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Sample records for mixed quantum classical

  1. Mixed quantum classical simulations of excitons in peptide helices.

    PubMed

    Goj, Anne; Bittner, Eric R

    2011-05-28

    We use mixed classical/quantum simulations to study the time dependence of an excitation of a C=O vibration on a 3-10 helix of α-aminoisobutyric acid, a system which represents a test case for the formation of self-trapped vibrational excitation states on protein helices. Due to the inherent disorder in the system caused by the finite temperature and fluctuations in hydrogen bonding, the excitation tunnels randomly among C=O sites along the helix. Quantum forces are insufficient to establish a coherent relationship between the location of the excitation and the contraction of hydrogen bonds around this site. Our simulations indicate that the excitation frequently becomes localized on the end of the helix due to the defect in helical structure caused by unwinding. Our results generally do not support the existence of Davydov type solitons in biological helix systems under physiological conditions. © 2011 American Institute of Physics

  2. Mixed quantum-classical Liouville molecular dynamics without momentum jump

    NASA Astrophysics Data System (ADS)

    Ando, Koji; Santer, Mark

    2003-06-01

    An alternative Liouville formulation of mixed quantum-classical dynamics outlined recently [K. Ando, Chem. Phys. Lett. 360, 240 (2002)] is expanded in detail by taking an explicit account of the parametric dependence of the electronic (adiabatic) basis on the nuclear coordinates. As a consequence of the different operational order of the partial Wigner transformation for the nuclear coordinates and the calculation of the matrix elements in the adiabatic electronic basis, the present formula differs from the previously proposed one, slightly in the appearance but significantly in the treatment of nonadiabatic transitions in the trajectory implementation in that the former does not contain the "off-diagonal Hellmann-Feynman forces" representing the so-called "momentum-jump" associated with the nonadiabatic transitions. Because of this, the present formula is free from the numerical instability intrinsically coming from the momentum-jump operation at around the classical turning points of the nuclear motion. It is also shown that the density matrices from the two approaches coincide when the electronic basis is independent of the nuclear coordinates (R), and hence the momentum-jump approximation stems from the R-dependence of the adiabatic electronic basis. Improved stability and comparable to better reproduction of the quantum reference calculations are demonstrated by applications to one and three dimensional spin-boson models and a two-state three-mode model of the S2→S1 internal conversion of pyrazine. Also discussed is the importance of electronic coherence for the proper treatment of nonadiabatic transition rates which is naturally described by the Liouville methods compared to the conventional independent trajectory approaches.

  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. 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.

  5. Computer simulation of mixed classical-quantum systems

    SciTech Connect

    Kalia, R.K.; Vashishta, P.

    1988-11-01

    We briefly review three important methods that are currently used in the simulation of mixed systems. Two of these techniques, path integral Monte Carlo or molecular dynamics and dynamical simulated annealing, have the limitation that they can only describe the structural properties in the ground state. The third so-called quantum molecular dynamics (QMD) method can provide not only the static properties but also the real-time dynamics of a quantum particle at finite temperatures. 10 refs.

  6. Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method.

    PubMed

    Kananenka, Alexei A; Hsieh, Chang-Yu; Cao, Jianshu; Geva, Eitan

    2016-12-01

    In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. Exact and asymptotic solutions of the mixed quantum-classical Liouville equation

    NASA Astrophysics Data System (ADS)

    Wan, Chun-Cheng; Schofield, Jeremy

    2000-03-01

    In this article, an exact surface-hopping procedure and an approximate asymptotic method for performing molecular dynamics based on a mixed quantum-classical Liouville equation [J. Chem. Phys. 110, 8919 (1999)] for partially Wigner transformed dynamical variables of a coupled quantum subsystem and classical bath are elaborated. The methods are based upon writing the equations of motion in a basis set in which quantum transitions do not alter the classical trajectory, and therefore avoid ad-hoc momentum jump approximations and are free of singular kernels associated with sampling momenta. Results obtained utilizing the new trajectory methods are presented for a model two-level system bilinearly coupled to a classical harmonic oscillator. These results are compared to results obtained from standard methods of performing mixed quantum-classical dynamics. The new methods perform well for the model system over a wide range of initial kinetic energies.

  12. A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism.

    PubMed

    Shi, Qiang; Geva, Eitan

    2004-08-22

    We show that the mixed quantum-classical Liouville equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a two-level system nonlinearly coupled to an anharmonic bath. (c) 2004 American Institute of Physics

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

    PubMed

    Hsieh, Chang-Yu; Kapral, Raymond

    2013-04-07

    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.

  14. Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantum-classical method.

