exhibit oscillations that can be determined from classical considerations but are sensitive to phase space structures that are smaller than Planck's constant. Families of quasienergies are determined from classical phase space structures. Substantial differences between the classical and quantum dynamics are found for time-dependent scattering. It is argued that the system can be experimentally realized by cold atoms kicked by a Gaussian light beam.

    8. Trigonometric version of quantum-classical duality in integrable systems

      NASA Astrophysics Data System (ADS)

      Beketov, M.; Liashyk, A.; Zabrodin, A.; Zotov, A.

      2016-02-01

      We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero-Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.

    9. Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin

      NASA Astrophysics Data System (ADS)

      Xue, Peng; Sanders, Barry C.

      2013-02-01

      We show that the standard quantum-walk quantum-to-classical transition, characterized by ballistic-to-diffusive spreading of the walker's position, can be controlled by externally modulating the coin state. We illustrate this by showing an oscillation between classical diffusive and quantum ballistic spreading using numerical and asymptotically exact closed-form solutions, and we prove that the walker is in a controllable incoherent mixture of classical and quantum walks with a reversible quantum-to-classical transition.

    10. Physics on the boundary between classical and quantum mechanics

      NASA Astrophysics Data System (ADS)

      't Hooft, Gerard

      2014-04-01

      Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?

    11. Classical and Quantum Vibration in a Nonseparable, Nonharmonic System

      NASA Astrophysics Data System (ADS)

      McDonald, Karen Marie

      Studies of vibrational dynamics have been performed on a two-dimensional model potential surface V(x,z; R), adapted from the ab initio surface previously used in this laboratory to analyze dynamics of the bifluoride ion (FHF) ^-. The model potential has C _{2v} symmetry, but is strongly anharmonic and nonseparable in the dynamical variables (x,z); its character changes as the parameter R is varied. Quantum and classical descriptions of vibrational states in this system are compared with corresponding Self-Consistent Field (SCF) approximations. Insights provided by each approach are assessed. Systematic Fermi resonances appear in the quantum mechanical states (at energies up to approximately 10,000 cm^{-1}) arising from crossings of quantum SCF levels with two quanta of vibration exchanged between x and z modes. The lowest quantum states of each symmetry are well described by the SCF approximation except near such crossings. Calculations using Configuration Interaction were done to obtain accurate eigenstates and examine correlations in the quantum mechanics. The Classical Self-Consistent Field (CSCF) method provides a description of the mechanics similar to that given by its quantum counterpart. Classical bound state methods based on semiclassical quantization of quasiperiodic trajectories are unable to give a corresponding description. At energies as low as the quantum ground state, the true classical dynamics is strongly disturbed by resonant interactions. At higher energies the number and strength of these disruptions is so great that the motion is largely irregular. The most prominent effect is a 1:1 frequency resonance associated with strong reorganization of the classical motion along pronounced valleys of the potential surface lying at +/-26^circ to the x-axis. This phenomenon has been studied by analysis of the true dynamics and by application of classical canonical perturbation theory to the zero-order CSCF description. It is found that the latter gives a

    12. Engineering arbitrary pure and mixed quantum states

      SciTech Connect

      Pechen, Alexander

      2011-10-15

      Controlled manipulation by atomic- and molecular-scale quantum systems has attracted a lot of research attention in recent years. A fundamental problem is to provide deterministic methods for controlled engineering of arbitrary quantum states. This work proposes a deterministic method for engineering arbitrary pure and mixed states of a wide class of quantum systems. The method exploits a special combination of incoherent and coherent controls (incoherent and coherent radiation) and has two properties which are specifically important for manipulating by quantum systems: it realizes the strongest possible degree of their state control, complete density matrix controllability, meaning the ability to steer arbitrary pure and mixed initial states into any desired pure or mixed final state, and it is all-to-one, such that each particular control transfers all initial system states into one target state.

    13. Classical and quantum temperature fluctuations via holography

      SciTech Connect

      Balatsky, Alexander V.; Gudnason, Sven Bjarke; Thorlacius, Larus; Zarembo, Konstantin; Krikun, Alexander; Kedem, Yaron

      2014-05-27

      We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS space-time. The fluctuation spectrum is governed by the lowest-lying hydrodynamic sound modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at large temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordstrom black hole in global AdS.

    14. Quantum stochastic walks: A generalization of classical random walks and quantum walks

      NASA Astrophysics Data System (ADS)

      Aspuru-Guzik, Alan

      2010-03-01

      We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases, but also includes more general probability distributions. As an example, we study the QSW on a line, the QW to CRW transition and transitions to genearlized QSWs that go beyond the CRW and QW. QSWs provide a new framework to the study of quantum algorithms as well as of quantum walks with environmental effects.

    15. Making the Transition from Classical to Quantum Physics

      ERIC Educational Resources Information Center

      Dutt, Amit

      2011-01-01

      This paper reports on the nature of the conceptual understandings developed by Year 12 Victorian Certificate of Education (VCE) physics students as they made the transition from the essentially deterministic notions of classical physics, to interpretations characteristic of quantum theory. The research findings revealed the fact that the…

    16. Bandt Pompe approach to the classical-quantum transition

      NASA Astrophysics Data System (ADS)

      Kowalski, A. M.; Martín, M. T.; Plastino, A.; Rosso, O. A.

      2007-09-01

      By regarding the celebrated classical-quantum transition problem as one pertaining to the domain of dynamic systems’ theory, we present a discussion that exhibits the superiority of the Bandt-Pompe approach to the extraction of a probability distribution from time series’ values.

    17. Quantum and classical thermoelectric transport in quantum dot nanocomposites

      NASA Astrophysics Data System (ADS)

      Zhou, Jun; Yang, Ronggui

      2011-10-01

      Quantum dot nanocomposites are potentially high-efficiency thermoelectric materials, which could outperform superlattices and random nanocomposites in terms of manufacturing cost-effectiveness and material properties because of the reduction of thermal conductivity due to the phonon-interface scattering, the enhancement of Seebeck coefficient due to the formation of minibands, and the enhancement of electrical conductivity due to the phonon-bottleneck effect in electron-phonon scattering for quantum-confined electrons. In this paper, we investigate the thermoelectric transport properties of quantum dot nanocomposites through a two-channel transport model that includes the transport of quantum-confined electrons through the hopping mechanism and the semiclassical transport of bulk-like electrons. For the quantum-confined electrons whose wave functions are confined in the quantum dots with overlapping tail extending to the matrix, we develop a tight-binding model together with the Kubo formula and the Green's function method to describe the transport processes of these electrons. The formation of minibands due to the quantum confinement and the phonon-bottleneck effect on carrier-phonon scattering are considered. For transport of bulk-like electrons, a Boltzmann-transport-equation-based semiclassical model is used to describe the multiband transport processes of carriers. The intrinsic carrier scatterings as well as the carrier-interface scattering of these bulk-like electrons are considered. We then apply the two-channel transport model to predict thermoelectric transport properties of n-type PbSe/PbTe quantum dot nanocomposites with PbSe quantum dots uniformly embedded in the PbTe matrix. The dependence of thermoelectric transport coefficients on the size of quantum dots, interdot distance, doping concentration, and temperature are studied in detail. Due to the formation of minibands and the phonon-bottleneck effect on carrier-phonon scattering, we show that

    18. Bridging quantum and classical plasmonics with a quantum-corrected model.

      PubMed

      Esteban, Ruben; Borisov, Andrei G; Nordlander, Peter; Aizpurua, Javier

      2012-01-01

      Electromagnetic coupling between plasmonic resonances in metallic nanoparticles allows for engineering of the optical response and generation of strong localized near-fields. Classical electrodynamics fails to describe this coupling across sub-nanometer gaps, where quantum effects become important owing to non-local screening and the spill-out of electrons. However, full quantum simulations are not presently feasible for realistically sized systems. Here we present a novel approach, the quantum-corrected model (QCM), that incorporates quantum-mechanical effects within a classical electrodynamic framework. The QCM approach models the junction between adjacent nanoparticles by means of a local dielectric response that includes electron tunnelling and tunnelling resistivity at the gap and can be integrated within a classical electrodynamical description of large and complex structures. The QCM predicts optical properties in excellent agreement with fully quantum mechanical calculations for small interacting systems, opening a new venue for addressing quantum effects in realistic plasmonic systems.

    19. The Quantum-to-Classical Transition of Primordial Cosmological Perturbations

      NASA Astrophysics Data System (ADS)

      Pinto-Neto, Nelson

      There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this contribution, it is shown how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit. This contribution is a compilation of the works done by Grasiele Santos, Ward Struyve and myself cited in Pinto-Neto et al. (Phys Rev D 85:083506, 2012; Phys Rev D 89:023517, 2014), where all details can be found.

    20. Renormalization from Classical to Quantum Physics

      NASA Astrophysics Data System (ADS)

      Kar, Arnab

      The concept of renormalization was first introduced by Dirac to investigate the infinite self energy of an electron classically. This radical theory was probably the first time when an infinity occurring in a physical system was systematically investigated. This thesis presents a new perspective of renormalization by introducing methods from metric geometry to control divergences. We start by extending Dirac's work and analyzing how the radiation reaction due to the precision of the electron's magnetic moment affects its motion. This is followed by modeling scalar field theory on lattices of various kinds. Scale invariance, which plays a major role in the very few renormalizable theories in nature, is inbuilt in our formalism. We also use Wilson's ideas of effective theory and finite element methods to study continuum systems. Renormalization group transformations form the central theme in this picture. By incorporating finite element methods, an idea borrowed from mechanical engineering, we study scalar fields on triangular lattices in a hierarchal manner. In our case, the cotangent formula turns out to be a fixed point of the renormalization group transformations. We end our thesis by introducing a new metric for space-time which emerges from the scalar field itself. The standard techniques used in the theory of renormalization so far attempt to redefine coupling constants of the theory to remove divergences at short distance scales. In our formalism, we deduce the distance scale itself. In our notion of distance, built from correlation functions of the fields, the divergences disappear.

      1. Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient

        NASA Astrophysics Data System (ADS)

        Mari, A.; Eisert, J.

        2012-12-01

        We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

      2. Quantum correlations of three-qubit states driven by a classical random external field

        NASA Astrophysics Data System (ADS)

        Guo, Youneng; Fang, Maofa; Zhang, Shiyang; Liu, Xiang

        2015-03-01

        In this paper, we exploit the notions of tripartite quantum discord {{D}(3)}, tripartite negativity {{N}(3)}, and entanglement witnesses (EWs), respectively, as a measure of quantum correlations in a model of three noninteracting qubits subject to a classical random external field. We compare the dynamics of {{D}(3)} with that of entanglement for the initial entangled pure or mixed GHZ- and W-type states. We find that the quantum correlations dynamics depend on the input configuration of the purity of the initial states. The results show that {{D}(3)} may be more robust than entanglement and no sudden death of the {{D}(3)} occurs, whereas entanglement displays periodically sudden death and revivals in the regions for GHZ- and W-type states driven by a classical random external field. Furthermore, we also show that the survival partial entanglement can be detected by means of the suitable EWs.

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

        NASA Astrophysics Data System (ADS)

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

        2007-04-01

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

      4. Autonomous quantum thermal machines and quantum to classical energy flow

        NASA Astrophysics Data System (ADS)

        Frenzel, Max; Jennings, David; Rudolph, Terry

        We address the issue of autonomous quantum thermal machines that are tailored to achieve some specific thermodynamic primitive, such as work extraction in the presence of a thermal environment, while having minimal or no control from the macroscopic regime. Beyond experimental implementations, this provides an arena in which to address certain foundational aspects such as the role of coherence in thermodynamics, the use of clock degrees of freedom and the simulation of local time-dependent Hamiltonians in a particular quantum subsystem. For small-scale systems additional issues arise. Firstly, it is not clear to what degree genuine ordered thermodynamic work has been extracted, and secondly non-trivial back-actions on the thermal machine must be accounted for. We find that both these aspects can be resolved through a judicious choice of quantum measurements that magnify thermodynamic properties up the ladder of length-scales, while simultaneously stabilizing the quantum thermal machine. Within this framework we show that thermodynamic reversibility is obtained in a particular Zeno limit, and finally illustrate these concepts with a concrete example involving spin-systems.

      5. Experimental multiplexing of quantum key distribution with classical optical communication

        SciTech Connect

        Wang, Liu-Jun; Chen, Luo-Kan; Ju, Lei; Xu, Mu-Lan; Zhao, Yong; Chen, Kai; Chen, Zeng-Bing; Chen, Teng-Yun Pan, Jian-Wei

        2015-02-23

        We demonstrate the realization of quantum key distribution (QKD) when combined with classical optical communication, and synchronous signals within a single optical fiber. In the experiment, the classical communication sources use Fabry-Pérot (FP) lasers, which are implemented extensively in optical access networks. To perform QKD, multistage band-stop filtering techniques are developed, and a wavelength-division multiplexing scheme is designed for the multi-longitudinal-mode FP lasers. We have managed to maintain sufficient isolation among the quantum channel, the synchronous channel and the classical channels to guarantee good QKD performance. Finally, the quantum bit error rate remains below a level of 2% across the entire practical application range. The proposed multiplexing scheme can ensure low classical light loss, and enables QKD over fiber lengths of up to 45 km simultaneously when the fibers are populated with bidirectional FP laser communications. Our demonstration paves the way for application of QKD to current optical access networks, where FP lasers are widely used by the end users.

      6. Experimental multiplexing of quantum key distribution with classical optical communication

        NASA Astrophysics Data System (ADS)

        Wang, Liu-Jun; Chen, Luo-Kan; Ju, Lei; Xu, Mu-Lan; Zhao, Yong; Chen, Kai; Chen, Zeng-Bing; Chen, Teng-Yun; Pan, Jian-Wei

        2015-02-01

        We demonstrate the realization of quantum key distribution (QKD) when combined with classical optical communication, and synchronous signals within a single optical fiber. In the experiment, the classical communication sources use Fabry-Pérot (FP) lasers, which are implemented extensively in optical access networks. To perform QKD, multistage band-stop filtering techniques are developed, and a wavelength-division multiplexing scheme is designed for the multi-longitudinal-mode FP lasers. We have managed to maintain sufficient isolation among the quantum channel, the synchronous channel and the classical channels to guarantee good QKD performance. Finally, the quantum bit error rate remains below a level of 2% across the entire practical application range. The proposed multiplexing scheme can ensure low classical light loss, and enables QKD over fiber lengths of up to 45 km simultaneously when the fibers are populated with bidirectional FP laser communications. Our demonstration paves the way for application of QKD to current optical access networks, where FP lasers are widely used by the end users.

      7. The classical and quantum dynamics of molecular spins on graphene.

        PubMed

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

        2016-02-01

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

      8. Controlling the sense of molecular rotation: Classical versus quantum analysis

        SciTech Connect

        Khodorkovsky, Yuri; Averbukh, Ilya Sh.; Kitano, Kenta; Hasegawa, Hirokazu; Ohshima, Yasuhiro

        2011-02-15

        Recently, it was predicted theoretically and verified experimentally that a pair of delayed and cross-polarized short laser pulses can create molecular ensembles with a well-defined sense of rotation (clockwise or counterclockwise). Here we provide a comparative study of the classical and quantum aspects of the underlying mechanism for linear molecules and for symmetric tops, like benzene molecules, that were used for the first experimental demonstration of the effect. Very good quantitative agreement is found between the classical description of the process and the rigorous quantum-mechanical analysis at the relevant experimental conditions. Both approaches predict the same optimal values for the delay between pulses and the angle between them, and deliver the same magnitude of the induced oriented angular momentum of the molecular ensemble. As expected, quantum and classical analyses substantially deviate when the delay between pulses is comparable with the period of quantum rotational revivals. However, time-averaged characteristics of the excited molecular ensemble are equally well described by these two approaches. This is illustrated by calculating the anisotropic time-averaged angular distribution of the double-pulse excited molecules, which reflects persistent confinement of the molecular axes to the rotation plane defined by two polarization vectors of the pulses.

      9. Team decision problems with classical and quantum signals.

        PubMed

        Brandenburger, Adam; La Mura, Pierfrancesco

        2016-01-13

        We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading.

      10. Team decision problems with classical and quantum signals

        PubMed Central

        Brandenburger, Adam; La Mura, Pierfrancesco

        2016-01-01

        We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570–576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193–216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79–96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. PMID:26621985

      11. Controlling the sense of molecular rotation: Classical versus quantum analysis

        NASA Astrophysics Data System (ADS)

        Khodorkovsky, Yuri; Kitano, Kenta; Hasegawa, Hirokazu; Ohshima, Yasuhiro; Averbukh, Ilya Sh.

        2011-02-01

        Recently, it was predicted theoretically and verified experimentally that a pair of delayed and cross-polarized short laser pulses can create molecular ensembles with a well-defined sense of rotation (clockwise or counterclockwise). Here we provide a comparative study of the classical and quantum aspects of the underlying mechanism for linear molecules and for symmetric tops, like benzene molecules, that were used for the first experimental demonstration of the effect. Very good quantitative agreement is found between the classical description of the process and the rigorous quantum-mechanical analysis at the relevant experimental conditions. Both approaches predict the same optimal values for the delay between pulses and the angle between them, and deliver the same magnitude of the induced oriented angular momentum of the molecular ensemble. As expected, quantum and classical analyses substantially deviate when the delay between pulses is comparable with the period of quantum rotational revivals. However, time-averaged characteristics of the excited molecular ensemble are equally well described by these two approaches. This is illustrated by calculating the anisotropic time-averaged angular distribution of the double-pulse excited molecules, which reflects persistent confinement of the molecular axes to the rotation plane defined by two polarization vectors of the pulses.

      12. Team decision problems with classical and quantum signals.

        PubMed

        Brandenburger, Adam; La Mura, Pierfrancesco

        2016-01-13

        We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. PMID:26621985

      13. A quantum algorithm for Viterbi decoding of classical convolutional codes

        NASA Astrophysics Data System (ADS)

        Grice, Jon R.; Meyer, David A.

        2015-07-01

        We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper, the proposed algorithm is applied to decoding classical convolutional codes, for instance, large constraint length and short decode frames . Other applications of the classical Viterbi algorithm where is large (e.g., speech processing) could experience significant speedup with the QVA. The QVA exploits the fact that the decoding trellis is similar to the butterfly diagram of the fast Fourier transform, with its corresponding fast quantum algorithm. The tensor-product structure of the butterfly diagram corresponds to a quantum superposition that we show can be efficiently prepared. The quantum speedup is possible because the performance of the QVA depends on the fanout (number of possible transitions from any given state in the hidden Markov model) which is in general much less than . The QVA constructs a superposition of states which correspond to all legal paths through the decoding lattice, with phase as a function of the probability of the path being taken given received data. A specialized amplitude amplification procedure is applied one or more times to recover a superposition where the most probable path has a high probability of being measured.

      14. Classical simulation of quantum many-body systems

        NASA Astrophysics Data System (ADS)

        Huang, Yichen

        Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D

      15. Quantum-classical correspondence principles for locally nonequilibrium driven systems.

        PubMed

        Smith, Eric

        2008-02-01

        Many of the core concepts and (especially field-theoretic) tools of statistical mechanics have developed within the context of thermodynamic equilibrium, where state variables are all taken to be charges, meaning that their values are inherently preserved under reversal of the direction of time. A principle concern of nonequilibrium statistical mechanics is to understand the emergence and stability of currents, quantities whose values change sign under time reversal. Whereas the correspondence between classical charge-valued state variables and their underlying statistical or quantum ensembles is quite well understood, the study of currents away from equilibrium has been more fragmentary, with classical descriptions relying on the asymmetric auxiliary-field formalism of Martin, Siggia, and Rose (and often restricted to the Markovian assumption of Doi and Peliti), while quantum descriptions employ a symmetric two-field formalism introduced by Schwinger and further clarified by Keldysh. In this paper we demonstrate that for quantum ensembles in which superposition is not violated by very strong conditions of decoherence, there is a large natural generalization of the principles and tools of equilibrium, which not only admits but requires the introduction of current-valued state variables. For these systems, not only do Martin-Siggia-Rose (MSR) and Schwinger-Keldysh (SK) field methods both exist, in some cases they provide inequivalent classical and quantum descriptions of identical ensembles. With these systems for examples, we can both study the correspondence between classical and quantum descriptions of currents, and also clarify the nature of the mapping between the structurally homologous but interpretationally different MSR and SK formalisms.

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

        PubMed

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

        2015-08-25

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

      17. Scale covariant physics: a 'quantum deformation' of classical electrodynamics

        NASA Astrophysics Data System (ADS)

        Knoll, Yehonatan; Yavneh, Irad

        2010-02-01

        We present a deformation of classical electrodynamics, continuously depending on a 'quantum parameter', featuring manifest gauge, Poincaré and scale covariance. The theory, dubbed extended charge dynamics (ECD), associates a certain length scale with each charge which, due to scale covariance, is an attribute of a solution, not a parameter of the theory. When the EM field experienced by an ECD charge is slowly varying over that length scale, the dynamics of the charge reduces to classical dynamics, its emitted radiation reduces to the familiar Liénard-Wiechert potential and the above length scale is identified as the charge's Compton length. It is conjectured that quantum mechanics describes statistical aspects of ensembles of ECD solutions, much like classical thermodynamics describes statistical aspects of ensembles of classical solutions. A unique 'remote sensing' feature of ECD, supporting that conjecture, is presented, along with an explanation for the illusion of a photon within a classical treatment of the EM field. Finally, a novel conservation law associated with the scale covariance of ECD is derived, indicating that the scale of a solution may 'drift' with time at a constant rate, much like translation covariance implies a uniform drift of the (average) position.