    PubMed

    Gelman, David; Schwartz, Steven D

    2009-04-07

    The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantum-classical method. The method is suited to treat many-body systems consisting of a low dimensional quantum primary part coupled to a classical bath. The dynamics of the primary part is governed by the quantum corrected propagator, with the corrections defined in terms of matrix elements of zeroth order propagators. The corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The ability of the method to describe dynamics of multidimensional systems has been tested. The results obtained by the method have been compared to previous quantum simulations performed with the quasiadiabatic path integral method.

  15. Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantum-classical method

    NASA Astrophysics Data System (ADS)

    Gelman, David; Schwartz, Steven D.

    2009-04-01

    The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantum-classical method. The method is suited to treat many-body systems consisting of a low dimensional quantum primary part coupled to a classical bath. The dynamics of the primary part is governed by the quantum corrected propagator, with the corrections defined in terms of matrix elements of zeroth order propagators. The corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The ability of the method to describe dynamics of multidimensional systems has been tested. The results obtained by the method have been compared to previous quantum simulations performed with the quasiadiabatic path integral method.

  16. Calculating two-dimensional spectra with the mixed quantum-classical Ehrenfest method.

    PubMed

    van der Vegte, C P; Dijkstra, A G; Knoester, J; Jansen, T L C

    2013-07-25

    We present a mixed quantum-classical simulation approach to calculate two-dimensional spectra of coupled two-level electronic model systems. We include the change in potential energy of the classical system due to transitions in the quantum system using the Ehrenfest method. We study how this feedback of the quantum system on the classical system influences the shape of two-dimensional spectra. We show that the feedback leads to the expected Stokes shift of the energy levels in the quantum system. This subsequently leads to changes in the population transfer between quantum sites, which in turn influence the intensities of the peaks in two-dimensional spectra. The obtained spectra are compared with spectra calculated using the Hierarchical Equations of Motion method which is exact. While the spectra match perfectly for short waiting times, clear differences are found for longer waiting times. This is attributed to a violation of detailed balance between the quantum states in the Ehrenfest method. The energy of the total quantum-classical system however does obey a Boltzmann distribution, when coupled to a stochastic heat bath.

  17. Mixed Quantum-Classical Liouville Approach for Calculating Proton-Coupled Electron-Transfer Rate Constants.

    PubMed

    Shakib, Farnaz; Hanna, Gabriel

    2016-07-12

    In this work, we derive a general mixed quantum-classical formula for calculating thermal proton-coupled electron-transfer (PCET) rate constants, starting from the time integral of the quantum flux-flux correlation function. This formula allows for the direct simulation of PCET reaction dynamics via the mixed quantum-classical Liouville approach. Owing to the general nature of the derivation, this formula does not rely on any prior mechanistic assumptions and can be applied across a wide range of electronic and protonic coupling regimes. To test the validity of this formula, we applied it to a reduced model of a condensed-phase PCET reaction. Good agreement with the numerically exact rate constant is obtained, demonstrating the accuracy of our formalism. We believe that this approach constitutes a solid foundation for future investigations of the rates and mechanisms of a wide range of PCET reactions.

  18. 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.

  19. Can Quantized Vibrational Effects Be Obtained from Ehrenfest Mixed Quantum-Classical Dynamics?

    PubMed

    Goings, Joshua J; Lingerfelt, David B; Li, Xiaosong

    2016-12-15

    We explore the question of whether mean-field or "Ehrenfest" mixed quantum-classical dynamics is capable of capturing the quantized vibrational features in photoabsorption spectra that result from infrared and Raman-active vibrational transitions. We show that vibrational and electronic absorption spectra can indeed be obtained together within a single Ehrenfest simulation. Furthermore, the electronic transitions show new sidebands that are absent in electronic dynamics simulations with fixed nuclei. Inspection of the electronic sidebands reveals that the spacing corresponds to vibrational frequencies of totally symmetric vibrational modes of the ground electronic state. A simple derivation of the time-evolving dipole in the presence of external fields and vibrational motion shows the origin of these features, demonstrating that mixed quantum-classical Ehrenfest dynamics is capable of producing infrared, Raman, and electronic absorption spectra from a single simulation.

  20. A new trajectory branching approximation to propagate the mixed quantum-classical Liouville equation.

    PubMed

    Bai, Shuming; Xie, Weiwei; Shi, Qiang

    2014-10-02

    Starting from the mixed quantum-classical Liouville (MQCL) equation, we derive a new trajectory branching method as a modification to the conventional mean field approximation. In the new method, the mean field approximation is used to propagate the mixed quantum-classical dynamics for short times. When the mean field description becomes invalid, new trajectories are added in the simulation by branching the single trajectory into multiple ones. To achieve this, a new set of variables are defined to monitor the deviations of the dynamics on different potential energy surfaces from the reference mean field trajectory, and their equations of motion are derived from the MQCL equation based on the method of first moment expansion. The new method is tested on several one-dimensional two surface problems and is shown to correctly solve the problem of the mean field approximation in several cases.