      18. Comparison of classical and quantum dynamics for collinear cluster scattering.

        PubMed

        Bäck, Andreas; Marković, Nikola

        2005-04-01

        The collinear dynamics of a cluster of four particles colliding with a fixed particle representing a surface is investigated using a four-dimensional wave packet approach. The properties of the system are chosen to resemble a water cluster interacting with graphite, but a deeper surface-particle potential is also considered causing significant dissociation of the cluster. Having four different product arrangement channels the system is quantum mechanically demanding but still manageable. The dynamical richness makes it a suitable benchmark system for evaluation of classical and quantum/classical schemes. The average energy transferred to the cluster and the three dissociation probabilities are presented as function of the initial state of the cluster. In addition to wave packet data, results obtained using quasiclassical as well as Wigner sampled classical trajectories are presented. The main conclusion is that classical mechanics can describe the dynamics of the system in a very satisfactory way. Including zero-point energy in the classical simulations is particularly important for a good description of dissociation but less important for energy transfer.

      19. Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates.

        PubMed

        Bravyi, Sergey; Gosset, David

        2016-06-24

        We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates. The first demonstrations of fault-tolerant quantum circuits based on 2D topological codes are likely to be dominated by Clifford gates due to a high implementation cost associated with logical T gates. Thus our algorithm may serve as a verification tool for near-term quantum computers which cannot in practice be simulated by other means. To demonstrate the power of the new method, we performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T gates. PMID:27391708

      20. Quantum tagging for tags containing secret classical data

        SciTech Connect

        Kent, Adrian

        2011-08-15

        Various authors have considered schemes for quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is potentially unbounded. All of the schemes proposed elsewhere in the literature assume that the adversary is able to inspect the interior of the tagging device. All of these schemes have been shown to be breakable if the adversary has unbounded predistributed entanglement. We consider here the case in which the tagging device contains a finite key string shared with distant sites but kept secret from the adversary, and show this allows the location of the tagging device to be authenticated securely and indefinitely. Our protocol relies on quantum key distribution between the tagging device and at least one distant site, and demonstrates a new practical application of quantum key distribution. It also illustrates that the attainable security in position-based cryptography can depend crucially on apparently subtle details in the security scenario considered.

      1. Impact of turbulence in long range quantum and classical communications.

        PubMed

        Capraro, Ivan; Tomaello, Andrea; Dall'Arche, Alberto; Gerlin, Francesca; Ursin, Ruper; Vallone, Giuseppe; Villoresi, Paolo

        2012-11-16

        The study of the free-space distribution of quantum correlations is necessary for any future application of quantum and classical communication aiming to connect two remote locations. Here we study the propagation of a coherent laser beam over 143 km (between Tenerife and La Palma Islands of the Canary archipelagos). By attenuating the beam we also studied the propagation at the single photon level. We investigated the statistic of arrival of the incoming photons and the scintillation of the beam. From the analysis of the data, we propose the exploitation of turbulence to improve the signal to noise ratio of the signal.

      2. Experimental hybrid entanglement between quantum and classical states of light

        NASA Astrophysics Data System (ADS)

        Costanzo, Luca S.; Zavatta, Alessandro; Grandi, Samuele; Bellini, Marco; Jeong, Hyunseok; Kang, Minsu; Lee, Seung-Woo; Ralph, Timothy C.

        2014-12-01

        The realization of hybrid entanglement between a microscopic (quantum) and a macroscopic (classical) system, in analogy to the situation of the famous Schrödinger's cat paradox, is an important milestone, both from the fundamental perspective and for possible applications in the processing of quantum information. The most straightforward optical implementation of this condition is that of the entanglement between a single-photon and a coherent state. In this work, we describe the first step towards the generation of this type of hybrid entanglement from the experimental perspective.

      3. Classical and Quantum features of the spin-curvature coupling

        NASA Astrophysics Data System (ADS)

        Cianfrani, Francesco; Montani, Giovanni

        2007-04-01

        We analyze the behavior of a spinning particle in gravity, both from a quantum and a classical perspective point of view. We infer that, since the interaction between the space-time curvature and a spinning test particle is expected, then the main features of such an interaction can get light on which degrees of freedom have physical meaning in a quantum gravity theory with fermions. Finally, the dimensional reduction of Papapetrou equations is performed in a 5-dimensional Kaluza-Klein background and Dixon-Souriau results for the motion of a charged spinning body are obtained.

      4. Quantum Darwinism for mixed-state environment

        NASA Astrophysics Data System (ADS)

        Quan, Haitao; Zwolak, Michael; Zurek, Wojciech

        2009-03-01

        We exam quantum darwinism when a system is in the presence of a mixed environment, and we find a general relation between the mutual information for the mixed-state environment and the change of the entropy of the fraction of the environment. We then look at a particular solvable model, and we numerically exam the time evolution of the ``mutual information" for large environment. Finally we discuss about the exact expressions for all entropies and the mutual information at special time.

      5. Quantum, classical, and total amount of correlations in a quantum state

        SciTech Connect

        Groisman, Berry; Popescu, Sandu; Winter, Andreas

        2005-09-15

        We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.

      6. Teleportation as a depolarizing quantum channel, relative entropy, and classical capacity.

        PubMed

        Bowen, G; Bose, S

        2001-12-24

        We show that standard teleportation with an arbitrary mixed state resource is equivalent to a generalized depolarizing channel with probabilities given by the maximally entangled components of the resource. This enables the usage of any quantum channel as a generalized depolarizing channel without additional twirling operations. It also provides a nontrivial upper bound on the entanglement of a class of mixed states. Our result allows a consistent and statistically motivated quantification of teleportation success in terms of the relative entropy and this quantification can be related to a classical capacity.

      7. Implementation of quantum and classical discrete fractional Fourier transforms

        PubMed Central

        Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

        2016-01-01

        Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

      8. Classical and quantum mechanics of the nonrelativistic Snyder model

        NASA Astrophysics Data System (ADS)

        Mignemi, S.

        2011-07-01

        The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale β and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to three-dimensional Euclidean space. We discuss the classical and the quantum mechanics of a free particle in this framework, and show that they strongly depend on the sign of a coupling constant λ, appearing in the fundamental commutators and proportional to β2. For example, if λ is negative, momenta are bounded. On the contrary, for positive λ, positions and areas are quantized. We also give the exact solution of the harmonic oscillator equations both in the classical and the quantum case, and show that its frequency is energy dependent.

      9. Direct detection of classically undetectable dark matter through quantum decoherence

        NASA Astrophysics Data System (ADS)

        Riedel, C. Jess

        2013-12-01

        Although various pieces of indirect evidence about the nature of dark matter have been collected, its direct detection has eluded experimental searches despite extensive effort. If the mass of dark matter is below 1 MeV, it is essentially imperceptible to conventional detection methods because negligible energy is transferred to nuclei during collisions. Here I propose directly detecting dark matter through the quantum decoherence it causes rather than its classical effects, such as recoil or ionization. I show that quantum spatial superpositions are sensitive to low-mass dark matter that is inaccessible to classical techniques. This provides new independent motivation for matter interferometry with large masses, especially on spaceborne platforms. The apparent dark matter wind we experience as the Sun travels through the Milky Way ensures interferometers and related devices are directional detectors, and so are able to provide unmistakable evidence that decoherence has Galactic origins.

      10. Implementation of quantum and classical discrete fractional Fourier transforms

        NASA Astrophysics Data System (ADS)

        Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

        2016-03-01

        Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

      11. Classical simulation of noninteracting-fermion quantum circuits

        NASA Astrophysics Data System (ADS)

        Terhal, Barbara M.; Divincenzo, David P.

        2002-03-01

        We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].

      12. Evolution of Fractal Patterns during a Classical-Quantum Transition

        SciTech Connect

        Micolich, A. P.; Taylor, R. P.; Davies, A. G.; Bird, J. P.; Newbury, R.; Fromhold, T. M.; Ehlert, A.; Linke, H.; Macks, L. D.; Tribe, W. R.

        2001-07-16

        We investigate how fractals evolve into nonfractal behavior as the generation process is gradually suppressed. Fractals observed in the conductance of semiconductor billiards are of particular interest because the generation process is semiclassical and can be suppressed by transitions towards either fully classical or fully quantum-mechanical conduction. Investigating a range of billiards, we identify a ''universal'' behavior in the changeover from fractal to nonfractal conductance, which is described by a smooth evolution rather than deterioration in the fractal scaling properties.

      13. Redundancy of classical and quantum correlations during decoherence

        SciTech Connect

        Paz, Juan Pablo; Roncaglia, Augusto J.

        2009-10-15

        We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model, we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced classicality. To study this, we present a measure of redundancy and compare it to the existing one.

      14. Authenticated semi-quantum key distributions without classical channel

        NASA Astrophysics Data System (ADS)

        Li, Chuan-Ming; Yu, Kun-Fei; Kao, Shih-Hung; Hwang, Tzonelih

        2016-07-01

        Yu et al. have proposed the first authenticated semi-quantum key distribution (ASQKD) without using an authenticated classical channel. This study further proposes two advanced ASQKD protocols. Compared to Yu et al.'s schemes, the proposed protocols ensure better qubit efficiency and require fewer pre-shared keys. Security analyses show that the proposed ASQKD protocols also can be secure against several well-known outside eavesdropper's attacks.

      15. Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence

        SciTech Connect

        Paoletti, M. S.; Fisher, Michael E.; Sreenivasan, K. R.; Lathrop, D. P.

        2008-10-10

        By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid {sup 4}He are strongly non-Gaussian with 1/v{sup 3} power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.

      16. Quantum-classical electron distributions in atoms and atomic ions

        NASA Technical Reports Server (NTRS)

        Kunc, Joseph A.

        1988-01-01

        A quantum-classical approach is used to obtain the velocity distributions in atoms and positive and negative ions in both ground and excited states. In the analysis, Hartree-Fock electronic wavefunctions are used to determine the radial electron distributions, and the central-field approximation is used to study the the dynamic properties of the localized electrons. The distributions for the outer and inner shells are found to agree well with exact results obtained by numerical calculations.

      17. Quantum double pendulum: study of an autonomous classically chaotic quantum system.

        PubMed

        Perotti, Luca

        2004-12-01

        A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows us to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter containing Planck's constant. Comparison with classical and semiclassical results is used to understand the behavior of the energy curves of the levels, to define regimes in terms of the gravity parameter, and to classify the (resonant) interactions among levels by connecting them to various classical phase space structures (resonance islands). PMID:15697495

      18. Modeling the quantum evolution of the universe through classical matter

        NASA Astrophysics Data System (ADS)

        Pitelli, João Paulo M.; Letelier, Patricio S.

        2013-07-01

        It is well known that the canonical quantization of the Friedmann-Lemaître-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor (t) never vanishes and, as t→ infty , we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.

      19. Crossover from Classical to Quantum Kibble-Zurek Scaling

        NASA Astrophysics Data System (ADS)

        Silvi, Pietro; Morigi, Giovanna; Calarco, Tommaso; Montangero, Simone

        2016-06-01

        The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here, we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ4 model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and classical cases. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to providing insight into recent experimental observations in systems of cold atoms and ions.

      20. Predictability sieve, pointer states, and the classicality of quantum trajectories

        SciTech Connect

        Dalvit, D. A. R.; Zurek, W. H.; Dziarmaga, J.

        2005-12-15

        We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states--the most predictable states of an open quantum system selected by the predictability sieve--are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, the predictability sieve does not select well defined pointer states)

      1. Crossover from Classical to Quantum Kibble-Zurek Scaling.

        PubMed

        Silvi, Pietro; Morigi, Giovanna; Calarco, Tommaso; Montangero, Simone

        2016-06-01

        The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here, we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ^{4} model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and classical cases. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to providing insight into recent experimental observations in systems of cold atoms and ions. PMID:27314729

      2. Quantum-classical interactions through the path integral

        NASA Astrophysics Data System (ADS)

        Metaxas, Dimitrios

        2007-03-01

        I consider the case of two interacting scalar fields, ϕ and ψ, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field which should be an improvement of the usual semiclassical procedure. As an application I use this method in order to enforce Gauss’s law as a classical equation in a non-Abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills theory as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field λ that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.

      3. Classical and quantum dynamics in an inverse square potential

        NASA Astrophysics Data System (ADS)

        Guillaumín-España, Elisa; Núñez-Yépez, H. N.; Salas-Brito, A. L.

        2014-10-01

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

      4. Classical and quantum dynamics in an inverse square potential

        SciTech Connect

        Guillaumín-España, Elisa; Núñez-Yépez, H. N.; Salas-Brito, A. L.

        2014-10-15

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

      5. Does Bohm's Quantum Force Have a Classical Origin?

        NASA Astrophysics Data System (ADS)

        Lush, David C.

        2016-08-01

        In the de Broglie-Bohm formulation of quantum mechanics, the electron is stationary in the ground state of hydrogenic atoms, because the quantum force exactly cancels the Coulomb attraction of the electron to the nucleus. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the Zitterbewegung interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.

      6. Quantum Phenomena Modeled by Interactions between Many Classical Worlds

        NASA Astrophysics Data System (ADS)

        Hall, Michael J. W.; Deckert, Dirk-André; Wiseman, Howard M.

        2014-10-01

        We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical "worlds," and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here, a "world" means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach, each world evolves deterministically, probabilities arise due to ignorance as to which world a given observer occupies, and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a "many interacting worlds" approach and show that it can reproduce some generic quantum phenomena—such as Ehrenfest's theorem, wave packet spreading, barrier tunneling, and zero-point energy—as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.

      7. Quantum phenomena modelled by interactions between many classical worlds

        NASA Astrophysics Data System (ADS)

        Wiseman, Howard; Hall, Michael; Deckert, Dirk-Andre

        2015-03-01

        We investigate how quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but countable, number of classical ``worlds,'' and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a ``world'' means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a ``many interacting worlds'' approach and show that it can reproduce some generic quantum phenomena-such as Ehrenfest's theorem, wavepacket spreading, barrier tunneling and zero point energy-as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.

      8. Quantum correlations of identical particles subject to classical environmental noise

        NASA Astrophysics Data System (ADS)

        Beggi, Andrea; Buscemi, Fabrizio; Bordone, Paolo

        2016-09-01

        In this work, we propose a measure for the quantum discord of indistinguishable particles, based on the definition of entanglement of particles given in Wiseman and Vaccaro (Phys Rev Lett 91:097902, 2003. doi: 10.1103/PhysRevLett.91.097902). This discord of particles is then used to evaluate the quantum correlations in a system of two identical bosons (fermions), where the particles perform a quantum random walk described by the Hubbard Hamiltonian in a 1D lattice. The dynamics of the particles is either unperturbed or subject to a classical environmental noise—such as random telegraph, pink or brown noise. The observed results are consistent with those for the entanglement of particles, and we observe that on-site interaction between particles have an important protective effect on correlations against the decoherence of the system.

      9. Quantum-to-classical transition for ekpyrotic perturbations

        NASA Astrophysics Data System (ADS)

        Battarra, Lorenzo; Lehners, Jean-Luc

        2014-03-01

        We examine the processes of quantum squeezing and decoherence of density perturbations produced during a slowly contracting ekpyrotic phase in which entropic perturbations are converted to curvature perturbations before the bounce to an expanding phase. During the generation phase, the entropic fluctuations evolve into a highly squeezed quantum state, analogous to the evolution of inflationary perturbations. Subsequently, during the conversion phase, quantum coherence is lost very efficiently due to the interactions of entropy and adiabatic modes. Moreover, while decoherence occurs, the adiabatic curvature perturbations inherit their semiclassicality from the entropic perturbations. Our results confirm that, just as for inflation, an ekpyrotic phase can generate nearly scale-invariant curvature perturbations which may be treated as a statistical ensemble of classical density perturbations, in agreement with observations of the cosmic background radiation.

      10. Quantum correlations of identical particles subject to classical environmental noise

        NASA Astrophysics Data System (ADS)

        Beggi, Andrea; Buscemi, Fabrizio; Bordone, Paolo

        2016-06-01

        In this work, we propose a measure for the quantum discord of indistinguishable particles, based on the definition of entanglement of particles given in Wiseman and Vaccaro (Phys Rev Lett 91:097902, 2003. doi: 10.1103/PhysRevLett.91.097902). This discord of particles is then used to evaluate the quantum correlations in a system of two identical bosons (fermions), where the particles perform a quantum random walk described by the Hubbard Hamiltonian in a 1D lattice. The dynamics of the particles is either unperturbed or subject to a classical environmental noise—such as random telegraph, pink or brown noise. The observed results are consistent with those for the entanglement of particles, and we observe that on-site interaction between particles have an important protective effect on correlations against the decoherence of the system.

      11. Parametric representation of open quantum systems and cross-over from quantum to classical environment

        PubMed Central

        Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I.; Verrucchi, Paola

        2013-01-01

        The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables , and broadened according to their quantum probability distribution. Such distribution is independent of φ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because φ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field. PMID:23572581

      12. Parametric representation of open quantum systems and cross-over from quantum to classical environment.

        PubMed

        Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I; Verrucchi, Paola

        2013-04-23

        The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the s = 1/2 Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables (θ, ϕ), and broadened according to their quantum probability distribution. Such distribution is independent of ϕ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because ϕ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field.

      13. Line mixing effects in isotropic Raman spectra of pure N{sub 2}: A classical trajectory study

        SciTech Connect

        Ivanov, Sergey V.; Boulet, Christian; Buzykin, Oleg G.; Thibault, Franck

        2014-11-14

        Line mixing effects in the Q branch of pure N{sub 2} isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N{sub 2} molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.

      14. Classical to Quantum Crossover in Driven Josephson Junctions

        NASA Astrophysics Data System (ADS)

        Tian, C. S.; Kamenev, A.; Larkin, A. I.

        2004-03-01

        We consider the classical-quantum behavior crossover in a small, externally driven Josephson junction. Charge of a small superconducting grain fluctuates strongly if its critical current J_c(t) is modulated (kicked) by short periodic pulses (e.g. by changing the tunneling strength). The system may be mapped onto the model of quantum kicked rotator [1]. For large amplitudes of J_c(t) and short enough times, the grain charge, Q(t), diffuses in time. That is, the charge correlation function K(t) = <(Q(t)-Q(0))^2> = 2Dt, where the classical diffusion coefficient, D, may be expressed through the microscopical parameters of the model. Quantum corrections develop at times longer than the Ehrenfest time of the corresponding dynamical system, t_E ˜ ln D/(2e)^2. We have calculated weak-localization one-loop renormalization of the diffusion coefficient, δ D(ω), and found δ K(t)= -4/3√ π 2e√ D (t-2t_E)^3/2 for 2tE ˜ t≪ t_L, where t_L ˜ D/(2e)^2 is the time to develop the strong localization [1,2]. The predicted classical-quantum crossover may be observed by performing time-resolved potentiometry on the kicked Josephson grain. Alternatively, the effect may be detected by driving a periodic current of a large amplitude, J≫ J_c, across the grain and monitoring fluctuations of voltage. We believe that such a crossover applies to other periodic driven systems. [1] G. Casati et. al., Lect. Notes Phys.93, 334 (1979). [2] S.Fishman et. al. Phys. Rev. Lett. 49, 509 (1982); A.Altland, ibid. 71, 69 (1993).

      15. Simultaneous classical communication and quantum key distribution using continuous variables

        DOE PAGES

        Qi, Bing

        2016-10-26

        Currently, classical optical communication systems employing strong laser pulses and quantum key distribution (QKD) systems working at single-photon levels are very different communication modalities. Dedicated devices are commonly required to implement QKD. In this paper, we propose a scheme which allows classical communication and QKD to be implemented simultaneously using the same communication infrastructure. More specially, we propose a coherent communication scheme where both the bits for classical communication and the Gaussian distributed random numbers for QKD are encoded on the same weak coherent pulse and decoded by the same coherent receiver. Simulation results based on practical system parameters showmore » that both deterministic classical communication with a bit error rate of 10–9 and secure key distribution could be achieved over tens of kilometers of single-mode fibers. It is conceivable that in the future coherent optical communication network, QKD will be operated in the background of classical communication at a minimal cost.« less

      16. Nonlinear periodic structures: From classical to quantum devices

        NASA Astrophysics Data System (ADS)

        Sarrafi, Peyman

        In this thesis, nonlinear periodic structures and their applications in both classical and quantum regime are investigated. New theoretical models are developed, and novel applications of nonlinear periodic structures are proposed and demonstrated. The theoretical studies, both design and simulation, are based on but not limited to InGaAsP material. A new method, namely the time-domain transfer-matrix (TDTM), is presented to simulate optical pulse propagation in layered media with resonant nonlinearity. As there were no satisfactory methods in the literature to model this problem, in order to validate and compare with the TDTM method, the standard FDTD method is generalized to include the rate equation in the analysis of semi-conductors. Also in this work, optical manipulation of absorption in periodic structures is studied for the first time. Thanks to the large accessible nonlinearity that results from the absorption saturation and frequency selectivity of periodic structures, a sensitive and compact optical limiter is designed. The novel design and modeling work developed in this thesis has provided new insights and tools to the utilization of resonant nonlinearities in compact all-optical devices. The experimental studies are based on quasi-phase matched AlGaAs superlattice waveguides. These devices have been previously designed and used for classical optical wavelength conversion such as second harmonic generation and difference frequency generation. In this work, these devices are exploited for spontaneous down conversion, which is a quantum effect, for the first time, through this process, entangled photon pairs are generated. Unprecedented performance, in terms of brightness and purity, of III-V semiconductor-based entangled photon sources has been demonstrated here. Moreover, the quantum properties of these entangled photons are characterized. The experimental studies presented in this thesis open up new application areas for III-V nonlinear optical

      17. Coherent eavesdropping attacks in tomographic quantum cryptography: Nonequivalence of quantum and classical key distillation

        SciTech Connect

        Kaszlikowski, Dagomir; Lim, J.Y.; Englert, Berthold-Georg; Kwek, L.C.

        2005-10-15

        The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. We show that - for protocols that use quantum channels of any dimension and completely characterize them by state tomography - the noise threshold for classical advantage distillation of a specific kind is substantially lower than the threshold for quantum entanglement distillation if the eavesdropper can perform powerful coherent attacks. In marked contrast, earlier investigations had shown that the thresholds are identical for incoherent attacks on the same classical distillation scheme. It remains an open question whether other schemes for classical advantage distillation have higher thresholds for coherent eavesdropping attacks.

      18. The Pendulum as a Vehicle for Transitioning from Classical to Quantum Physics: History, Quantum Concepts, and Educational Challenges

        ERIC Educational Resources Information Center

        Barnes, Marianne B.; Garner, James; Reid, David

        2004-01-01

        In this article we use the pendulum as the vehicle for discussing the transition from classical to quantum physics. Since student knowledge of the classical pendulum can be generalized to all harmonic oscillators, we propose that a quantum analysis of the pendulum can lead students into the unanticipated consequences of quantum phenomena at the…

      19. Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics

        NASA Astrophysics Data System (ADS)

        Lamb, Willis E.

        2001-04-01

        It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory "super classical quantum mechanics" (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

      20. Classical and quantum cosmology of Born-Infeld type models

        NASA Astrophysics Data System (ADS)

        Kamenshchik, Alexander; Kiefer, Claus; Kwidzinski, Nick

        2016-04-01

        We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.

      1. Gauge transformations and conserved quantities in classical and quantum mechanics

        NASA Astrophysics Data System (ADS)

        Berche, Bertrand; Malterre, Daniel; Medina, Ernesto

        2016-08-01

        We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless, here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not preserved in the usual manner; (ii) non-gauge-invariant quantities can be associated with physical observables; and (iii) there are changes in the physical boundary conditions of the wave function that render it non-single-valued. We give worked examples that illustrate these points, in contrast to general opinions from classic texts. We also give a historical perspective on the development of Abelian gauge theory in relation to our particular points. Our aim is to provide a discussion of these issues at the graduate level.

      2. Ultimate classical communication rates of quantum optical channels

        NASA Astrophysics Data System (ADS)

        Giovannetti, V.; García-Patrón, R.; Cerf, N. J.; Holevo, A. S.

        2014-10-01

        Optical channels, such as fibres or free-space links, are ubiquitous in today's telecommunication networks. They rely on the electromagnetic field associated with photons to carry information from one point to another in space. A complete physical model of these channels must necessarily take quantum effects into account to determine their ultimate performances. Single-mode, phase-insensitive bosonic Gaussian channels have been extensively studied over past decades, given their importance for practical applications. In spite of this, a long-standing unsolved conjecture on the optimality of Gaussian encodings has prevented finding their classical communication capacity. Here, this conjecture is solved by proving that the vacuum state achieves the minimum output entropy of these channels. This establishes the ultimate achievable bit rate under an energy constraint, as well as the long awaited proof that the single-letter classical capacity of these channels is additive.

      3. Quantum secret sharing via local operations and classical communication

        PubMed Central

        Yang, Ying-Hui; Gao, Fei; Wu, Xia; Qin, Su-Juan; Zuo, Hui-Juan; Wen, Qiao-Yan

        2015-01-01

        We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or “ramp”), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect. PMID:26586412

      4. Quantum algorithmic integrability: the metaphor of classical polygonal billiards

        PubMed

        Mantica

        2000-06-01

        We study the algorithmic complexity of motions in classical polygonal billiards, which, as the number of sides increases, tend to curved billiards, both regular and chaotic. This study unveils the equivalence of this problem to the procedure of quantization: the average complexity of symbolic trajectories in polygonal billiards features the same scaling relations (with respect to the number of sides) that govern quantum systems when a semiclassical parameter is varied. Two cases, the polygonal approximations of the circle and of the stadium, are examined in detail and are presented as paradigms of quantization of integrable and chaotic systems.

      5. Scattering theory for the quantum envelope of a classical system

        SciTech Connect

        Sudarshan, E.C.G.

        1993-12-31

        Classical dynamics, reformulated in terms of its quantum envelope is studied for the stationary states of the interacting system. The dynamical variable of ``elapsed time`` plays a crucial role in this study. It is shown that the perturbation series for the elapsed time can be summed in various simple cases even when standard perturbation series diverge. For the special class of systems where the interactions fall off sufficiently fast at infinity one could define ``in`` and ``out`` states; and consequently the wave matrices and scattering matrices. The scattering phase shifts bear a simple relation to the time delay in scattering.

      6. Quantum secret sharing via local operations and classical communication.

        PubMed

        Yang, Ying-Hui; Gao, Fei; Wu, Xia; Qin, Su-Juan; Zuo, Hui-Juan; Wen, Qiao-Yan

        2015-01-01

        We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.

      7. Quantum algorithmic integrability: The metaphor of classical polygonal billiards

        NASA Astrophysics Data System (ADS)

        Mantica, Giorgio

        2000-06-01

        We study the algorithmic complexity of motions in classical polygonal billiards, which, as the number of sides increases, tend to curved billiards, both regular and chaotic. This study unveils the equivalence of this problem to the procedure of quantization: the average complexity of symbolic trajectories in polygonal billiards features the same scaling relations (with respect to the number of sides) that govern quantum systems when a semiclassical parameter is varied. Two cases, the polygonal approximations of the circle and of the stadium, are examined in detail and are presented as paradigms of quantization of integrable and chaotic systems.

      8. Minimum length from quantum mechanics and classical general relativity.

        PubMed

        Calmet, Xavier; Graesser, Michael; Hsu, Stephen D H

        2004-11-19

        We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.

      9. Quantum and classical correlations in electron-nuclear spin echo

        SciTech Connect

        Zobov, V. E.

        2014-11-15

        The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization β{sub I} in addition to the electron polarization β{sub S} have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β{sub S} ≈ β{sub I} and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.

      10. Classical Wave Model of Quantum-Like Processing in Brain

        NASA Astrophysics Data System (ADS)

        Khrennikov, A.

        2011-01-01

        We discuss the conjecture on quantum-like (QL) processing of information in the brain. It is not based on the physical quantum brain (e.g., Penrose) - quantum physical carriers of information. In our approach the brain created the QL representation (QLR) of information in Hilbert space. It uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology. The violation of the law of total probability in these experiments is an important sign of nonclassicality of data. In so called "constructive wave function approach" such data can be represented by complex amplitudes. We presented 1,2 the QL model of decision making. In this paper we speculate on a possible physical realization of QLR in the brain: a classical wave model producing QLR . It is based on variety of time scales in the brain. Each pair of scales (fine - the background fluctuations of electromagnetic field and rough - the cognitive image scale) induces the QL representation. The background field plays the crucial role in creation of "superstrong QL correlations" in the brain.

      11. The classical and quantum dynamics of molecular spins on graphene

        PubMed Central

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

        2015-01-01

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

      12. Proton transport in barium stannate: classical, semi-classical and quantum regimes.

        PubMed

        Geneste, Grégory; Ottochian, Alistar; Hermet, Jessica; Dezanneau, Guilhem

        2015-07-15

        Density-functional theory calculations are performed to investigate proton transport in BaSnO3. Structural optimizations in the stable and saddle point configurations for transfer (hopping) and reorientation allow description of the high-temperature classical and semi-classical regimes, in which diffusion occurs by over-barrier motion. At lower temperature (typically below 300 K), we describe the thermally-assisted quantum regime, in which protonic motion is of quantum nature and occurs in "coincidence" configurations favored by thermal fluctuations of the surrounding atoms. Both the non-adiabatic and the adiabatic limits are examined. In the adiabatic limit, the protonic energy landscape in the coincidence configuration is very flat. Path-integral molecular dynamics simulations of the proton in the coincidence potential reveal, in the transfer case, that the density of probability of H(+) has its maximum at the saddle point, because the zero-point energy exceeds the coincidence barrier. Arguments are given that support the adiabatic picture for the transfer mechanism. In the case of reorientation, the time scales for the existence of the coincidence and for protonic motion, as estimated from the time-energy uncertainty principle by using a simple one-dimensional model, are of the same order of magnitude, suggesting that the adiabatic limit is not reached. Protonic transfer and reorientation in this oxide are therefore governed by different mechanisms below room temperature. PMID:26126772

      13. BOOK REVIEW: Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit

        NASA Astrophysics Data System (ADS)

        Turner, L.

        2004-11-01

        In only 150 pages, not counting appendices, references, or the index, this book is one author’s perspective of the massive theoretical and philosophical hurdles in the no-man’s-land separating the classical and quantum domains of physics. It ends with him emphasizing his own theoretical contribution to this area. In his own words, he has attempted to answer: 1. ‘How can we obtain the quantum dynamics of open systems initially described by the equations of motion of classical physics (quantization process)? 2. ‘How can we retrieve classical dynamics from the quantum mechanical equations of motion by means of a classical limiting process (dequantization process)?’ However, this monograph seems overly ambitious. Although the publisher’s description refers to this book as ‘an accessible entrée’, we find that this author scrambles too hastily over the peaks of information that are contained in his large collection of 272 references. Introductory motivating discussions are lacking. Profound ideas are glossed over superficially and shoddily. Equations morph. But no new convincing understanding of the physical world results. The author takes the viewpoint that physical systems are always in interaction with their environment and are thus not isolated and, therefore, not Hamiltonian. This impels him to produce a method of quantization of these stochastic systems without the need of a Hamiltonian. He also has interest in obtaining the classical limit of the quantized results. However, this reviewer does not understand why one needs to consider open systems to understand ‘quantum-classical correspondence’. The author demonstrates his method using various examples of the Smoluchowski form of the Fokker--Planck equation. He then renders these equations in a Wigner representation, uses what he terms ‘an infinitesimality condition’, and associates with a constant having the dimensions of an action. He thereby claims to develop master equations, such as

      14. On the Mean Field and Classical Limits of Quantum Mechanics

        NASA Astrophysics Data System (ADS)

        Golse, François; Mouhot, Clément; Paul, Thierry

        2016-04-01

        The main result in this paper is a new inequality bearing on solutions of the N-body linear Schrödinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of N identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of C 1,1 interaction potentials. The quantity measuring the approximation of the N-body quantum dynamics by its mean field limit is analogous to the Monge-Kantorovich (or Wasserstein) distance with exponent 2. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13, 115-123, (1979)]. Our approach to this problem is based on a direct analysis of the N-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.

      15. Introduction of a Classical Level in Quantum Theory

        NASA Astrophysics Data System (ADS)

        Prosperi, G. M.

        2016-11-01

        In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics (QM). The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities.

      16. Introduction of a Classical Level in Quantum Theory - Continuous Monitoring

        NASA Astrophysics Data System (ADS)

        Prosperi, G. M.

        2016-07-01

        In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics (QM). The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities.

      17. Direct detection of classically undetectable dark matter through quantum decoherence

        NASA Astrophysics Data System (ADS)

        Riedel, C. Jess

        2014-03-01

        Although various pieces of indirect evidence about the nature of dark matter have been collected, its direct detection has eluded experimental searches despite extensive effort. If the mass of dark matter is below 1 MeV, it is essentially imperceptible to conventional detection methods because negligible energy is transferred to nuclei during collisions. Here I propose directly detecting dark matter through the quantum decoherence it causes rather than its classical effects such as recoil or ionization. I show that quantum spatial superpositions are sensitive to low-mass dark matter which is inaccessible to classical techniques. This provides new independent motivation for matter interferometry with large masses, especially on spaceborne platforms. The apparent dark matter wind we experience as the Sun travels through the Milky Way ensures interferometers and related devices are directional detectors, and so are able to provide unmistakable evidence that decoherence has galactic origins. This research was partially supported by the U.S. Department of Energy through the LANL/LDRD program, and by the John Templeton Foundation through grant number 21484.

      18. Sufficient Conditions for Efficient Classical Simulation of Quantum Optics

        NASA Astrophysics Data System (ADS)

        Rahimi-Keshari, Saleh; Ralph, Timothy C.; Caves, Carlton M.

        2016-04-01

        We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.

      19. The Bistable Potential:. AN Archetype for Classical and Quantum Systems

        NASA Astrophysics Data System (ADS)

        Spagnolo, B.; Caldara, P.; La Cognata, A.; Valenti, D.; Fiasconaro, A.; Dubkov, A. A.; Falci, G.

        In this work we analyze the transient dynamics of three different classical and quantum systems. First, we consider a classical Brownian particle moving in an asymmetric bistable potential, subject to a multiplicative and additive noise source. We investigate the role of these two noise sources on the life time of the metastable state. A nonmonotonic behavior of the lifetime as a function of both additive and multiplicative noise intensities is found, revealing the phenomenon of noise enhanced stability. Afterward, by using a Lotka-Volterra model, the dynamics of two competing species in the presence of Lévy noise sources is analyzed. Quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species are found. Finally the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir is investigated. We use the Caldeira-Leggett model and the approach of the Feynman-Vernon functional in discrete variable representation. We obtain the time evolution of the population distributions in energy eigenstates of the particle, for different values of the coupling strength with the thermal bath.

      20. From quantum to classical: Schrödinger cats, entanglement, and decoherence

        NASA Astrophysics Data System (ADS)

        Davidovich, L.

        2016-06-01

        Since the beginning of quantum physics, the relation between the properties of the microscopic quantum and the macroscopic classical world has been an important source for the development of the theory, and has led to new insights on the role of the environment in the transition from quantum to classical physics. Decoherence affects both coherence and entanglement of open systems. Quantum optics and cavity quantum electrodynamics have allowed detailed investigations of this phenomenon, within the framework of microwaves and light waves. In this paper, I present a personal account of theoretical and experimental developments that have led to the probing of the subtle frontier between quantum and classical phenomena.

      1. BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory

        NASA Astrophysics Data System (ADS)

        Mann, Robert

        2013-02-01

        Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is

      2. Occam’s Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel

        PubMed Central

        Mahoney, John R.; Aghamohammadi, Cina; Crutchfield, James P.

        2016-01-01

        A stochastic process’ statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process’ cryptic order–a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost–one trades off prediction for generation complexity. PMID:26876796

      3. Can decoherence make quantum theories unfalsifiable? Understanding the quantum-to-classical transition without it

        NASA Astrophysics Data System (ADS)

        Oriols, X.

        2016-03-01

        Exact predictions for most quantum systems are computationally inaccessible. This is the so-called many body problem, which is present in most common interpretations of quantum mechanics. Therefore, predictions of natural quantum phenomena have to rely on some approximations (assumptions or simplifications). In the literature, there are different types of approximations, ranging from those whose justification is basically based on theoretical developments to those whose justification lies on the agreement with experiments. This last type of approximations can convert a quantum theory into an “unfalsifiable” quantum theory, true by construction. On the practical side, converting some part of a quantum theory into an “unfalsifiable” one ensures a successful modeling (i.e. compatible with experiments) for quantum engineering applications. An example of including irreversibility and dissipation in the Bohmian modeling of open systems is presented. On the ontological level, however, the present-day foundational problems related to controversial quantum phenomena have to avoid (if possible) being contaminated by the unfalsifiability originated from the many body problem. An original attempt to show how the Bohmian theory itself (minimizing the role of many body approximations) explains the transitions from a microscopic quantum system towards a macroscopic classical one is presented.

      4. Nonmonotonic quantum-to-classical transition in multiparticle interference

        PubMed Central

        Ra, Young-Sik; Tichy, Malte C.; Lim, Hyang-Tag; Kwon, Osung; Mintert, Florian; Buchleitner, Andreas; Kim, Yoon-Ho

        2013-01-01

        Quantum-mechanical wave–particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference—e.g., on transit across a double slit—for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability—in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems. PMID:23297196

      5. Classical and Quantum Consistency of the DGP Model

        NASA Astrophysics Data System (ADS)

        Nicolis, Alberto; Rattazzi, Riccardo

        2004-06-01

        We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode pi consistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space pi becomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline a non-generic but consistent choice of counterterms for which this disaster does not happen and for which the model remains calculable and successful in all the astrophysical situations of interest. By this choice, the extrinsic curvature Kmunu acts roughly like a dilaton field controlling the strength of the interaction and the cut-off scale at each space-time point. At the surface of Earth the cutoff is ~ 1 cm but it is unlikely that the associated quantum effects be observable in table top experiments.

      6. Locality and nonlocality of classical restrictions of quantum spin systems with applications to quantum large deviations and entanglement

        SciTech Connect

        De Roeck, W. E-mail: christian.maes@fys.kuleuven.be E-mail: marius.schutz@fys.kuleuven.be; Maes, C. E-mail: christian.maes@fys.kuleuven.be E-mail: marius.schutz@fys.kuleuven.be; Schütz, M. E-mail: christian.maes@fys.kuleuven.be E-mail: marius.schutz@fys.kuleuven.be; Netočný, K. E-mail: christian.maes@fys.kuleuven.be E-mail: marius.schutz@fys.kuleuven.be

        2015-02-15

        We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle.

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

        SciTech Connect

        Lee, Sang-Bong

        1993-09-01

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

      8. Classical and quantum Big Brake cosmology for scalar field and tachyonic models

        SciTech Connect

        Kamenshchik, A. Yu.; Manti, S.

        2013-02-21

        We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.

      9. Quantum Darwinism in a Mixed Environment

        NASA Astrophysics Data System (ADS)

        Zwolak, Michael; Quan, H. T.; Zurek, Wojciech H.

        2009-09-01

        Quantum Darwinism recognizes that we—the observers—acquire our information about the “systems of interest” indirectly from their imprints on the environment. Here, we show that information about a system can be acquired from a mixed-state, or hazy, environment, but the storage capacity of an environment fragment is suppressed by its initial entropy. In the case of good decoherence, the mutual information between the system and the fragment is given solely by the fragment’s entropy increase. For fairly mixed environments, this means a reduction by a factor 1-h, where h is the haziness of the environment, i.e., the initial entropy of an environment qubit. Thus, even such hazy environments eventually reveal the state of the system, although now the intercepted environment fragment must be larger by ˜(1-h)-1 to gain the same information about the system.

      10. Quantum darwinism in a mixed environment.

        PubMed

        Zwolak, Michael; Quan, H T; Zurek, Wojciech H

        2009-09-11

        Quantum Darwinism recognizes that we-the observers-acquire our information about the "systems of interest" indirectly from their imprints on the environment. Here, we show that information about a system can be acquired from a mixed-state, or hazy, environment, but the storage capacity of an environment fragment is suppressed by its initial entropy. In the case of good decoherence, the mutual information between the system and the fragment is given solely by the fragment's entropy increase. For fairly mixed environments, this means a reduction by a factor 1-h, where h is the haziness of the environment, i.e., the initial entropy of an environment qubit. Thus, even such hazy environments eventually reveal the state of the system, although now the intercepted environment fragment must be larger by approximately (1-h)(-1) to gain the same information about the system.

      11. Public classical communication in quantum cryptography: Error correction, integrity, and authentication

        SciTech Connect

        Timofeev, A. V.; Pomozov, D. I.; Makkaveev, A. P.; Molotkov, S. N.

        2007-05-15

        Quantum cryptography systems combine two communication channels: a quantum and a classical one. (They can be physically implemented in the same fiber-optic link, which is employed as a quantum channel when one-photon states are transmitted and as a classical one when it carries classical data traffic.) Both channels are supposed to be insecure and accessible to an eavesdropper. Error correction in raw keys, interferometer balancing, and other procedures are performed by using the public classical channel. A discussion of the requirements to be met by the classical channel is presented.

      12. On the complexity of classical and quantum algorithms for numerical problems in quantum mechanics

        NASA Astrophysics Data System (ADS)

        Bessen, Arvid J.