  1. 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.

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

    PubMed

    Schubert, Alexander; Falvo, Cyril; Meier, Christoph

    2016-08-07

    We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking 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.

  3. Mixed Quantum/Classical Approach for Description of Molecular Collisions in Astrophysical Environments.

    PubMed

    Semenov, Alexander; Babikov, Dmitri

    2015-05-21

    An efficient and accurate mixed quantum/classical theory approach for computational treatment of inelastic scattering is extended to describe collision of an atom with a general asymmetric-top rotor polyatomic molecule. Quantum mechanics, employed to describe transitions between the internal states of the molecule, and classical mechanics, employed for description of scattering of the atom, are used in a self-consistent manner. Such calculations for rotational excitation of HCOOCH3 in collisions with He produce accurate results at scattering energies above 15 cm(-1), although resonances near threshold, below 5 cm(-1), cannot be reproduced. Importantly, the method remains computationally affordable at high scattering energies (here up to 1000 cm(-1)), which enables calculations for larger molecules and at higher collision energies than was possible previously with the standard full-quantum approach. Theoretical prediction of inelastic cross sections for a number of complex organic molecules observed in space becomes feasible using this new computational tool.

  4. Classical and Mixed Quantum-Classical Dynamics of Adsorbate-Surface Systems: Application to Non-Thermal Desorption

    NASA Astrophysics Data System (ADS)

    Dzegilenko, Fedor N.

    1995-01-01

    Both classical and mixed quantum-classical approaches have been used to study the non-thermal desorption of CO from a variety of model surfaces to which it is weakly adsorbed. In addition to three degrees of freedom for the CO adsorbate (bond stretching, physisorption, libration) which are treated quantum mechanically in the mixed method, a significant number of lattice degrees of freedom have been included using the generalized Langevin approximation. In the mixed method, two sets of equations for the quantum and classical subsystems (coupled via the Ehrenfest theorem) are solved self-consistently using the discrete variable representation method for the propagation of the quantum wave function. Non-thermal amounts of energy have been put into both the CO stretching and librational modes at t = 0. We find that for initial values of the stretching quantum number vstr = 0 -4 desorption does not take place at all within the simulation time unless there is also significant librational excitation. The detailed mechanism by which librational energy causes desorption is discussed. The role of the surface is also explored; we find that the probability of desorption is a non-monotonic function of the Debye frequency of the solid in the range 28-5000 cm^{-1}, and is larger for "non-rigid" lattices with low Debye frequencies in both of the methods. The classical results are explained in terms of resonances between low frequency libration and physisorption modes and high frequency phonon modes. For the combined method, two different mechanisms for desorption (due to lattice effects and due to symmetry properties of wave function) have been found and analyzed in detail. A comparative analysis of the two methods is presented and the limitations of the mixed scheme are discussed. An indirect mechanism for populating rapidly desorbing, highly excited levels of surface CO, based on intermolecular V to V,R energy exchange between the CO and vibrationally excited surface hydroxyl

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

    NASA Astrophysics Data System (ADS)

    Gelman, David; Schwartz, Steven D.

    2008-07-01

    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.

  6. 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.

  7. Fast Numerical Evaluation of Time-Derivative Nonadiabatic Couplings for Mixed Quantum-Classical Methods.

    PubMed

    Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F

    2015-11-05

    We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.

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

    NASA Astrophysics Data System (ADS)

    Giorgi, Gian Luca; Campbell, Steve

    2016-11-01

    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.

  9. 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.

  10. 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.

  11. Mixed Quantum-Classical Dynamics Using Collective Electronic Variables: A Better Alternative to Electronic Friction Theories.

    PubMed

    Ryabinkin, Ilya G; Izmaylov, Artur F

    2017-01-19

    An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely spaced electronic states. We propose a mixed quantum-classical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic block-diagonalization applied to the time-dependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with a simplified Ehrenfest approach and with a full-memory electronic friction model on a 1D "adatom + atomic chain" model. Our simulations demonstrate that collective-mode dynamics with only a few (two to three) electronic variables is robust and can describe a variety of situations: from a chemisorbed atom on an insulator to an atom on a metallic surface. Our molecular model also reveals that the friction approach is prone to unpredictable and catastrophic failures.