        Our understanding of complex quantum mechanical processes is limited by our inability to solve the equations that govern them except for simple cases. Numerical simulation of quantum systems appears to be our best option to understand, design and improve quantum systems. It turns out, however, that computational problems in quantum mechanics are notoriously difficult to treat numerically. The computational time that is required often scales exponentially with the size of the problem. One of the most radical approaches for treating quantum problems was proposed by Feytiman in 1982 [46]: he suggested that quantum mechanics itself showed a promising way to simulate quantum physics. This idea, the so called quantum computer, showed its potential convincingly in one important regime with the development of Shor's integer factorization algorithm which improves exponentially on the best known classical algorithm. In this thesis we explore six different computational problems from quantum mechanics, study their computational complexity and try to find ways to remedy them. In the first problem we investigate the reasons behind the improved performance of Shor's and similar algorithms. We show that the key quantum part in Shor's algorithm, the quantum phase estimation algorithm, achieves its good performance through the use of power queries and we give lower bounds for all phase estimation algorithms that use power queries that match the known upper bounds. Our research indicates that problems that allow the use of power queries will achieve similar exponential improvements over classical algorithms. We then apply our lower bound technique for power queries to the Sturm-Liouville eigenvalue problem and show matching lower bounds to the upper bounds of Papageorgiou and Wozniakowski [85]. It seems to be very difficult, though, to find nontrivial instances of the Sturm-Lionville problem for which power queries can be simulated efficiently. A quantum computer differs from a

      13. Molecular machines operating on the nanoscale: from classical to quantum.

        PubMed

        Goychuk, Igor

        2016-01-01

        The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed. PMID:27335728

      14. Classical and quantum particle dynamics in univariate background fields

        NASA Astrophysics Data System (ADS)

        Heinzl, T.; Ilderton, A.; King, B.

        2016-09-01

        We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or spacelike field dependence. For a special scenario in the classical regime we show how the radiation spectrum in the spacelike (undulator) case becomes well-approximated by the plane wave model in the high-energy limit, despite the two systems being Lorentz inequivalent. In the quantum problem, there is no analogue of the WKB-exact Volkov solution. Nevertheless, WKB and uniform-WKB approaches give good approximations in all cases considered. Other approaches that reduce the underlying differential equations from second to first order are found to miss the correct physics for situations corresponding to barrier transmission and wide-angle scattering.

      15. Classical and quantum dynamics of the Faraday lines of force

        SciTech Connect

        Frittelli, S.; Koshti, S.; Newman, E.T.; Rovelli, C. )

        1994-06-15

        We study the vacuum Maxwell theory by expressing the electric field in terms of its Faraday lines of force. This representation allows us to capture the two physical degrees of freedom of the electric field by means of two scalar fields. The corresponding classical canonical theory is constructed in terms of four scalar fields, is fully gauge invariant, has an attractive kinematics, but a rather complicated dynamics. The corresponding quantum theory can be constructed in a well-defined functional representation, which we refer to as the Euler representation. This representation turns out to be related to the loop representation. The resulting quantization scheme is, perhaps, of relevance for non-Abelian theories and for gravity.

      16. Molecular machines operating on the nanoscale: from classical to quantum.

        PubMed

        Goychuk, Igor

        2016-01-01

        The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

      17. Molecular machines operating on the nanoscale: from classical to quantum

        PubMed Central

        2016-01-01

        Summary The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed. PMID:27335728

      18. Phase space localization and matrix element distributions in systems with mixed classical phase space.

        PubMed

        Mehlig, B; Müller, K; Eckhardt, B

        1999-05-01

        We consider distributions of diagonal matrix elements for smooth observables in systems whose classical phase space has a mixture of chaotic and nearly integrable regions. The quantum distributions agree very well with distributions obtained from classical trajectory segments whose length is the Heisenberg time. Non-Gaussian wings in the distributions can be linked to classical trapping in certain parts of phase space, sometimes connected to islands, but also to regions separated by other barriers to transport. Thus classical deviations from ergodicity are quantitatively reflected in quantum matrix elements. The relation to scars is discussed.

      19. From Classical to Quantum and Back: A Hamiltonian Scheme for Adaptive Multiresolution Classical/Path-Integral Simulations.

        PubMed

        Kreis, Karsten; Tuckerman, Mark E; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello

        2016-07-12

        Quantum delocalization of atomic nuclei affects the physical properties of many hydrogen-rich liquids and biological systems even at room temperature. In computer simulations, quantum nuclei can be modeled via the path-integral formulation of quantum statistical mechanics, which implies a substantial increase in computational overhead. By restricting the quantum description to a small spatial region, this cost can be significantly reduced. Herein, we derive a bottom-up, rigorous, Hamiltonian-based scheme that allows molecules to change from quantum to classical and vice versa on the fly as they diffuse through the system, both reducing overhead and making quantum grand-canonical simulations possible. The method is validated via simulations of low-temperature parahydrogen. Our adaptive resolution approach paves the way to efficient quantum simulations of biomolecules, membranes, and interfaces. PMID:27214610

      20. Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field

        SciTech Connect

        Murguia, Gabriela; Moreno, Matias; Torres, Manuel

        2009-04-20

        A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.

      1. Observation of the Quantum-Classical Transition via Electron Diffraction

        NASA Astrophysics Data System (ADS)

        Beierle, Peter; Batelaan, Herman

        2016-05-01

        A collimated electron beam with an energy ranging from .5 keV- 5 keV is passed over a 1 cm long conducting surface. The electrons are diffracted from a 100 nm periodic SiN free-standing grating. The surface is place within the electron near-field diffraction distance. The loss of visibility of the far-field diffraction pattern is measured, which indicates the amount of decoherence that the electrons experienced as they passed over the surface. It has been determined through the visibility as a function of the height with respect to the surface that a) one can observe the transition of the electron's behavior between classical and quantum mechanics, b) that our experiment can be used to rule out a classical theoretical model of the surface decohering mechanism (consistent with Hasselbach's work), and c) this experimental setup is simpler than the use of an interferometer. Comparing a silicon to a gold surface, we are in the process of testing a wider array of theoretical models for the mechanism of decoherence. This work is supported by the National Science Foundation under award number 1306565.

      2. Post-Markovian quantum master equations from classical environment fluctuations.

        PubMed

        Budini, Adrián A

        2014-01-01

        In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its associated approximated integrodifferential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unraveled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics. PMID:24580212

      3. Classical and quantum behavior of the generic cosmological solution

        NASA Astrophysics Data System (ADS)

        Imponente, Giovanni; Montani, Giovanni

        2006-11-01

        In the present paper we generalize the original work of C.W. Misner about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity. We extend the analysis to the generic inhomogeneous universe by solving the super-momentum constraint and outlining the dynamical decoupling of spatial points. Firstly, we discuss the classical evolution of the model in terms of the Hamilton-Jacobi approach as applied to the super-momentum and super-Hamiltonian constraints; then we quantize it in the approximation of a square potential well after an ADM reduction of the dynamics with respect to the super-momentum constraint only. Such a reduction relies on a suitable form for the generic three-metric tensor which allows the use of its three functions as the new spatial coordinates. We get a functional representation of the quantum dynamics which is equivalent to the Misner-like one when extended point by point, since the Hilbert space factorizes into ∞3 independent components due to the parametric role that the three-coordinates assume in the asymptotic potential term. Finally, we discuss the conditions for having a semiclassical behavior of the dynamics and we recognize that this already corresponds to having mean occupation numbers of order O(102).

      4. Novel classical post-processing for quantum key distribution-based quantum private query

        NASA Astrophysics Data System (ADS)

        Yang, Yu-Guang; Liu, Zhi-Chao; Chen, Xiu-Bo; Cao, Wei-Feng; Zhou, Yi-Hua; Shi, Wei-Min

        2016-09-01

        Existing classical post-processing (CPP) schemes for quantum key distribution (QKD)-based quantum private queries (QPQs) including the kN→ N, N→ N, and rM→ N ones have been found imperfect in terms of communication efficiency and security. In this paper, we propose a novel CPP scheme for QKD-based QPQs. The proposed CPP scheme reduces the communication complexity and improves the security of QKD-based QPQ protocols largely. Furthermore, the proposed CPP scheme can provide a multi-bit query efficiently.

      5. Trajectory description of the quantum-classical transition for wave packet interference

        NASA Astrophysics Data System (ADS)

        Chou, Chia-Chun

        2016-08-01

        The quantum-classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum-classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum-classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum-classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet interference.

      6. Dynamics, Processes and Characterization in Classical and Quantum Optics

        NASA Astrophysics Data System (ADS)

        Gamel, Omar

        We pursue topics in optics that follow three major themes; time averaged dynamics with the associated Effective Hamiltonian theory, quantification and transformation of polarization, and periodicity within quantum circuits. Within the first theme, we develop a technique for finding the dynamical evolution in time of a time averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms that sometimes manifest in a Lindblad-like form. We also apply the theory to examples of the AC Stark Shift and Three-Level Raman Transitions. In the theme of polarization, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrix transformations, equivalent to a completely positive map on the polarization matrix. This has been directly assumed without proof by most authors. We follow a novel approach to derive this expression from simple physical principles, basic coherence optics and the matrix theory of positive maps. Addressing polarization measurement, we first establish the equivalence of classical polarization and quantum purity, which leads to the identical structure of the Poincare and Bloch spheres. We analyze and compare various measures of polarization / purity for general dimensionality proposed in the literature, with a focus on the three dimensional case. In pursuit of the final theme of periodic quantum circuits, we introduce a procedure that synthesizes the circuit for the simplest periodic function that is one-to-one within a single period, of a given period p. Applying this procedure, we synthesize these circuits for p up to five bits. We conjecture that such a circuit will need at most n Toffoli gates, where p is an n-bit number. Moreover, we apply our circuit synthesis to compiled versions of Shor's algorithm, showing that it can create more efficient circuits than ones previously proposed. We provide some new compiled circuits for

      7. Multiparty Quantum Secret Sharing of Classical Message using Cavity Quantum Electrodynamic System

        NASA Astrophysics Data System (ADS)

        Han, Lian-Fang; Liu, Yi-Min; Zhang, Zhan-Jun

        2006-08-01

        An experimental feasible scheme of multiparty secret sharing of classical messages is proposed, based on a cavity quantum electrodynamic system. The secret messages are imposed on atomic Bell states initially in the sender's possession by local unitary operations. By swapping quantum entanglement of atomic Bell states, the secret messages are split into several parts and each part is distributed to a separate party. In this case, any subset of the entire party group can not read out the secret message but the entirety via mutual cooperations. In this scheme, to discriminate atomic Bell states, additional classical fields are employed besides the same highly-detuned single-mode cavities used to prepare atomic Bell states. This scheme is insensitive to the cavity decay and the thermal field, and usual joint Bell-state measurements are unnecessary.

      8. A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

        ERIC Educational Resources Information Center

        Pujol, O.; Perez, J. P.

        2007-01-01

        The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…

      9. Quantum and classical chaos in kicked coupled Jaynes-Cummings cavities

        SciTech Connect

        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.

      10. Non-local classical optical correlation and implementing analogy of quantum teleportation.

        PubMed

        Sun, Yifan; Song, Xinbing; Qin, Hongwei; Zhang, Xiong; Yang, Zhenwei; Zhang, Xiangdong

        2015-01-01

        This study reports an experimental realization of non-local classical optical correlation from the Bell's measurement used in tests of quantum non-locality. Based on such a classical Einstein-Podolsky-Rosen optical correlation, a classical analogy has been implemented to the true meaning of quantum teleportation. In the experimental teleportation protocol, the initial teleported information can be unknown to anyone and the information transfer can happen over arbitrary distances. The obtained results give novel insight into quantum physics and may open a new field of applications in quantum information. PMID:25779977

      11. Non-local classical optical correlation and implementing analogy of quantum teleportation

        PubMed Central

        Sun, Yifan; Song, Xinbing; Qin, Hongwei; Zhang, Xiong; Yang, Zhenwei; Zhang, Xiangdong

        2015-01-01

        This study reports an experimental realization of non-local classical optical correlation from the Bell's measurement used in tests of quantum non-locality. Based on such a classical Einstein–Podolsky–Rosen optical correlation, a classical analogy has been implemented to the true meaning of quantum teleportation. In the experimental teleportation protocol, the initial teleported information can be unknown to anyone and the information transfer can happen over arbitrary distances. The obtained results give novel insight into quantum physics and may open a new field of applications in quantum information. PMID:25779977

      12. Non-local classical optical correlation and implementing analogy of quantum teleportation.

        PubMed

        Sun, Yifan; Song, Xinbing; Qin, Hongwei; Zhang, Xiong; Yang, Zhenwei; Zhang, Xiangdong

        2015-01-01

        This study reports an experimental realization of non-local classical optical correlation from the Bell's measurement used in tests of quantum non-locality. Based on such a classical Einstein-Podolsky-Rosen optical correlation, a classical analogy has been implemented to the true meaning of quantum teleportation. In the experimental teleportation protocol, the initial teleported information can be unknown to anyone and the information transfer can happen over arbitrary distances. The obtained results give novel insight into quantum physics and may open a new field of applications in quantum information.

      13. Redundant Information and the Quantum-Classical Transition

        NASA Astrophysics Data System (ADS)

        Riedel, Charles Jess

        A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality—the fact that multiple observers can each agree on the state of a subsystem after measuring just a small fraction of its environment—implies that the correlations found in nature between macroscopic systems and their environments are very exceptional. This is understood through the redundant recording of information about the preferred states of a decohering system by its environment, a phenomenon known as quantum Darwinism. To see this in action in the real world, we first consider the ubiquitous case of blackbody illumination. We show that it exhibits fast and extensive proliferation of information about an object into the environment, yielding redundancies orders of magnitude larger than the exactly soluble models considered previously. Turning to a universe of qubits, we examine the conditions needed for the creation of branching states and study their demise through many-body interactions. We show that even constrained dynamics can suppress redundancies to the values typical of random states on relaxation timescales, and prove that these results hold exactly in the thermodynamic limit. Finally, we connect these ideas to the consistent histories framework. Building on the criterion of partial-trace consistency, we introduce a sensible notion of mutual information between a fragment of the universe and a history itself.

      14. Bell's measure and implementing quantum Fourier transform with orbital angular momentum of classical light.

        PubMed

        Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong

        2015-09-15

        We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally.

      15. Casimir effects for classical and quantum liquids in slab geometry: A brief review

        SciTech Connect

        Biswas, Shyamal

        2015-05-15

        We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.

      16. A quantum mechanical point of view to perturbative problems in classical mechanics

        NASA Astrophysics Data System (ADS)

        Dattoli, G.; Torre, A.

        1993-11-01

        In this article it is shown that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of noncollisional particles. The method discussed is based on the concepts of an evolution operator and interaction picture, which can be introduced for a classical Hamiltonian in full analogy with quantum mechanics. The usefulness of the developed method to treat the quantum extension of the Liouville equation is also stressed.

      17. Spin-orbit laser mode transfer via a classical analogue of quantum teleportation

        NASA Astrophysics Data System (ADS)

        Pinheiro da Silva, B.; Astigarreta Leal, M.; Souza, C. E. R.; Galvão, E. F.; Khoury, A. Z.

        2016-03-01

        We translate the quantum teleportation protocol into a sequence of coherent operations involving three degrees of freedom of a classical laser beam. The protocol, which we demonstrate experimentally, transfers the polarization state of the input beam to the transverse mode of the output beam. The role of quantum entanglement is played by a non-separable mode describing the path and transverse degrees of freedom. Our protocol illustrates the possibility of new optical applications based on this intriguing classical analogue of quantum entanglement.

      18. Path-integral approach to 't Hooft's derivation of quantum physics from classical physics

        SciTech Connect

        Blasone, Massimo; Jizba, Petr; Kleinert, Hagen

        2005-05-15

        We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.

      19. Control aspects of quantum computing using pure and mixed states.

        PubMed

        Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J

        2012-10-13

        Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

      20. Control aspects of quantum computing using pure and mixed states

        PubMed Central

        Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J.

        2012-01-01

        Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

      1. Quantum and classical thermal correlations in the XY spin-(1/2) chain

        SciTech Connect

        Maziero, J.; Guzman, H. C.; Celeri, L. C.; Serra, R. M.; Sarandy, M. S.

        2010-07-15

        We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.

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

        NASA Astrophysics Data System (ADS)

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

        2016-10-01

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

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

        PubMed Central

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

        2016-01-01

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

      4. Metric freeness and projectivity for classical and quantum normed modules

        NASA Astrophysics Data System (ADS)

        Helemskii, A. Ya

        2013-07-01

        In functional analysis, there are several diverse approaches to the notion of projective module. We show that a certain general categorical scheme contains all basic versions as special cases. In this scheme, the notion of free object comes to the foreground, and, in the best categories, projective objects are precisely retracts of free ones. We are especially interested in the so-called metric version of projectivity and characterize the metrically free classical and quantum (= operator) normed modules. Informally speaking, so-called extremal projectivity, which was known earlier, is interpreted as a kind of 'asymptotical metric projectivity'. In addition, we answer the following specific question in the geometry of normed spaces: what is the structure of metrically projective modules in the simplest case of normed spaces? We prove that metrically projective normed spaces are precisely the subspaces of l_1(M) (where M is a set) that are denoted by l_1^0(M) and consist of finitely supported functions. Thus, in this case, projectivity coincides with freeness. Bibliography: 28 titles.

      5. Flux formulation of loop quantum gravity: classical framework

        NASA Astrophysics Data System (ADS)

        Dittrich, Bianca; Geiller, Marc

        2015-07-01

        We recently introduced a new representation for loop quantum gravity (LQG), which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in LQG, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.

      6. Cleaning graphene: A first quantum/classical molecular dynamics approach

        NASA Astrophysics Data System (ADS)

        Delfour, L.; Davydova, A.; Despiau-Pujo, E.; Cunge, G.; Graves, D. B.; Magaud, L.

        2016-03-01

        Graphene outstanding properties created a huge interest in the condensed matter community and unprecedented fundings at the international scale in the hope of application developments. Recently, there have been several reports of incomplete removal of the polymer resists used to transfer as-grown graphene from one substrate to another, resulting in altered graphene transport properties. Finding a large-scale solution to clean graphene from adsorbed residues is highly desirable and one promising possibility would be to use hydrogen plasmas. In this spirit, we couple here quantum and classical molecular dynamics simulations to explore the kinetic energy ranges required by atomic hydrogen to selectively etch a simple residue—a CH3 group—without irreversibly damaging the graphene. For incident energies in the 2-15 eV range, the CH3 radical can be etched by forming a volatile CH4 compound which leaves the surface, either in the CH4 form or breaking into CH3 + H fragments, without further defect formation. At this energy, adsorption of H atoms on graphene is possible and further annealing will be required to recover pristine graphene.

      7. Sum Rules, Classical and Quantum - A Pedagogical Approach

        NASA Astrophysics Data System (ADS)

        Karstens, William; Smith, David Y.

        2014-03-01

        Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.

      8. Metric freeness and projectivity for classical and quantum normed modules

        SciTech Connect

        Helemskii, A Ya

        2013-07-31

        In functional analysis, there are several diverse approaches to the notion of projective module. We show that a certain general categorical scheme contains all basic versions as special cases. In this scheme, the notion of free object comes to the foreground, and, in the best categories, projective objects are precisely retracts of free ones. We are especially interested in the so-called metric version of projectivity and characterize the metrically free classical and quantum (= operator) normed modules. Informally speaking, so-called extremal projectivity, which was known earlier, is interpreted as a kind of 'asymptotical metric projectivity'. In addition, we answer the following specific question in the geometry of normed spaces: what is the structure of metrically projective modules in the simplest case of normed spaces? We prove that metrically projective normed spaces are precisely the subspaces of l{sub 1}(M) (where M is a set) that are denoted by l{sub 1}{sup 0}(M) and consist of finitely supported functions. Thus, in this case, projectivity coincides with freeness. Bibliography: 28 titles.

      9. Classical impurities and boundary Majorana zero modes in quantum chains

        NASA Astrophysics Data System (ADS)

        Müller, Markus; Nersesyan, Alexander A.

        2016-09-01

        We study the response of classical impurities in quantum Ising chains. The Z2 degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.

      10. Bi-photon spectral correlation measurements from a silicon nanowire in the quantum and classical regimes

        PubMed Central

        Jizan, Iman; Helt, L. G.; Xiong, Chunle; Collins, Matthew J.; Choi, Duk-Yong; Joon Chae, Chang; Liscidini, Marco; Steel, M. J.; Eggleton, Benjamin J.; Clark, Alex S.

        2015-01-01

        The growing requirement for photon pairs with specific spectral correlations in quantum optics experiments has created a demand for fast, high resolution and accurate source characterisation. A promising tool for such characterisation uses classical stimulated processes, in which an additional seed laser stimulates photon generation yielding much higher count rates, as recently demonstrated for a χ(2) integrated source in A. Eckstein et al. Laser Photon. Rev. 8, L76 (2014). In this work we extend these results to χ(3) integrated sources, directly measuring for the first time the relation between spectral correlation measurements via stimulated and spontaneous four wave mixing in an integrated optical waveguide, a silicon nanowire. We directly confirm the speed-up due to higher count rates and demonstrate that this allows additional resolution to be gained when compared to traditional coincidence measurements without any increase in measurement time. As the pump pulse duration can influence the degree of spectral correlation, all of our measurements are taken for two different pump pulse widths. This allows us to confirm that the classical stimulated process correctly captures the degree of spectral correlation regardless of pump pulse duration, and cements its place as an essential characterisation method for the development of future quantum integrated devices. PMID:26218609

      11. The Optimal Cloner for Mixed States as a Quantum Operation

        NASA Astrophysics Data System (ADS)

        Gardiner, John G.; van Huele, Jean-Francois S.

        2012-10-01

        The no-cloning theorem in quantum information says that it is impossible to produce two copies of an arbitrary quantum state. This precludes the possibility of a perfect universal quantum cloner, a process that could copy any quantum state perfectly. It is possible, however, to find optimal approximations of such a cloner. Using the formalism of quantum operations we obtain the optimal quantum cloner for arbitrary mixed states of a given purity and find that it is equivalent to the Buzek-Hillery optimal cloner for pure states. We also find the fidelity of this cloner as a function of the chosen purity.

      12. From the attempt of certain classical reformulations of quantum mechanics to quasi-probability representations

        SciTech Connect

        Stulpe, Werner

        2014-01-15

        The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.

      13. Correspondence behavior of classical and quantum dissipative directed transport via thermal noise.

        PubMed

        Carlo, Gabriel G; Ermann, Leonardo; Rivas, Alejandro M F; Spina, María E

        2016-04-01

        We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏ_{eff} values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏ_{eff} and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states. PMID:27176280

      14. Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

        NASA Astrophysics Data System (ADS)

        Carlo, Gabriel G.; Ermann, Leonardo; Rivas, Alejandro M. F.; Spina, María E.

        2016-04-01

        We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏeff values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏeff and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.

      15. Coupled harmonic oscillators for the measurement of a weak classical force at the standard quantum limit

        SciTech Connect

        Leaci, Paola; Ortolan, Antonello

        2007-12-15

        We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.

      16. Theoretical study of mixing in liquid clouds - Part 1: Classical concepts

        NASA Astrophysics Data System (ADS)

        Korolev, Alexei; Khain, Alex; Pinsky, Mark; French, Jeffrey

        2016-07-01

        The present study considers final stages of in-cloud mixing in the framework of classical concept of homogeneous and extreme inhomogeneous mixing. Simple analytical relationships between basic microphysical parameters were obtained for homogeneous and extreme inhomogeneous mixing based on the adiabatic consideration. It was demonstrated that during homogeneous mixing the functional relationships between the moments of the droplets size distribution hold only during the primary stage of mixing. Subsequent random mixing between already mixed parcels and undiluted cloud parcels breaks these relationships. However, during extreme inhomogeneous mixing the functional relationships between the microphysical parameters hold both for primary and subsequent mixing. The obtained relationships can be used to identify the type of mixing from in situ observations. The effectiveness of the developed method was demonstrated using in situ data collected in convective clouds. It was found that for the specific set of in situ measurements the interaction between cloudy and entrained environments was dominated by extreme inhomogeneous mixing.

      17. Using measurement-induced disturbance to characterize correlations as classical or quantum

        SciTech Connect

        Luo Shunlong

        2008-02-15

        In contrast to the seminal entanglement-separability paradigm widely used in quantum information theory, we introduce a quantum-classical dichotomy in order to classify and quantify statistical correlations in bipartite states. This is based on the idea that while in the classical description of nature measurements can be carried out without disturbance, in the quantum description, generic measurements often disturb the system and the disturbance can be exploited to quantify the quantumness of correlations therein. It turns out that certain separable states still possess correlations of a quantum nature and indicates that quantum correlations are more general than entanglement. The results are illustrated in the Werner states and the isotropic states, and are applied to quantify the quantum advantage of the model of quantum computation proposed by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)].

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

        SciTech Connect

        Khrennikov, Andrei

        2010-08-15

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

      19. Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information

        NASA Astrophysics Data System (ADS)

        Blume-Kohout, Robin; Zurek, Wojciech H.

        2006-06-01

        We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of “singly branching” states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment’s size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or “nonredundant,” information.

      20. Efficient quantum-classical method for computing thermal rate constant of recombination: application to ozone formation.

        PubMed

        Ivanov, Mikhail V; Babikov, Dmitri

        2012-05-14

        Efficient method is proposed for computing thermal rate constant of recombination reaction that proceeds according to the energy transfer mechanism, when an energized molecule is formed from reactants first, and is stabilized later by collision with quencher. The mixed quantum-classical theory for the collisional energy transfer and the ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)] is employed to treat the dynamics of molecule + quencher collision. Efficiency is achieved by sampling simultaneously (i) the thermal collision energy, (ii) the impact parameter, and (iii) the incident direction of quencher, as well as (iv) the rotational state of energized molecule. This approach is applied to calculate third-order rate constant of the recombination reaction that forms the (16)O(18)O(16)O isotopomer of ozone. Comparison of the predicted rate vs. experimental result is presented.

      1. Nonstationary Quantum Mechanics. III. Quantum Mechanics Does Not Incorporate Classical Physics

        NASA Astrophysics Data System (ADS)

        Todorov, Nickola Stefanov

        1981-01-01

        It is shown that disagreement between the prediction of classical and conventional quantum mechanics about momentum probabilities exists in the case of a quasiclassical motion. The discussion is based on the detailed consideration of two specific potentials: U( x)= x and the oscillatory potential U( x)= mω 2 x 2/2. The results of the present Part III represent a further development of the idea in Todorov (1980) about the possible inefficiency of conventional theory in the case of potentials swiftly varying with time.

      2. General approach to quantum-classical hybrid systems and geometric forces.

        PubMed

        Zhang, Qi; Wu, Biao

        2006-11-10

        We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics. PMID:17155596

      3. Evolution of Rydberg states in half-cycle pulses: Classical, semiclassical, and quantum dynamics

        SciTech Connect

        Burgdoerfer, J.; Reinhold, C. |

        1994-12-31

        We summarize recent theoretical advances in the description of the evolution of Rydberg atoms subject to ultrashort pulses extending only a fraction of an optical cycle. We have performed classical. semiclassical and full quantum calculations in order to delineate the classical-quantum correspondence for impulsively perturbed atomic systems. We observe classical and quantum (or semiclassical) oscillations in excitation and ionization which depend on the initial state of atoms and on the strength of the perturbation. These predictions can be experimentally tested. 4 figs.

      4. Quantum-classical correspondence for motion on a plane with deficit angle

        SciTech Connect

        Makowski, Adam J.

        2010-08-15

        A particle constrained to move on a cone and bound to its tip by harmonic oscillator and Coulomb-Kepler potentials is considered both in the classical as well as in the quantum formulations. The SU(2) coherent states are formally derived for the former model and used for showing some relations between closed classical orbits and quantum probability densities. Similar relations are shown for the Coulomb-Kepler problem. In both cases a perfect localization of the densities on the classical solutions is obtained even for low values of quantum numbers.

      5. Quantization of the Maxwell fish-eye problem and the quantum-classical correspondence

        SciTech Connect

        Makowski, A. J.; Gorska, K. J.

        2009-05-15

        The so-called fish-eye model, originally investigated by Maxwell in geometrical optics, is studied both in the classical as well as in the quantum formulations. The best agreement between the two approaches is achieved by using a suitably constructed coherent state, which is of the SU(2) type. The perfect quantum-classical correspondence is obtained in the sense that classical rays go exactly over maxima of the corresponding quantum probability distributions. The distributions are made of linear combinations of the E=0 bound states of the considered model.

      6. Classical and quantum chaos in a circular billiard with a straight cut

        SciTech Connect

        Ree, S.; Reichl, L.E.

        1999-08-01

        We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with {ital soft chaos}, or nonintegrable with {ital hard chaos} as we vary the size of the cut. We plot Poincar{acute e} surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. {copyright} {ital 1999} {ital The American Physical Society}

      7. To Quantum Mechanics Through Projection of Classical Statistical Mechanics on Prespace

        NASA Astrophysics Data System (ADS)

        Khrennikov, Andrei

        2005-10-01

        We show that in opposite to a common opinion quantum mechanics can be represented as projection of classical statistical model on prequantum space -- prespace. All distinguishing features of the quantum probabilistic model (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, classical model should be considered as a contextual model (in the sense that all probabilities are determined by contexts - complexes of physical conditions). Moreover, the prequantum→quantum map is well defined only for two fundamental physical variables (in quantum mechanics these are position and momentum). Quantum mechanics is a projection of classical statistical model through these two "reference observables". Similarly, ordinary classical statistical mechanics on physical phase space is a projection of classical statistical mechanics on prespace, We also introduce a mental prespace and consider its quantum-like representation. Mental prespace describes subconsciousness and its quantum-like representation gives a model of consciousness.

      8. Finite-time quantum-to-classical transition for a Schroedinger-cat state

        SciTech Connect

        Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina

        2011-07-15

        The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.

      9. Classical Antiquity and One Mixed-Ability, Team-Taught, Interrelated Humanities Course

        ERIC Educational Resources Information Center

        Smith, John Sharwood

        1977-01-01

        A humanities program is described in which the students learn geography, history, English, religious education, classical studies, social anthropology, and art history as a single subject. All classes have students of mixed abilities. Intellectual and social skills required for mixed-ability teaching are outlined. (SW)

      10. Dynamics of quantum-classical hybrid systems: Effect of matter-wave pressure

        NASA Astrophysics Data System (ADS)

        Shen, J.; Huang, X. L.; Yi, X. X.; Wu, Chunfeng; Oh, C. H.

        2010-12-01

        Radiation pressure affects the kinetics of a system exposed to radiation and it constitutes the basis of laser cooling. In this article, we study matter-wave pressure through examining the dynamics of a quantum-classical hybrid system. The quantum and classical subsystems are affected mutually via a changing boundary condition. Two systems, that is, an atom and a Bose-Einstein condensate (BEC), are considered as the quantum subsystems, while an oscillating wall is taken as the classical subsystem. We show that the classical subsystem would experience a force proportional to Q-3 from the quantum atom, where Q denotes the distance between the two walls, whereas it acquires an additional force proportional to Q-2 from the BEC due to the atom-atom interaction in the BEC. These forces can be understood as the matter-wave pressure.

      11. Semi-classical and quantum Rabi models: in celebration of 80 years

        NASA Astrophysics Data System (ADS)

        Braak, Daniel; Chen, Qing-Hu; Batchelor, Murray T.; Solano, Enrique

        2016-07-01

        This is an introduction to the special issue collection of articles on Semi-classical and quantum Rabi models to be published in J. Phys. A: Mathematical and Theoretical to mark the 80th anniversary of the Rabi model.

      12. Minimum best success probability by classical strategies for quantum pseudo-telepathy

        NASA Astrophysics Data System (ADS)

        Gao, Fei; Fang, Wei; Wen, QiaoYan

        2014-07-01

        Quantum pseudo-telepathy (QPT) is a new type of game where the quantum team can win with certainty while the classical one cannot. It means the advantages of quantum participants over classical ones in game. However, there has been no systematic and formal analysis on the QPT game before. Here we present the formal description of the QPT game and the definition of the most simplified QPT. Based on the above definitions, we simplify a famous QPT game, i.e. the Cabllo game. Then, according to some instances, we analyze the minimum best success probability by classical strategies of the two-player QPT, which reflects the advantage of the quantum strategies. Finally, we prove the best success probability by classical strategies for the most simplified QPT is totally related to the number of all possible question combinations.

      13. A Compact Code for Simulations of Quantum Error Correction in Classical Computers

        SciTech Connect

        Nyman, Peter

        2009-03-10

        This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.

      14. Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction

        SciTech Connect

        Liu Benqiong; Shao Bin; Li Jungang; Zou Jian; Wu Lianao

        2011-05-15

        We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the XY model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.

      15. Simulation of quantum random walks using the interference of a classical field

        SciTech Connect

        Jeong, H.; Paternostro, M.; Kim, M.S.

        2004-01-01

        We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.

      16. Redundant Information and the Quantum-Classical Transition

        ERIC Educational Resources Information Center

        Riedel, Charles Jess

        2012-01-01

        A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality--the fact that multiple observers can each…

      17. The equation of motion of an electron : a debate in classical and quantum physics.

        SciTech Connect

        Kim, K.-J.

        1999-01-27

        The current status of understanding of the equation of motion of an electron is summarized. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a tine theory even in the point-particle limit.

      18. Classical-Quantum Correspondence by Means of Probability Densities

        NASA Technical Reports Server (NTRS)

        Vegas, Gabino Torres; Morales-Guzman, J. D.

        1996-01-01

        Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

      19. Quantum-Classical Connection for Hydrogen Atom-Like Systems

        ERIC Educational Resources Information Center

        Syam, Debapriyo; Roy, Arup

        2011-01-01

        The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…

      20. Heat control in opto-mechanical system using quantum non-classicality

        NASA Astrophysics Data System (ADS)

        Sharma, Sushamana; Senwar, Subash

        2016-05-01

        Cooling of matter to the quantum ground state is a primary directive of quantum control. In other words, to extract entropy from a quantum system, efficient indirect quantum measurements may be implemented. The main objective is the cooling of the oscillator either to its motional ground state or to non-classical states, such as low-number Fock states, squeezed states or entangled states. It is shown that the use of quantum control procedure is better choice for even experimental realizations because it leads to a squeezed steady state with less than one phonon on average. The steady state of system corresponds to cooling of the system.

      1. Comparative role of potential structure in classical, semiclassical, and quantum mechanics

        SciTech Connect

        Judson, R.S.; Shi, S.; Rabitz, H.

        1989-02-15

        The corresponding effects of features in the potential on classical, semiclassical, and quantum mechanics are probed using the technique of functional sensitivity analysis. It is shown that the classical and quantum functional sensitivities are equivalent in the classical (small (h/2..pi..)) and harmonic limits. Classical and quantum mechanics are known to react in qualitatively similar ways provided that features on the potential are smooth on the length scale of oscillations in the quantum wave function. By using functional sensitivity analysis, we are able to show in detail how the classical and quantum dynamics differ in the way that they sense the potential. Two examples are given, the first of which is the harmonic oscillator. This problem is well understood by other means but is useful to examine because it illustrates the detailed information about the interaction of the potential and the dynamics which can be provided by functional sensitivity analysis, simplifying the analysis of more complex systems. The second example is the collinear H+H/sub 2/ reaction. In that case there are a number of detailed and striking differences between the ways that classical and quantum mechanics react to features on the potential. For features which are broad compared to oscillations in the wave function, the two react in qualitatively the same way. The sensitivities are oscillatory, however, and there are phasing differences between the classical and quantum sensitivity functions. This means that using classical mechanics plus experimental data in an inversion scheme intended to find the ''true'' potential will necessarily introduce sizeable errors.

      2. Additivity of the classical capacity of entanglement-breaking quantum channels

        NASA Astrophysics Data System (ADS)

        Shor, Peter W.

        2002-09-01

        We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur.

      3. Simulation of chemical reactions in solution by a combination of classical and quantum mechanical approach

        NASA Astrophysics Data System (ADS)

        Onida, Giovanni; Andreoni, Wanda

        1995-09-01

        A classical trajectory mapping method was developed to study chemical reactions in solution and in enzymes. In this method, the trajectories were calculated on a classical potential surface and the free energy profile was obtained by mapping the classical surface to the quantum mechanical surface obtained by the semiempirical AM1 method. There is no need to perform expensive quantum mechanical calculations at each iteration step. This method was applied to proton transfer reactions both in aqueous solution and in papain. The results are encouraging, indicating the applicability of this hybrid method to chemical reactions both in solution and in enzymes.

      4. On the connection between quantum and classical descriptions

        NASA Astrophysics Data System (ADS)

        Manjavidze, J.

        2012-07-01

        The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum force ħj, ∀ ħ. Spatial attention is dedicated to the systems with (hidden) symmetries. It is shown how the symmetry reduces the number of quantum degrees of freedom down to the independent ones. The sin-Gordon model is considered as an example of such field theory with symmetry. It is shown why the particles S-matrix is trivial in that model.

      5. Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

        NASA Astrophysics Data System (ADS)

        Rohrlich, Daniel

        Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

      6. Quantum-classical correspondence principle for work distributions in a chaotic system

        NASA Astrophysics Data System (ADS)

        Zhu, Long; Gong, Zongping; Wu, Biao; Quan, H. T.

        2016-06-01

        We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015), 10.1103/PhysRevX.5.031038]. Our investigation further justifies the definition of quantum work via two-point energy measurements.

      7. Quantum-classical correspondence principle for work distributions in a chaotic system.

        PubMed

        Zhu, Long; Gong, Zongping; Wu, Biao; Quan, H T

        2016-06-01

        We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)1063-651X10.1103/PhysRevX.5.031038]. Our investigation further justifies the definition of quantum work via two-point energy measurements. PMID:27415209

      8. Exponentially improved classical and quantum algorithms for three-body Ising models

        NASA Astrophysics Data System (ADS)

        Van den Nest, M.; Dür, W.

        2014-01-01

        We present an algorithm to approximate partition functions of three-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely, the color codes. The algorithm performance (in achievable accuracy) is exponentially better than other approaches that employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.

      9. Quantum-mechanical machinery for rational decision-making in classical guessing game.

        PubMed

        Bang, Jeongho; Ryu, Junghee; Pawłowski, Marcin; Ham, Byoung S; Lee, Jinhyoung

        2016-02-15

        In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call 'reasoning') to generate the best strategy, which may occur internally, e.g., in the player's brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.

      10. Quantum-mechanical machinery for rational decision-making in classical guessing game

        PubMed Central

        Bang, Jeongho; Ryu, Junghee; Pawłowski, Marcin; Ham, Byoung S.; Lee, Jinhyoung

        2016-01-01

        In quantum game theory, one of the most intriguing and important questions is, “Is it possible to get quantum advantages without any modification of the classical game?” The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call ‘reasoning’) to generate the best strategy, which may occur internally, e.g., in the player’s brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences. PMID:26875685

      11. Quantum-mechanical machinery for rational decision-making in classical guessing game

        NASA Astrophysics Data System (ADS)

        Bang, Jeongho; Ryu, Junghee; Pawłowski, Marcin; Ham, Byoung S.; Lee, Jinhyoung

        2016-02-01

        In quantum game theory, one of the most intriguing and important questions is, “Is it possible to get quantum advantages without any modification of the classical game?” The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call ‘reasoning’) to generate the best strategy, which may occur internally, e.g., in the player’s brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.

      12. Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

        NASA Technical Reports Server (NTRS)

        Erkmen, Baris I.; Hardy, Nicholas D.; Venkatraman, Dheera; Wong, Franco N. C.; Shapiro, Jeffrey H.

        2011-01-01

        The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

      13. Quantum-like model of processing of information in the brain based on classical electromagnetic field.

        PubMed

        Khrennikov, Andrei

        2011-09-01

        We propose a model of quantum-like (QL) processing of mental information. This model is based on quantum information theory. However, in contrast to models of "quantum physical brain" reducing mental activity (at least at the highest level) to quantum physical phenomena in the brain, our model matches well with the basic neuronal paradigm of the cognitive science. QL information processing is based (surprisingly) on classical electromagnetic signals induced by joint activity of neurons. This novel approach to quantum information is based on representation of quantum mechanics as a version of classical signal theory which was recently elaborated by the author. The brain uses the QL representation (QLR) for working with abstract concepts; concrete images are described by classical information theory. Two processes, classical and QL, are performed parallely. Moreover, information is actively transmitted from one representation to another. A QL concept given in our model by a density operator can generate a variety of concrete images given by temporal realizations of the corresponding (Gaussian) random signal. This signal has the covariance operator coinciding with the density operator encoding the abstract concept under consideration. The presence of various temporal scales in the brain plays the crucial role in creation of QLR in the brain. Moreover, in our model electromagnetic noise produced by neurons is a source of superstrong QL correlations between processes in different spatial domains in the brain; the binding problem is solved on the QL level, but with the aid of the classical background fluctuations.

      14. Critical comparison of classical and quantum mechanical treatments of the phase equilibria of water

        SciTech Connect

        Wick, Collin D.; Schenter, Gregory K.

        2006-03-17

        The Gibbs ensemble Monte Carlo simulation technique was used to compare the phase equilibria of the rigid TIP4P water model [J.\\ Chem.\\ Phys.\\ {\\bf 79}, 926, (1983)] utilizing classical and quantum statistical mechanical treatments. The quantum statistical mechanical treatment generally resulted in lower liquid densities and higher vapor densities, showing a narrowing in the phase envelope. As a result, the calculated critical temperature and normal boiling point were higher from the quantum simulations than the classical by 20~and 17~K, respectively, but the critical densities were very close. A semiclassical treatment, involving a low order expansion in Plank's constant, resulted in densities and vapor pressures that fluctuated between the values for the classical and quantum statistical mechanics values, with no definite agreement with either.

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

        SciTech Connect

        Dimitrijević, Dragoljub D. Djordjević, Goran S. Milošević, Milan; Vulcanov, Dumitru

        2014-11-24

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

      16. Macrostates Thermodynamics and Its Stable Classical Limit in Global One-Dimensional Quantum General Relativity

        NASA Astrophysics Data System (ADS)

        Glinka, L. A.

        2009-01-01

        Global One-Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3 + 1 metric, where the dimension is a volume of threedimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3 + 1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirm that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.

      17. The incongruent correspondence: Seven non-classical years of old quantum theory

        NASA Astrophysics Data System (ADS)

        Kaveh, Shahin

        2014-05-01

        The Correspondence Principle (CP) of old quantum theory is commonly considered to be the requirement that quantum and classical theories converge in their empirical predictions in the appropriate asymptotic limit. That perception has persisted despite the fact that Bohr and other early proponents of CP clearly did not intend it as a mere requirement, and despite much recent historical work. In this paper, I build on this work by first giving an explicit formulation to the mentioned asymptotic requirement (which I shall call the Congruence Requirement (CR)) and then discussing various possible formulations of CP for emission on the basis of the primary literature as well as general physical and metaphysical considerations. I shall then show that, in all of the most probable interpretations of CP that consider quantum theory as a universal theory, any system incorporating both CR and CP for emission would in fact be inconsistent. Old quantum theory measurably contradicts classical physics in the classical regime.

      18. Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

        NASA Astrophysics Data System (ADS)

        Trapani, Jacopo; Bina, Matteo; Maniscalco, Sabrina; Paris, Matteo G. A.

        2015-02-01

        We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schrödinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.

      19. Classical and quantum mechanical studies of HF in an intense laser field

        SciTech Connect

        Dardi, P.S.; Gray, S.K.

        1982-08-01

        The behavior of an HF molecule in an intense laser field is investigated with both classical trajectories and quantum dynamics. Vibration-rotation transition probabilities and energy absorption as a function of laser pulse time are calculated for the diatomic initially in its ground state. For comparison, results are also reported for a model nonrotating HF molecule. It is found that classical mechanics does not predict the correct time behavior of the system, nor does it predict the correct rotational state distributions. Classical mechanics does, however, predict pulse time averaged quantities to be the correct order of magnitude. There is also a correct general trend of increased multiphoton excitation for laser frequencies red-shifted from the one-photon resonance, although multiphoton resonance peaks are not observed in the classical results and far too little multiphoton excitation is predicted. The effect of laser phase has also been investigated and shown to be relatively unimportant in both the classical and quantum dynamics.

      20. Classical-quantum correspondence for ionization in fast ion-atom collisions

        SciTech Connect

        Burgdoerfer, J. |; Reinhold, C.O.

        1994-10-01

        We analyze the interplay between classical and quantum dynamics in ionization of atoms by fast charged particles The convergence to the classical limit is studied as a function of the momentum transferred to the electron during the collision, the impact parameter. the energy and angle of the emitted electron, and the initial state of the target. One goal is to assess the validity of exact classical (CTMC) methods and approximate classical models such as the Thomson model. Applications to data for electron ejection at large angles are presented. The connection between collisional ionization by charged particles and ionization by half-cycle pulses is discussed.

      1. Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory

        NASA Astrophysics Data System (ADS)

        Andreev, A. V.; Agam, O.; Simons, B. D.; Altshuler, B. L.

        1996-05-01

        The Bohigas-Giannoni-Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory (RMT) is proved. A new semiclassical field theory for individual chaotic systems is constructed in the framework of a nonlinear σ model. The low lying modes are shown to be associated with the Perron-Frobenius (PF) spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the PF spectrum results in RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

      2. Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators

        NASA Astrophysics Data System (ADS)

        Montero, Miquel

        2016-06-01

        Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I show that this is not the only way: I introduce a quantum walk driven by an inhomogeneous, time-dependent coin operator, which mimics the statistical properties of a random walk at all time scales. The quantum particle undergoes unitary evolution and, in fact, the high correlation evidenced by the components of the wave function can be used to revert the outcome of an accidental measurement of its chirality.

      3. Quantum versus classical dynamics in a driven barrier: The role of kinematic effects.

        PubMed

        Papachristou, P K; Katifori, E; Diakonos, F K; Constantoudis, V; Mavrommatis, E

        2012-09-01

        We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances, and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. In that frequency region, the classical and quantum transmission coefficients are in optimal agreement. Moreover, the transmission threshold (i.e., the energy above which the transmission coefficient becomes larger than a specific small threshold value) is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well-separated coherent pulses, a phenomenon that admits purely classical kinematic interpretation.

      4. Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

        NASA Astrophysics Data System (ADS)

        Lee, Mark D.; Ruostekoski, Janne

        2014-08-01

        We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic Bose-Einstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasiprobability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.

      5. The Philosophy of Fields and Particles in Classical and Quantum Mechanics, Including the Problem of Renormalisation.

        NASA Astrophysics Data System (ADS)

        Huggett, Nick

        1995-01-01

        This work first explicates the philosophy of classical and quantum fields and particles. I am interested in determining how science can have a metaphysical dimension, and then with the claim that the quantum revolution has an important metaphysical component. I argue that the metaphysical implications of a theory are properties of its models, as classical mechanics determines properties of atomic diversity and temporal continuity with its representations of distinct, continuous trajectories. It is often suggested that classical statistical physics requires that many particle states be represented so that permuting properties leads to distinct states; this implies that individuals can be reidentified across possible worlds in a non-qualitative way. I show there is no evidence for this conclusion, an important result, for it is claimed that quantum particles are not individuals. This claim is based on the misconception about classical statistics, but also on a conflation of notions of identity; I show that, while transworld identity is incompatible with quantum mechanics, other classical notions may be consistently ascribed. I also give a field-particle distinction that applies usefully in both quantum and classical domains. In the former the distinction helps defeat claims of underdetermined by data, in the latter it helps provide a minimal field metaphysics. Next I tackle renormalisation: I show how divergences occur in approximate, perturbative calculations, and demonstrate how finite, empirically verified, answers are obtained. These techniques seem to show that the predictions are not logical consequences of the exact theory. I use the techniques of the renormalisation group to establish that perturbative renormalised quantum field theory does indeed approximate the consequences of field theory. Finally, I discuss the idea (Cao and Schweber, 1994) that renormalisation proves that there can be no quantum theory of everything, only a patchwork of effective

      6. Quantum broadcasting problem in classical low-power signal processing

        SciTech Connect

        Janzing, Dominik; Steudel, Bastian

        2007-02-15

        We prove a no-broadcasting theorem for the Holevo information of a noncommuting ensemble stating that no operation can generate a bipartite ensemble such that both copies have the same information as the original. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transferring at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy.

      7. Fidelity between Gaussian mixed states with quantum state quadrature variances

        NASA Astrophysics Data System (ADS)

        Hai-Long, Zhang; Chun, Zhou; Jian-Hong, Shi; Wan-Su, Bao

        2016-04-01

        In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation (quantum clone) experiment since the variances of the input (output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the Foundation of Science and Technology on Information Assurance Laboratory (Grant No. KJ-14-001).

      8. Fidelity between Gaussian mixed states with quantum state quadrature variances

        NASA Astrophysics Data System (ADS)

        Hai-Long, Zhang; Chun, Zhou; Jian-Hong, Shi; Wan-Su, Bao

        2016-04-01

        In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation (quantum clone) experiment since the variances of the input (output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the Foundation of Science and Technology on Information Assurance Laboratory (Grant No. KJ-14-001).

      9. Classically and quantum stable emergent universe from conservation laws

        NASA Astrophysics Data System (ADS)

        del Campo, Sergio; Guendelman, Eduardo I.; Herrera, Ramón; Labraña, Pedro

        2016-08-01

        It has been recently pointed out by Mithani-Vilenkin [1-4] that certain emergent universe scenarios which are classically stable are nevertheless unstable semiclassically to collapse. Here, we show that there is a class of emergent universes derived from scale invariant two measures theories with spontaneous symmetry breaking (s.s.b) of the scale invariance, which can have both classical stability and do not suffer the instability pointed out by Mithani-Vilenkin towards collapse. We find that this stability is due to the presence of a symmetry in the "emergent phase", which together with the non linearities of the theory, does not allow that the FLRW scale factor to be smaller that a certain minimum value a0 in a certain protected region.

      10. Quantum versus classical foundation of statistical mechanics under experimentally realistic conditions.

        PubMed

        Reimann, Peter; Evstigneev, Mykhaylo

        2013-11-01

        Focusing on isolated macroscopic systems, described in terms of either a quantum mechanical or a classical model, our two key questions are how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior (equilibration) and how far is this steady state in agreement with the microcanonical ensemble as predicted by statistical mechanics (thermalization). A recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and nonequilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. An analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.

      11. Quantum-classical correspondence for a particle in a homogeneous field

        NASA Astrophysics Data System (ADS)

        Singh, Sumita; Suman, Smriti P.; Singh, Vijay A.

        2016-11-01

        The correspondence principle provides a prescription to connect quantum physics to classical. It asserts that the physical quantities evaluated quantum mechanically approach their respective classical values for large quantum numbers. This has been shown for the pedagogically important cases of the particle in a box and a harmonic oscillator. However, a particle in a constant field has a wave function related to the Airy function and has at best been treated numerically. Employing energy eigenstates we obtain the expectation values of the position, the momentum and their moments upto fourth order, rigorously and without resorting to numerical or graphical techniques. We compare them with the corresponding classical values. We also examine the uncertainty product for the system.

      12. Quantum and classical analysis of circular and sectorial billiards with central harmonic potential

        NASA Astrophysics Data System (ADS)

        Jurado-Taracena, Manuel; Plascencia, Alexis D.; Gutierrez-Vega, Julio C.

        2012-06-01

        We present the classical and quantum solutions to a particle confined in a circular sectorial billiard under a central harmonic potential, attractive and repulsive. The classical analysis is done by applying the Hamilton-Jacobi formalism; we derive the characteristic equations for periodic orbits, give expressions for the length of the trajectories in terms of elliptic integrals and study some geometrical constructions for the billiard. The quantum analysis leads to the study of the confluent hypergeometric function, from which we obtain the characteristic values for the energy spectra and the probability distributions inside the circular and sectorial billiard. As verification for the attractive case, as we increase the billiard radius our results approach the unbounded solutions. Finally we compare the classical probability distributions, obtained by assuming the probability as proportional to the time spent by the particle in each space interval, with the quantum ones.

      13. GENERAL: Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

        NASA Astrophysics Data System (ADS)

        Salimi, S.; Jafarizadeh, M. A.

        2009-06-01

        In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete Kn, charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied.

      14. Integrated Quantum/Classical Modeling of Hydrogenic Materials

        SciTech Connect

        CURRO,JOHN G.; VAN SWOL,FRANK B.; FYE,RICHARD M.; WANG,Q.; JOHNSON,J.K.; PATRA,C.; YETHIRAJ,A.

        1999-11-01

        Path integral Monte Carlo simulations and calculations were performed on molecular hydrogen liquids. The equation-of-state, internal energies, and vapor liquid phase diagrams from simulation were found to be in quantitative agreement with experiments. Analytical calculations were performed on,H2 liquids using integral equation methods to study the degree of localization of the hydrogen molecules. Very little self-trapping or localization was found as a function of temperature and density. Good qualitative agreement was found between the integral equation calculations and the quantum Monte Carlo simulations for the radius of gyration of the hydrogen molecules. Path integral simulations were also performed on molecular hydrogen on graphite surfaces, slit pores, and in carbon nanotubes. Significant quantum effects on the adsorption of hydrogen were observed.

      15. Properties of classical and quantum Jensen-Shannon divergence

        SciTech Connect

        Brieet, Jop; Harremoees, Peter

        2009-05-15

        Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (JD{sub {alpha}} for {alpha}>0), the Jensen divergences of order {alpha}, which generalize JD as JD{sub 1}=JD. Using a result of Schoenberg, we prove that JD{sub {alpha}} is the square of a metric for {alpha} is an element of (0,2], and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order {alpha} (QJD{sub {alpha}}). We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, QJD{sub {alpha}}{sup 1/2} is a metric space which can be isometrically embedded in a real Hilbert space when {alpha} is an element of (0,2]. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.

      16. Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

        SciTech Connect

        Prigogine, I.

        1995-01-05

        Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger`s equation, on the one hand, and on the {open_quotes}collapse{close_quotes} of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a {open_quotes}collapse{close_quotes} of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices.

      17. Private classical capacity with a symmetric side channel and its application to quantum cryptography

        NASA Astrophysics Data System (ADS)

        Smith, Graeme

        2008-08-01

        We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we provide a single-letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassisted private capacity. While a channel’s (unassisted) capacity for private classical communication may be strictly larger than its quantum capacity, we will show that these capacities are equal for degradable channels, thus demonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to find new bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. For the Bennett-Brassard 1984 protocol, our results demonstrate that collective attacks are strictly stronger than individual attacks.

      18. A novel framework of classical and quantum prisoner's dilemma games on coupled networks.

        PubMed

        Deng, Xinyang; Zhang, Qi; Deng, Yong; Wang, Zhen

        2016-01-01

        Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner's dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner's dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner's dilemma is greatly impacted by the combined effect of entanglement and coupling.

      19. Quantum-locked key distribution at nearly the classical capacity rate.

        PubMed

        Lupo, Cosmo; Lloyd, Seth

        2014-10-17

        Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.

      20. Quantum-locked key distribution at nearly the classical capacity rate.

        PubMed

        Lupo, Cosmo; Lloyd, Seth

        2014-10-17

        Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit. PMID:25361242

      1. Generalized trace-distance measure connecting quantum and classical non-Markovianity

        NASA Astrophysics Data System (ADS)

        Wißmann, Steffen; Breuer, Heinz-Peter; Vacchini, Bassano

        2015-10-01

        We establish a direct connection of quantum Markovianity of an open system to its classical counterpart by generalizing the criterion based on the information flow. Here the flow is characterized by the time evolution of Helstrom matrices, given by the weighted difference of statistical operators, under the action of the quantum dynamical map. It turns out that the introduced criterion is equivalent to P divisibility of a quantum process, namely, divisibility in terms of positive maps, which provides a direct connection to classical Markovian stochastic processes. Moreover, it is shown that mathematical representations similar to those found for the original trace-distance-based measure hold true for the associated generalized measure for quantum non-Markovianity. That is, we prove orthogonality of optimal states showing a maximal information backflow and establish a local and universal representation of the measure. We illustrate some properties of the generalized criterion by means of examples.

      2. A novel framework of classical and quantum prisoner’s dilemma games on coupled networks

        PubMed Central

        Deng, Xinyang; Zhang, Qi; Deng, Yong; Wang, Zhen

        2016-01-01

        Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner’s dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner’s dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner’s dilemma is greatly impacted by the combined effect of entanglement and coupling. PMID:26975447

      3. Classical-quantum arbitrarily varying wiretap channel: Ahlswede dichotomy, positivity, resources, super-activation

        NASA Astrophysics Data System (ADS)

        Boche, Holger; Cai, Minglai; Deppe, Christian; Nötzel, Janis

        2016-08-01

        We establish the Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels, i.e., either the deterministic secrecy capacity of the channel is zero, or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of these channels when the sender and the receiver use various resources. It turns out that randomness, common randomness, and correlation as resources are very helpful for achieving a positive secrecy capacity. We prove the phenomenon "super-activation" for arbitrarily varying classical-quantum wiretap channels, i.e., two channels, both with zero deterministic secrecy capacity, if used together allow perfect secure transmission.

      4. Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization

        NASA Astrophysics Data System (ADS)

        Paul, Sanku; Pal, Harinder; Santhanam, M. S.

        2016-06-01

        The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem, namely, the kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on subdiffusion exponents. We briefly comment on the experimental feasibility of this system.

      5. Bremsstrahlung radiation from slow electrons in a Coulomb field: Classical limit and quantum correction

        SciTech Connect

        Manakov, N. L. Krylovetsky, A. A.; Marmo, S. I.

        2015-11-15

        Compact analytic expressions have been derived by a direct expansion in ħ → 0 for the nonrelativistic amplitude of Coulomb bremsstrahlung radiation (BR), the differential (in frequency and angles of the scattered electron) BR cross section, and the triply differential BR cross section that takes into account the bremsstrahlung photon direction and polarization and the scattered electron direction. They contain the classical limit and a quantum correction of the order of ħ at an arbitrary BR frequency ω. An explicit expression has been found for the quantum correction of the order of ħ to the classical BR spectrum.

      6. Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations

        SciTech Connect

        Chen, Y. F.

        2011-03-15

        The geometry of classical dynamics in coupled oscillators with SU(2) transformations is explored and found to be relevant to a family of continuous-transformation orbits between Lissajous and trochoidal curves. The quantum wave-packet coherent states are derived analytically to correspond exactly to the transformation geometry of classical dynamics. By using the quantum wave-packet coherent states derived herein, stationary coherent states are constructed and are shown to possess spatial patterns identical to the transformation geometry between Lissajous and trochoidal orbits.

      7. Quantum limits on optical phase estimation accuracy from classical rate-distortion theory

        SciTech Connect

        Nair, Ranjith

        2014-12-04

        The classical information-theoretic lower bound on the distortion of a random variable upon transmission through a noisy channel is applied to quantum-optical phase estimation. An approach for obtaining Bayesian lower bounds on the phase estimation accuracy is described that employs estimates of the classical capacity of the relevant quantum-optical channels. The Heisenberg limit for lossless phase estimation is derived for arbitrary probe state and prior distributions of the phase, and shot-noise scaling of the phase accuracy is established in the presence of nonzero loss for a parallel entanglement-assisted strategy with a single probe mode.

      8. Exponential communication gap between weak and strong classical simulations of quantum communication

        NASA Astrophysics Data System (ADS)

        Montina, Alberto

        2013-04-01

        The most trivial way to simulate classically the communication of a quantum state is to transmit the classical description of the quantum state itself. However, this requires an infinite amount of classical communication if the simulation is exact. A more intriguing and potentially less demanding strategy would encode the full information about the quantum state into the probability distribution of the communicated variables so that this information is never sent in each single shot. This kind of simulation is called weak, as opposed to strong simulations, where the quantum state is communicated in individual shots. In this paper, we introduce a bounded-error weak protocol for simulating the communication of an arbitrary number of qubits and a subsequent two-outcome measurement consisting of an arbitrary pure state projector and its complement. This protocol requires an amount of classical communication independent of the number of qubits and proportional to Δ-1, where Δ is the error and a free parameter of the protocol. Conversely, a bounded-error strong protocol requires an amount of classical communication growing exponentially with the number of qubits for a fixed error. Our result improves a previous protocol, based on the Johnson-Lindenstrauss lemma, with communication cost scaling as Δ-2lnΔ-1.

      9. Quantum-network generation based on four-wave mixing

        NASA Astrophysics Data System (ADS)

        Cai, Yin; Feng, Jingliang; Wang, Hailong; Ferrini, Giulia; Xu, Xinye; Jing, Jietai; Treps, Nicolas

        2015-01-01

        We present a scheme to realize versatile quantum networks by cascading several four-wave mixing (FWM) processes in warm rubidium vapors. FWM is an efficient χ(3 ) nonlinear process, already used as a resource for multimode quantum state generation and which has been proved to be a promising candidate for applications to quantum information processing. We analyze theoretically the multimode output of cascaded FWM systems, derive its independent squeezed modes, and show how, with phase controlled homodyne detection and digital postprocessing, they can be turned into a versatile source of continuous variable cluster states.

      10. Time-Resolved Photoelectron Studies of IBr^-: a Classical and Quantum Tug-Of

        NASA Astrophysics Data System (ADS)

        Horvath, Samantha; McCoy, Anne B.

        2010-06-01

        To understand the dynamics of molecular species, especially those involved in photochemistry, we often turn to classical mechanics, which, despite the assumed quantum nature of small, light particles, has been extremely helpful in describing the underlying photophysics and can often explain the big picture of the dynamics. One such example is the recent duel experimental and theoretical study on the photodissociation of IBr^- performed by Sanov and co-workers. Of greater interest, though, is when does classical mechanics break down? More generally, when is a quantum approach needed to fully describe the system at the resolution of the experiment? In this work, we address these questions by investigating quantum interference effects on the time-resolved spectra of IBr^- where we look at how pulse width affects the overall signal. In the limit of an infinitely narrow pulse, we regain the Franck-Condon picture and the classical limit because all transitions are energetically allowed. In the limit of an infinitely wide pulse width, quantum interference effects become important and give rise to the bimodal character of the spectrum at short delay times (Δ t < 350 fs). Results of the calculated IBr^- spectra are in good agreement with experiment and serve to illustrate how varying the pulse widths can shift the description of the dynamics from a classical picture to a quantum one. R. Mabbs, K. Pichugin, and A. Sanov, J. Chem. Phys., 2005, 122, 174305.

      11. Non-classical role of potential energy in adiabatic quantum annealing

        NASA Astrophysics Data System (ADS)

        Das, Arnab

        2009-12-01

        Adiabatic quantum annealing is a paradigm of analog quantum computation, where a given computational job is converted to the task of finding the global minimum of some classical potential energy function and the search for the global potential minimum is performed by employing external kinetic quantum fluctuations and subsequent slow reduction (annealing) of them. In this method, the entire potential energy landscape (PEL) may be accessed simultaneously through a delocalized wave-function, in contrast to a classical search, where the searcher has to visit different points in the landscape (i.e., individual classical configurations) sequentially. Thus in such searches, the role of the potential energy might be significantly different in the two cases. Here we discuss this in the context of searching of a single isolated hole (potential minimum) in a golf-course type gradient free PEL. We show, that the quantum particle would be able to locate the hole faster if the hole is deeper, while the classical particle of course would have no scope to exploit the depth of the hole. We also discuss the effect of the underlying quantum phase transition on the adiabatic dynamics.

      12. Probabilities for time-dependent properties in classical and quantum mechanics

        NASA Astrophysics Data System (ADS)

        Losada, Marcelo; Vanni, Leonardo; Laura, Roberto

        2013-05-01

        We present a formalism which allows one to define probabilities for expressions that involve properties at different times for classical and quantum systems and we study its lattice structure. The formalism is based on the notion of time translation of properties. In the quantum case, the properties involved should satisfy compatibility conditions in order to obtain well-defined probabilities. The formalism is applied to describe the double-slit experiment.

      13. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.

        PubMed

        Okuyama, Manaka; Takahashi, Kazutaka

        2016-08-12

        Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.

      14. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

        NASA Astrophysics Data System (ADS)

        Okuyama, Manaka; Takahashi, Kazutaka

        2016-08-01

        Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.

      15. Classical and quantum aspects of brane-world cosmology

        SciTech Connect

        Cordero, Ruben; Rojas, Efrain

        2011-10-14

        We give a brief overview of several models in brane-world cosmology. In particular, we focus on the asymmetric DGP and Regge-Teiltelboim models. We present the associated equations of motion governing the dynamics of the brane and their corresponding Friedmann-like equations. In order to develop the quantum Regge-Teiltelboim type cosmology we construct its Ostrogradski Hamiltonian formalism which naturally leads to the corresponding Wheeler-DeWitt equation. In addition, we comment on possible generalizations for these models including second order derivative geometrical terms.

      16. Classical and quantum chaotic angular-momentum pumps.

        PubMed

        Dittrich, T; Dubeibe, F L

        2015-03-01

        We study directed transport of charge and intrinsic angular momentum by periodically driven scattering in the regime of fast and strong driving. A spin-orbit coupling through a kicked magnetic field confined to a compact region in space leads to irregular scattering and triggers spin flips in a spatially asymmetric manner which allows us to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory based on the Floquet formalism is confirmed by numerical solutions of the time-dependent inhomogeneous Schrödinger equation with a continuous source term.

      17. Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

        SciTech Connect

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

        2015-04-07

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

      18. Beating the Classical Limits of Information Transmission using a Quantum Decoder

        NASA Astrophysics Data System (ADS)

        Karim, Akib; Huang, Zixin; Chapman, Rob; Tomamichel, Marco; Flammia, Steve; Peruzzo, Alberto

        Reliable transmission of information over a noisy channel is a fundamental challenge in communication theory. The emergence of quantum technologies has created a new class of strategies that allow for message recovery greater than purely classical methods. Despite this, for minimal uses of the channel, finding such schemes remains a challenge. We investigate the amplitude damping channel which describes physical systems that suffer energy loss such as in cavity quantum electrodynamics or spin chain excitations. We derive and experimentally demonstrate the fundamental limit for message recovery possible with only classical methods. We then propose a quantum decoder and experimentally demonstrate message recovery past this classical limit. We use polarisation-encoded photonic qubits. The post-amplitude damping states are generated by an unbalanced Mach-Zehnder interferometer and entanglement is accomplished with a linear optical probabilistic controlled z gate. Our quantum decoder uses a single entangling gate at the receiver where other similar schemes rely on both the sender and the receiver having quantum devices. Our results present an advance in discovering the quantum capabilities of finite resource communications, with specific regard to the amplitude damping channel.

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

        NASA Astrophysics Data System (ADS)

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

        2015-04-01

        We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ2 at ħ0 (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O ( ħ 2 ) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

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

        PubMed

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

        2015-04-01

        We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods. PMID:25854224

      1. Controlling photons in a box and exploring the quantum to classical boundary (Nobel Lecture).

        PubMed

        Haroche, Serge

        2013-09-23

        Microwave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. The interaction of these trapped photons with Rydberg atoms crossing the cavity illustrates fundamental aspects of measurement theory. The experiments performed with this "photon box" at Ecole Normale Supérieure (ENS) belong to the domain of quantum optics called "Cavity Quantum Electrodynamics". We have realized the non-destructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of "Schrödinger cat" states of radiation and the study of their decoherence, which provides a striking illustration of the transition from the quantum to the classical world. These experiments have also led to the demonstration of basic steps in quantum information processing, including the deterministic entanglement of atoms and the realization of quantum gates using atoms and photons as quantum bits. This lecture starts by an introduction stressing the connection between the ENS photon box and the ion trap experiments of David Wineland, whose accompanying lecture recalls his own contribution to the field of single particle control. I give then a personal account of the early days of Cavity Quantum Electrodynamics before describing the main experiments performed at ENS during the last twenty years and concluding by a discussion comparing our work to other researches dealing with the control of single quantum particles. PMID:24038846

      2. Controlling photons in a box and exploring the quantum to classical boundary (Nobel Lecture).

        PubMed

        Haroche, Serge

        2013-09-23

        Microwave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. The interaction of these trapped photons with Rydberg atoms crossing the cavity illustrates fundamental aspects of measurement theory. The experiments performed with this "photon box" at Ecole Normale Supérieure (ENS) belong to the domain of quantum optics called "Cavity Quantum Electrodynamics". We have realized the non-destructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of "Schrödinger cat" states of radiation and the study of their decoherence, which provides a striking illustration of the transition from the quantum to the classical world. These experiments have also led to the demonstration of basic steps in quantum information processing, including the deterministic entanglement of atoms and the realization of quantum gates using atoms and photons as quantum bits. This lecture starts by an introduction stressing the connection between the ENS photon box and the ion trap experiments of David Wineland, whose accompanying lecture recalls his own contribution to the field of single particle control. I give then a personal account of the early days of Cavity Quantum Electrodynamics before describing the main experiments performed at ENS during the last twenty years and concluding by a discussion comparing our work to other researches dealing with the control of single quantum particles.

      3. Quantum chaotic scattering in graphene systems in the absence of invariant classical dynamics.

        PubMed

        Wang, Guang-Lei; Ying, Lei; Lai, Ying-Cheng; Grebogi, Celso

        2013-05-01

        Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.

      4. Quantum chaotic scattering in graphene systems in the absence of invariant classical dynamics

        NASA Astrophysics Data System (ADS)

        Wang, Guang-Lei; Ying, Lei; Lai, Ying-Cheng; Grebogi, Celso

        2013-05-01

        Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.

      5. Connection between quantum-mechanical and classical time evolution via a dynamical invariant

        SciTech Connect

        Schuch, Dieter; Moshinsky, Marcos

        2006-06-15

        The time evolution of a quantum system with at most quadratic Hamiltonian is described with the help of different methods, namely the time-dependent Schroedinger equation, the time propagator or Feynman kernel, and the Wigner function. It is shown that all three methods are connected via a dynamical invariant, the so-called Ermakov invariant. This invariant introduces explicitly the quantum aspect via the position uncertainty and its possible time dependence. The importance of this aspect, also for the difference between classical and quantum dynamics, and in particular the role of the initial position uncertainty is investigated.

      6. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.

        PubMed

        Okuyama, Manaka; Takahashi, Kazutaka

        2016-08-12

        Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail. PMID:27563938

      7. Cosmological constraints on a classical limit of quantum gravity

        SciTech Connect

        Easson, Damien A.; Trodden, Mark; Schuller, Frederic P.; Wohlfarth, Mattias N.R.

        2005-08-15

        We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors - one accelerating and the other dramatically decelerating. It is also shown that nonaccelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements.

      8. On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

        NASA Astrophysics Data System (ADS)

        Plotnitsky, Arkady

        2011-03-01

        The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

      9. Spin Foam Models for Quantum Gravity and semi-classical limit

        NASA Astrophysics Data System (ADS)

        Dupuis, Maité

        2011-04-01

        The spinfoam framework is a proposal for a regularized path integral for quantum gravity. Spinfoams define quantum space-time structures describing the evolution in time of the spin network states for quantum geometry derived from Loop Quantum Gravity (LQG). The construction of this covariant approach is based on the formulation of General Relativity as a topological theory plus the so-called simplicity constraints which introduce local degrees of freedom. The simplicity constraints are essential in turning the non-physical topological theory into 4d gravity. In this PhD manuscript, an original way to impose the simplicity constraints in 4d Euclidean gravity using harmonic oscillators is proposed and new coherent states, solutions of the constraints, are given. Moreover, a consistent spinfoam model for quantum gravity has to be connected to LQG and must have the right semi-classical limit. An explicit map between the spin network states of LQG and the boundary states of spinfoam models is given connecting the canonical and the covariant approaches. Finally, new techniques to compute semiclassical asymptotic expressions for the transition amplitudes of 3d quantum gravity and to extract semi-classical information from a spinfoam model are introduced. Explicit computations based on approximation methods and on the use of recurrence relations on spinfoam amplitudes have been performed. The results are relevant to derive quantum corrections to the dynamics of the gravitational field.

      10. Transient temperature and mixing times of quantum walks on cycles

        NASA Astrophysics Data System (ADS)

        Díaz, Nicolás; Donangelo, Raul; Portugal, Renato; Romanelli, Alejandro

        2016-07-01

        The definition of entanglement temperature for a quantum walk on a line is extended to N cycles, which are more amenable to a physical implementation. We show that, for these systems, there is a linear connection between the thermalization time and the mixing time and, also, that these characteristic times become insensitive to the system size when N is larger than a few units.

      11. Coherent-state transfer via highly mixed quantum spin chains

        SciTech Connect

        Cappellaro, Paola; Viola, Lorenza; Ramanathan, Chandrasekhar

        2011-03-15

        Spin chains have been proposed as quantum wires in many quantum-information processing architectures. Coherent transmission of quantum information in spin chains over short distances is enabled by their internal dynamics, which drives the transport of single-spin excitations in perfectly polarized chains. Given the practical challenge of preparing the chain in a pure state, we propose to use a chain that is initially in the maximally mixed state. We compare the transport properties of pure and mixed-state chains and find similarities that enable the experimental study of pure-state transfer via mixed-state chains. We also demonstrate protocols for the perfect transfer of quantum information in these chains. Remarkably, mixed-state chains allow the use of Hamiltonians that do not preserve the total number of single-spin excitations and are more readily obtainable from the naturally occurring magnetic dipolar interaction. We discuss experimental implementations using solid-state nuclear magnetic resonance and defect centers in diamond.

      12. Rise and fall of quantum and classical correlations in open-system dynamics

        SciTech Connect

        Khasin, Michael; Kosloff, Ronnie

        2007-07-15

        Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations--entanglement. As a consequence, a local description of interacting quantum systems is impossible as a rule. A unitarily evolving (isolated) quantum system generically develops extensive entanglement: the magnitude of the generated entanglement will increase without bounds with the effective Hilbert space dimension of the system. It is conceivable that coupling of the interacting subsystems to local dephasing environments will restrict the generation of entanglement to such extent that the evolving composite system may be considered as approximately disentangled. This conjecture is addressed in the context of some common models of a bipartite system with linear and nonlinear interactions and local coupling to dephasing environments. Analytical and numerical results obtained imply that the conjecture is generally false. Open dynamics of the quantum correlations is compared to the corresponding evolution of the classical correlations and a qualitative difference is found.

      13. Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

        NASA Astrophysics Data System (ADS)

        Benatti, Fabio; Gouba, Laure

        2015-11-01

        When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

      14. Modelling Systems of Classical/Quantum Identical Particles by Focusing on Algorithms

        ERIC Educational Resources Information Center

        Guastella, Ivan; Fazio, Claudio; Sperandeo-Mineo, Rosa Maria

        2012-01-01

        A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

      15. Spectrum of quantum transfer matrices via classical many-body systems

        NASA Astrophysics Data System (ADS)

        Gorsky, A.; Zabrodin, A.; Zotov, A.

        2014-01-01

        In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous n -invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N -body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N -dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the n Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.

      16. Classical and quantum theories of proton disorder in hexagonal water ice

        NASA Astrophysics Data System (ADS)

        Benton, Owen; Sikora, Olga; Shannon, Nic

        2016-03-01

        It has been known since the pioneering work of Bernal, Fowler, and Pauling that common, hexagonal (Ih) water ice is the archetype of a frustrated material: a proton-bonded network in which protons satisfy strong local constraints (the "ice rules") but do not order. While this proton disorder is well established, there is now a growing body of evidence that quantum effects may also have a role to play in the physics of ice at low temperatures. In this paper, we use a combination of numerical and analytic techniques to explore the nature of proton correlations in both classical and quantum models of ice Ih. In the case of classical ice Ih, we find that the ice rules have two, distinct, consequences for scattering experiments: singular "pinch points," reflecting a zero-divergence condition on the uniform polarization of the crystal, and broad, asymmetric features, coming from its staggered polarization. In the case of the quantum model, we find that the collective quantum tunneling of groups of protons can convert states obeying the ice rules into a quantum liquid, whose excitations are birefringent, emergent photons. We make explicit predictions for scattering experiments on both classical and quantum ice Ih, and show how the quantum theory can explain the "wings" of incoherent inelastic scattering observed in recent neutron scattering experiments [Bove et al., Phys. Rev. Lett. 103, 165901 (2009), 10.1103/PhysRevLett.103.165901]. These results raise the intriguing possibility that the protons in ice Ih could form a quantum liquid at low temperatures, in which protons are not merely disordered, but continually fluctuate between different configurations obeying the ice rules.

      17. Equivalence between classical and quantum dynamics. Neutral kaons and electric circuits

        SciTech Connect

        Caruso, M. Fanchiotti, H.; Canal, C.A. Garcia

        2011-10-15

        An equivalence between the Schroedinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant {epsilon} parameter that measures CP violation in the kaon system is completely determined in terms of network parameters. - Highlights: > We provide a formal equivalence between classical and quantum dynamics. > We make use of the decomplexification concept. > Neutral kaon systems can be represented by electric circuits. > CP symmetry violation can be taken into account by non-reciprocity. > Non-reciprocity is represented by gyrators.

      18. Classical and quantum reflection of bright matter-wave solitons

        NASA Astrophysics Data System (ADS)

        Marchant, Anna; Billam, Thomas; Yu, Manfred; Rakonjac, Ana; Helm, John; Weiss, Christoph; Polo, Juan; Gardiner, Simon; Cornish, Simon

        2016-05-01

        We report the controlled formation of a bright matter-wave soliton from a Bose-Einstein condensate of 85 Rb. We demonstrate the reflection of the soliton from a broad repulsive Gaussian barrier and contrast this to the case of a repulsive condensate, in both cases finding excellent agreement with theoretical simulations using the 3D Gross-Pitaevskii equation. Using a tightly focussed red-detuned light sheet, we create a narrow attractive potential well, comparable in the narrow direction to the size of the soliton. Using a low incident velocity, we observe a splitting of the atomic wavepacket when it reaches the well, resulting in quantum reflection of ~ 25 % of the atoms. In addition, a smaller fraction of atoms (~ 10 %) become trapped at the well. These results pave the way for new experimental studies of bright matter-wave soliton dynamics to elucidate the wealth of existing theoretical work and to explore an array of potential applications such as the study of short-range atom-surface potentials.

      19. Classical and quantum dynamics on p-adic trees of ideas.

        PubMed

        Khrennikov, A

        2000-01-01

        We propose mathematical models of information processes of unconscious and conscious thinking (based on p-adic number representation of mental spaces). Unconscious thinking is described by classical cognitive mechanics (which generalizes Newton's mechanics). Conscious thinking is described by quantum cognitive mechanics (which generalizes the pilot wave model of quantum mechanics). The information state and motivation of a conscious cognitive system evolve under the action of classical information forces and a new quantum information force, namely, conscious force. Our model might provide mathematical foundations for some cognitive and psychological phenomena: collective conscious behavior, connection between physiological and mental processes in a biological organism, Freud's psychoanalysis, hypnotism, homeopathy. It may be used as the basis of a model of conscious evolution of life. PMID:10880858

      20. Hybrid quantum-classical Monte Carlo study of a molecule-based magnet

        NASA Astrophysics Data System (ADS)

        Henelius, P.; Fishman, R. S.

        2008-12-01

        Using a Monte Carlo (MC) method, we study an effective model for the Fe(II)Fe(III) bimetallic oxalates. Within a hybrid quantum-classical MC algorithm, the Heisenberg S=2 and S'=5/2 spins on the Fe(II) and Fe(III) sites are updated using a quantum MC loop while the Ising-type orbital angular momenta on the Fe(II) sites are updated using a single-spin classical MC flip. The effective field acting on the orbital angular momenta depends on the quantum state of the system. We find that the mean-field phase diagram for the model is surprisingly robust with respect to fluctuations. In particular, the region displaying two compensation points shifts and shrinks but remains finite.

      1. Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains.

        PubMed

        Ivanov, Dmitri A; Abanov, Alexander G

        2013-02-01

        We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the anisotropic spin-1/2 XY chain in a transverse magnetic field, we compute the full counting statistics of the magnetization and use it to classify quantum phases of the chain. The method, in this case, reproduces the previously known phase diagram. We also discuss the relation between our approach and the Lee-Yang theory of zeros of the partition function. PMID:23496467

      2. Quantum and classical control of single photon states via a mechanical resonator

        NASA Astrophysics Data System (ADS)

        Basiri-Esfahani, Sahar; Myers, Casey R.; Combes, Joshua; Milburn, G. J.

        2016-06-01

        Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor.

      3. Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and the butterfly network

        SciTech Connect

        Grudka, Andrzej; Horodecki, Pawel

        2010-06-15

        We analyze quantum network primitives which are entanglement breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channels and the quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. The present effects provide a qualitative borderline between superadditivities of bipartite and multipartite systems.

      4. Mixed semiclassical-classical propagators for the Wigner phase space representation.

        PubMed

        Koda, Shin-Ichi

        2016-04-21

        We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency. PMID:27389210

      5. Mixed semiclassical-classical propagators for the Wigner phase space representation

        NASA Astrophysics Data System (ADS)

        Koda, Shin-ichi

        2016-04-01

        We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

      6. Quantum backreaction through the Bohmian particle.

        PubMed

        Prezhdo, O V; Brooksby, C

        2001-04-01

        A novel solution to the quantum backreaction problem in a mixed quantum-classical simulation is provided using the Bohmian interpretation of quantum mechanics. The Bohmian backreaction is unique, computationally simple, features reaction channel branching, and easily gives the full classical limit. The Bohmian quantum-classical method is illustrated by application to a model of O2 interacting with a Pt surface.

      7. Classicalization of nonclassical quantum states in loss and noise: Some no-go theorems

        NASA Astrophysics Data System (ADS)

        Yuen, Horace P.; Nair, Ranjith

        2009-08-01

        The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical no-go theorem is enunciated that rules out the possibility of significant advantage of nonclassical over classical states. The recent work on quantum illumination is discussed as an example of our no-go approach.

      8. Proposing new experiments to test the quantum-to-classical transition

        NASA Astrophysics Data System (ADS)

        Bahrami, M.; Bassi, A.

        2015-07-01

        An open problem in modern physics is why microscopic quantum objects can be at two places at once (i.e. a superposed quantum state) while macroscpoic classical object never show such a behaviour. Collapse models provides a quantitative answer for this problem and explain how macroscopic classical world emerges out of microscopic quantum world. A universal noise field is postulated in collapse models, inducing appropriate Brownian- motion corrections to standard quantum dynamics. The strength of collapse-driven Brownian fluctuations depend on: (i) the parameters characterizing the system (e.g., mass, size, density), and (ii) two phenomenological parameters defining the statistical properties of the collapse noise. The collapse-driven Brownian motion works such that microscopic systems behave quantum mechanically, while macroscopic objects are classical. At the intermediate mesocopic scale, collapse models predict deviations from standard quantum predictions. This issue has been subject of experimental tests. All experiments to date have been at the scales where collapse effects are negligible for all practical purposes. However, recent experimental progress in revealing quantum features of larger objects, increases the hope for testing at unprecedented scales where collapse models can be falsified. Current experiments are mainly focused on the preparation of macroscopic systems in a spatial quantum superposition state. The collapse effects would then manifest as loss of visibility in the observed inference pattern. However, one needs a quantum interference with single particles of mass ∼ 1010amu for a decisive test of collapse models. Creating such massive superpositionsis quite challenging, and beyond currectstate-of-the-art. Quite recently, an alternative approach has been proposed where the collapse manifests in the fluctuating properties of light interacting with the quantum system. The great advantage of this new approach is that here there is no need for the

      9. Quantum-holographic and classical Hopfield-like associative nnets: implications for modeling two cognitive modes of consciousness

        NASA Astrophysics Data System (ADS)

        Rakovic, D.; Dugic, M.

        2005-05-01

        Quantum bases of consciousness are considered with psychosomatic implications of three front lines of psychosomatic medicine (hesychastic spirituality, holistic Eastern medicine, and symptomatic Western medicine), as well as cognitive implications of two modes of individual consciousness (quantum-coherent transitional and altered states, and classically reduced normal states) alongside with conditions of transformations of one mode into another (considering consciousness quantum-coherence/classical-decoherence acupuncture system/nervous system interaction, direct and reverse, with and without threshold limits, respectively) - by using theoretical methods of associative neural networks and quantum neural holography combined with quantum decoherence theory.

      10. A unified approach to quantum and classical TTW systems based on factorizations

        SciTech Connect

        Celeghini, E.; Kuru, Ş.; Negro, J.; Olmo, M.A. del

        2013-05-15

        A unifying method based on factorization properties is introduced for finding symmetries of quantum and classical superintegrable systems using the example of the Tremblay–Turbiner–Winternitz (TTW) model. It is shown that the symmetries of the quantum system can be implemented in a natural way to its classical version. Besides, by this procedure we get also other type of constants of motion depending explicitly on time that allow to find directly the motion of the system whose corresponding trajectories coincide with those obtained previously by using its symmetries. -- Highlights: ► A unified method is given to find symmetries of classical and quantum systems. ► Ladder–shift operators and functions have analog expressions and relations. ► This method is applied to the TTW system to obtain its symmetries. ► For the classical cases a set of time dependent constants of motion are obtained. ► They allow us to find directly the motion and trajectories.

      11. Classical and quantum dynamics of a periodically driven particle in a triangular well

        SciTech Connect

        Flatte, M.E.; Holthaus, M.

        1996-01-01

        We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits subharmonic resonances, the corresponding Floquet states maintain the driving field{close_quote}s periodicity through dynamical tunneling. This principle applies both to Floquet states associated with classical invariant vortex tubes surrounding stable, elliptic periodic orbits and to Floquet states that are associated with unstable, hyperbolic periodic orbits. The triangular well model also poses a yet unsolved mathematical problem, related to perturbation theory for systems with a dense pure point spectrum. The present approximate analytical and numerical results indicate that quantum tunneling between different resonance zones is of crucial importance for the question whether the driven triangular well has a dense point or an absolutely continuous quasienergy spectrum, or whether there is a transition from the one to the other. Copyright {copyright} 1996 Academic Press, Inc.

      12. Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses

        NASA Astrophysics Data System (ADS)

        Figueira de Morisson Faria, C.; Liu, X.; Sanpera, A.; Lewenstein, M.

        2004-10-01

        We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of “quantum orbits,” which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymmetric electron momentum distributions, which strongly depend on the absolute phase, i.e., on the phase difference between the pulse envelope and its carrier frequency. Around a particular value of this parameter, the distributions shift from the region of positive to that of negative momenta, or vice versa, in a radical fashion. This behavior is investigated in detail for several driving-field parameters, and provides a very efficient method for measuring the absolute phase. Both models yield very similar distributions, which share the same physical explanation. There exist, however, minor discrepancies due to the fact that, beyond the region for which electron-impact ionization is classically allowed, the yields from the quantum-mechanical computation decay exponentially, whereas their classical counterparts vanish.

      13. On the Hamilton-Jacobi method in classical and quantum nonconservative systems

        NASA Astrophysics Data System (ADS)

        Dutra, A. de Souza; Correa, R. A. C.; Moraes, P. H. R. S.

        2016-08-01

        In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature, and we extend these complete solutions to the quantum mechanical case. In addition, we obtain the solution of the quantum Hamilton-Jacobi equation for an electric charge in an oscillating pulsing magnetic field. We also argue that for the case where a charged particle is under the action of an oscillating magnetic field, one can apply nuclear magnetic resonance techniques in order to find experimental results regarding this problem. We obtain all results analytically, showing that the quantum Hamilton-Jacobi formalism is a powerful tool to describe quantum mechanics.

      14. The classical limit of quantum optics: not what it seems at first sight

        NASA Astrophysics Data System (ADS)

        Aharonov, Yakir; Botero, Alonso; Nussinov, Shmuel; Popescu, Sandu; Tollaksen, Jeff; Vaidman, Lev

        2013-09-01

        What light is and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has also been considered to be a very simple business. It is not so. As we show here the classical limit of quantum optics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects.

      15. Classical and Quantum Singularities of Levi-Civita Spacetimes with and without a Positive Cosmological Constant

        NASA Astrophysics Data System (ADS)

        Konkowski, Deborah; Reese, Cassidi; Helliwell, T. M.; Wieland, C.

        2004-05-01

        Levi-Civita spacetimes have classical naked singularities. They also have quantum singularities. Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is said to be quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint on a $C_{0}^{\\infty}$ domain in $L^{2}$, a Hilbert space of square integrable functions. Here we summarize how Weyl's limit point-limit circle criterion can be used to determine whether a wave operator is essentially self-adjoint and how this test can then be applied to scalar wave packets in Levi-Civita spacetimes with and without a cosmological constant to help elucidate the physical properties of these spacetimes.

      16. Classical geometry to quantum behavior correspondence in a virtual extra dimension

        SciTech Connect

        Dolce, Donatello

        2012-09-15

        In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) . Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology. - Highlights: Black-Right-Pointing-Pointer Quantum behavior is related to the intrinsic periodicity of isolated systems. Black-Right-Pointing-Pointer A periodic phenomenon can be parameterized by a virtual extra dimension. Black-Right-Pointing-Pointer KK modes are used to describe the quantum excitations. Black-Right-Pointing-Pointer 5D classical geometry encodes 4D quantum behavior. Black-Right-Pointing-Pointer Geometrodynamical description of AdS/QCD as modulation of space-time periodicity.

      17. Shortcuts to adiabaticity in classical and quantum processes for scale-invariant driving

        NASA Astrophysics Data System (ADS)

        Deffner, Sebastian; Jarzynski, Christopher; Del Campo, Adolfo

        2014-03-01

        All real physical processes in classical as well as in quantum devices operate in finite-time. For most applications, however, adiabatic, i.e. infinitely-slow processes, are more favorable, as these do not cause unwanted, parasitic excitations. A shortcut to adiabaticity is a driving protocol which reproduces in a short time the same final state that would result from an adiabatic process. A particular powerful technique to engineer such shortcuts is transitionless quantum driving by means of counterdiabatic fields. However, determining closed form expressions for the counterdiabatic field has generally proven to be a daunting task. In this paper, we introduce a novel approach, with which we find the explicit form of the counterdiabatic driving field in arbitrary scale-invariant dynamical processes, encompassing expansions and transport. Our approach originates in the formalism of generating functions, and unifies previous approaches independently developed for classical and quantum systems. We show how this new approach allows to design shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems. SD and CJ acknowledge support from the National Science Foundation (USA) under grant DMR-1206971. This research is further supported by the U.S Department of Energy through the LANL/LDRD Program and a LANL J. Robert Oppenheimer fellowship (AdC).

      18. Niels Bohr on the wave function and the classical/quantum divide

        NASA Astrophysics Data System (ADS)

        Zinkernagel, Henrik

        2016-02-01

        It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.

      19. Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology

        NASA Astrophysics Data System (ADS)

        Khodadi, M.; Nozari, K.; Vakili, B.

        2016-05-01

        Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and Bohmian interpretation of quantum cosmology.

      20. Classical and quantum dynamics of a perfect fluid scalar-metric cosmology

        NASA Astrophysics Data System (ADS)

        Vakili, Babak

        2010-05-01

        We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.

      1. Superposition of quantum and classical rotational motions in Sc2C2@C84 fullerite

        NASA Astrophysics Data System (ADS)

        Michel, K. H.; Verberck, B.; Hulman, M.; Kuzmany, H.; Krause, M.

        2007-02-01

        The superposition of the quantum rotational motion (tunneling) of the encapsulated Sc2C2 complex with the classical rotational motion of the surrounding C84 molecule in a powder crystal of Sc2C2@C84 fullerite is investigated by theory. Since the quantum rotor is dragged along by the C84 molecule, any detection method which couples to the quantum rotor (in casu the C2 bond of the Sc2C2 complex) also probes the thermally excited classical motion (uniaxial rotational diffusion and stochastic meroaxial jumps) of the surrounding fullerene. The dynamic rotation-rotation response functions in frequency space are obtained as convolutions of quantum and classical dynamic correlation functions. The corresponding Raman scattering laws are derived, and the overall shape of the spectra and the width of the resonance lines are studied as functions of temperature. The results of the theory are confronted with experimental low-frequency Raman spectra on powder crystals of Sc2C2@C84 [M. Krause et al., Phys. Rev. Lett. 93, 137403 (2004)]. The agreement of theory with experiment is very satisfactory in a broad temperature range.

      2. Real-time quantum trajectories for classically allowed dynamics in strong laser fields

        NASA Astrophysics Data System (ADS)

        Plimak, L. I.; Ivanov, Misha Yu.

        2015-10-01

        Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here, we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit ?. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wave packet in momentum space. This way, if the electronic wave packet produced by optical tunnelling in strong infrared fields is localised both in coordinate and momentum, its motion after tunnelling ipso facto cannot be described with purely classical trajectories - in contrast to popular models in the literature.

      3. Exact, E = 0, classical and quantum solutions for general power-law oscillators

        NASA Technical Reports Server (NTRS)

        Nieto, Michael Martin; Daboul, Jamil

        1995-01-01

        For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

      4. Exact, E = 0, classical and quantum solutions for general power-law oscillators

        SciTech Connect

        Nieto, M.M.; Daboul, J.

        1994-07-01

        For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.

      5. Ice and water droplets on graphite: A comparison of quantum and classical simulations

        SciTech Connect

        Ramírez, Rafael; Singh, Jayant K.; Müller-Plathe, Florian; Böhm, Michael C.

        2014-11-28

        Ice and water droplets on graphite have been studied by quantum path integral and classical molecular dynamics simulations. The point-charge q-TIP4P/F potential was used to model the interaction between flexible water molecules, while the water-graphite interaction was described by a Lennard-Jones potential previously used to reproduce the macroscopic contact angle of water droplets on graphite. Several energetic and structural properties of water droplets with sizes between 10{sup 2} and 10{sup 3} molecules were analyzed in a temperature interval of 50–350 K. The vibrational density of states of crystalline and amorphous ice drops was correlated to the one of ice Ih to assess the influence of the droplet interface and molecular disorder on the vibrational properties. The average distance of covalent OH bonds is found 0.01 Å larger in the quantum limit than in the classical one. The OO distances are elongated by 0.03 Å in the quantum simulations at 50 K. Bond distance fluctuations are large as a consequence of the zero-point vibrations. The analysis of the H-bond network shows that the liquid droplet is more structured in the classical limit than in the quantum case. The average kinetic and potential energy of the ice and water droplets on graphite has been compared with the values of ice Ih and liquid water as a function of temperature. The droplet kinetic energy shows a temperature dependence similar to the one of liquid water, without apparent discontinuity at temperatures where the droplet is solid. However, the droplet potential energy becomes significantly larger than the one of ice or water at the same temperature. In the quantum limit, the ice droplet is more expanded than in a classical description. Liquid droplets display identical density profiles and liquid-vapor interfaces in the quantum and classical limits. The value of the contact angle is not influenced by quantum effects. Contact angles of droplets decrease as the size of the water droplet

      6. Light-wave mixing and scattering with quantum gases

        NASA Astrophysics Data System (ADS)

        Deng, L.; Hagley, E. W.; Zhu, C. J.

        2015-03-01

        We show that optical processes originating from elementary excitations with dominant collective atomic recoil motion in a quantum gas can profoundly change many nonlinear optical processes routinely observed in a normal gas. Not only multi-photon wave mixing processes all become stimulated Raman or hyper-Raman in nature but the usual forward wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor. On the other hand, in the backward direction the Bogoliubov dispersion automatically compensates the optical- wave phase mismatch, resulting in efficient backward light field generation that usually is not supported in normal gases.

      7. Ideal Negative Measurements in Quantum Walks Disprove Theories Based on Classical Trajectories

        NASA Astrophysics Data System (ADS)

        Robens, Carsten; Alt, Wolfgang; Meschede, Dieter; Emary, Clive; Alberti, Andrea

        2015-01-01

        We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6 σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom's position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.

      8. Inferring the statistical interpretation of quantum mechanics from the classical limit

        PubMed

        Gottfried

        2000-06-01

        It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrodinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrodinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.

      9. The classical trigonometric r-matrix for the quantum-deformed Hubbard chain

        NASA Astrophysics Data System (ADS)

        Beisert, Niklas

        2011-07-01

        The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra \\mathfrak {gl}(2|2). Here we investigate the quantum deformation of the Hubbard model in the classical limit. This leads to a novel classical r-matrix of trigonometric kind. We derive the corresponding one-parameter family of Lie bialgebras as a deformation of the affine \\mathfrak {gl}(2|2) Kac-Moody superalgebra. In particular, we discuss the affine extension as well as discrete symmetries, and we scan for simpler limiting cases, such as the rational r-matrix for the undeformed Hubbard model.

      10. Equivalence between classical and quantum dynamics. Neutral kaons and electric circuits

        NASA Astrophysics Data System (ADS)

        Caruso, M.; Fanchiotti, H.; Canal, C. A. Garcia

        2011-10-01

        An equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant ɛ parameter that measures CP violation in the kaon system is completely determined in terms of network parameters.

      11. Classical universe emerging from quantum cosmology without horizon and flatness problems

        NASA Astrophysics Data System (ADS)

        Fathi, M.; Jalalzadeh, S.; Moniz, P. V.

        2016-10-01

        We apply the complex de Broglie-Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007), Gozzi (Phys Lett B 165: 351, 1985), Bhalla et al. (Am J Phys 65: 1187, 1997) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems.

      12. Coexistence of classical and quantum plasmonics in large plasmonic structures with subnanometer gaps

        SciTech Connect

        Kadkhodazadeh, Shima; Wagner, Jakob B.; Kneipp, Harald; Kneipp, Katrin

        2013-08-19

        Large metal nanostructures with subnanometer interparticle separations (gaps) can provide extremely high local fields and are of particular interest in surface enhanced spectroscopy, as well as for basic understanding of plasmonics. In this experimental electron energy loss study, we monitor the transition of plasmonic dimers from a classical to a quantum system by decreasing gaps to dimensions when tunneling occurs and a conductive nanobridge evolves. Our studies show that silver dimers with atomic scale gaps can exhibit a regime, in which charge transfer plasmon modes, as a hallmark of a quantum nature, and “classical” bright and dark dipolar plasmon modes can be seen simultaneously.

      13. Probing the quantumness of channels with mixed states

        SciTech Connect

        Haeseler, Hauke; Luetkenhaus, Norbert

        2009-10-15

        We present an alternative approach to the derivation of benchmarks for quantum channels, such as memory or teleportation channels. Using the concept of effective entanglement and the verification thereof, a testing procedure is derived which demands very few experimental resources. The procedure is generalized by allowing for mixed test states. By constructing optimized measure and reprepare channels, the benchmarks are found to be very tight in the considered experimental regimes.

      14. Mixed convolved action for classical and fractional-derivative dissipative dynamical systems.

        PubMed

        Dargush, G F

        2012-12-01

        The principle of mixed convolved action provides a new rigorous weak variational formalism for a broad range of initial value problems in mathematical physics and mechanics. Here, the focus is initially on classical single-degree-of-freedom oscillators incorporating either Kelvin-Voigt or Maxwell dissipative elements and then, subsequently, on systems that utilize fractional-derivative constitutive models. In each case, an appropriate mixed convolved action is formulated, and a corresponding weak form is discretized in time using temporal shape functions to produce an algorithm suitable for numerical solution. Several examples are considered to validate the mixed convolved action principles and to investigate the performance of the numerical algorithms. For undamped systems, the algorithm is found to be symplectic and unconditionally stable with respect to the time step. In the case of dissipative systems, the approach is shown to be robust and to be accurate with good convergence characteristics for both classical and fractional-derivative based models. As part of the derivations, some interesting results in the calculus of Caputo fractional derivatives also are presented.

      15. Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures

        NASA Astrophysics Data System (ADS)

        Li, Xin-Zheng; Walker, Brent; Probert, Matthew I. J.; Pickard, Chris J.; Needs, Richard J.; Michaelides, Angelos

        2013-02-01

        A combination of state-of-the-art theoretical methods has been used to obtain an atomic-level picture of classical and quantum ordering of protons in cold high-pressure solid hydrogen. We focus mostly on phases II and III of hydrogen, exploring the effects of quantum nuclear motion on certain features of these phases (through a number of ab initio path integral molecular dynamics (PIMD) simulations at particular points on the phase diagram). We also examine the importance of van der Waals forces in this system by performing calculations using the optB88-vdW density functional, which accounts for non-local correlations. Our calculations reveal that the transition between phases I and II is strongly quantum in nature, resulting from a competition between anisotropic inter-molecular interactions that restrict molecular rotation and thermal plus quantum fluctuations of the nuclear positions that facilitate it. The transition from phase II to III is more classical because quantum nuclear motion plays only a secondary role and the transition is determined primarily by the underlying potential energy surface. A structure of P21/c symmetry with 24 atoms in the primitive unit cell is found to be stable when anharmonic quantum nuclear vibrational motion is included at finite temperatures using the PIMD method. This structure gives a good account of the infra-red and Raman vibron frequencies of phase II. We find additional support for a C2/c structure as a strong candidate for phase III, since it remains transparent up to 300 GPa, even when quantum nuclear effects are included. Finally, we find that accounting for van der Waals forces improves the agreement between experiment and theory for the parts of the phase diagram considered, when compared to previous work which employed the widely-used Perdew-Burke-Ernzerhof exchange-correlation functional.

      16. Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures.

        PubMed

        Li, Xin-Zheng; Walker, Brent; Probert, Matthew I J; Pickard, Chris J; Needs, Richard J; Michaelides, Angelos

        2013-02-27

        A combination of state-of-the-art theoretical methods has been used to obtain an atomic-level picture of classical and quantum ordering of protons in cold high-pressure solid hydrogen. We focus mostly on phases II and III of hydrogen, exploring the effects of quantum nuclear motion on certain features of these phases (through a number of ab initio path integral molecular dynamics (PIMD) simulations at particular points on the phase diagram). We also examine the importance of van der Waals forces in this system by performing calculations using the optB88-vdW density functional, which accounts for non-local correlations. Our calculations reveal that the transition between phases I and II is strongly quantum in nature, resulting from a competition between anisotropic inter-molecular interactions that restrict molecular rotation and thermal plus quantum fluctuations of the nuclear positions that facilitate it. The transition from phase II to III is more classical because quantum nuclear motion plays only a secondary role and the transition is determined primarily by the underlying potential energy surface. A structure of P2(1)/c symmetry with 24 atoms in the primitive unit cell is found to be stable when anharmonic quantum nuclear vibrational motion is included at finite temperatures using the PIMD method. This structure gives a good account of the infra-red and Raman vibron frequencies of phase II. We find additional support for a C2/c structure as a strong candidate for phase III, since it remains transparent up to 300 GPa, even when quantum nuclear effects are included. Finally, we find that accounting for van der Waals forces improves the agreement between experiment and theory for the parts of the phase diagram considered, when compared to previous work which employed the widely-used Perdew-Burke-Ernzerhof exchange-correlation functional.

      17. Libra: An open-Source "methodology discovery" library for quantum and classical dynamics simulations.

        PubMed

        Akimov, Alexey V

        2016-06-30

        The "methodology discovery" library for quantum and classical dynamics simulations is presented. One of the major foci of the code is on nonadiabatic molecular dynamics simulations with model and atomistic Hamiltonians treated on the same footing. The essential aspects of the methodology, design philosophy, and implementation are discussed. The code capabilities are demonstrated on a number of model and atomistic test cases. It is demonstrated how the library can be used to study methodologies for quantum and classical dynamics, as well as a tool for performing detailed atomistic studies of nonadiabatic processes in molecular systems. The source code and additional information are available on the Web at http://www.acsu.buffalo.edu/~alexeyak/libra/index.html. © 2016 Wiley Periodicals, Inc. PMID:27016373

      18. Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving

        NASA Astrophysics Data System (ADS)

        Deffner, Sebastian; Jarzynski, Christopher; del Campo, Adolfo

        2014-04-01

        A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe, for instance, expansion and transport. To this end, we use the formalism of generating functions and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, nonlinear, and many-body systems.

      19. Projected equations of motion approach to hybrid quantum/classical dynamics in dielectric-metal composites

        NASA Astrophysics Data System (ADS)

        McMillan, Ryan J.; Stella, Lorenzo; Grüning, Myrta

        2016-09-01

        We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically while retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM), and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.

      20. Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

        SciTech Connect

        Santos, G.; Tonel, A.; Foerster, A.; Links, J.

        2006-02-15

        We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.