  12. 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.

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

    PubMed

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

    2014-04-07

    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(-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.

  14. Nonadiabatic mixed quantum-classical dynamic simulation of pi-stacked oligophenylenevinylenes.

    PubMed

    Sterpone, Fabio; Bedard-Hearn, Michael J; Rossky, Peter J

    2009-04-16

    We present results from the first nonadiabatic (NA), nonequilibrium mixed quantum-classical molecular dynamics simulations of pi-stacked oligophenylvinylene (OPV) chains with a quantum electronic Hamiltonian (Pariser-Parr-Pople with excited states given by configuration interaction) that goes beyond the tight-binding approximation. The chains pack approximately 3.6 A apart in the ground state at 300 K, and we discuss how thermal motions, chiefly a relative sliding motion along the oligomer backbone, affect the electronic structure. We assign the electronic absorption spectrum primarily to the S(0) --> S(2) transition as transitions from the ground state to S(1) and S(3) are particularly weak. After photoexcitation, the system rapidly decays via NA transitions to S(1) in under 150 fs. On S(1), the system relaxes as a bound exciton, localized on one chain that may hop between chains with a characteristic time between 300 and 800 fs. We find that the system does not make a rapid transition to the ground state because both the NA and radiative couplings between S(1) and S(0) are weak.

  15. Mixed quantum-classical studies of energy partitioning in unimolecular chemical reactions

    NASA Astrophysics Data System (ADS)

    Bladow, Landon Lowell

    A mixed quantum-classical reaction path Hamiltonian method is utilized to study the dynamics of unimolecular reactions. The method treats motion along the reaction path classically and treats the transverse vibrations quantum mechanically. The theory leads to equations that predict the disposai of the exit-channel potential energy to product translation and vibration. In addition, vibrational state distributions are obtained for the product normal modes. Vibrational excitation results from the curvature of the minimum energy reaction path. The method is applied to six unimolecular reactions: HF elimination from fluoroethane, 1,1-difluoroethane, 1,1-difluoroethene, and trifluoromethane; and HCl elimination from chloroethane and acetyl chloride. The minimum energy paths were calculated at either the MP2 or B3LYP level of theory. In all cases, the majority of the vibrational excitation of the products occurs in the HX fragment. The results are compared to experimental data and other theoretical results, where available. The best agreement between the experimental and calculated HX vibrational distributions is found for the halogenated ethanes, and the experimental deduction that the majority of the HX vibrational excitation arises from the potential energy release is supported. It is believed that the excess energy provided in experiments contributes to the poorer agreement between experiment and theory observed for HF elimination from 1,1-difluoroethene and trifluoromethane. An attempt is described to incorporate a treatment of the excess energy into the present method. However, the sign of the curvature coupling elements is then found to affect the dynamics. Overall, the method appears to be an efficient dynamical tool for modeling the disposal of the exit-channel potential energy in unimolecular reactions.

  16. Multidimensional spectra via the mixed quantum-classical Liouville method: signatures of nonequilibrium dynamics.

    PubMed

    Hanna, Gabriel; Geva, Eitan

    2009-07-09

    Multidimensional optical spectra are often expressed in terms of optical response functions. These optical response functions consist of contributions from a number of Liouville pathways that differ with respect to the chromophore's quantum state during the time intervals between light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals are dictated by potential energy surfaces that are explicitly dependent on the chromophore's quantum state. One therefore expects the system to hop between potential surfaces in a manner dictated by the Liouville pathways and the spectra to reflect the dynamics during the resulting nonequilibrium process. However, the approach commonly used to model spectra of complex condensed-phase systems is based on the ad hoc assumption that the photoinactive degrees of freedom undergo equilibrium dynamics on the potential surface that corresponds to the chromophore's ground state. In this paper, we formulate optical response in terms of mixed quantum-classical Liouville dynamics, which inherently accounts for the underlying nonequilibrium dynamics. It is shown that, when nonadiabatic transitions are neglected, the resulting formulation is equivalent to that obtained via the linearized semiclassical approximation. We demonstrate the feasibility and utility of the approach by using it to calculate the one- and two-dimensional infrared spectra of the hydrogen stretch of a moderately strong hydrogen-bonded complex dissolved in a dipolar liquid. The results are compared with previously reported spectra that were calculated within the framework of the standard equilibrium ground-state dynamical approach [ J. Phys. Chem. B 2008 , 112 , 12991. ], thereby shedding light on the spectral signatures of nonequilibrium dynamics in systems of this type.

  17. 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

  18. Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations

    NASA Astrophysics Data System (ADS)

    Gelman, David; Schwartz, Steven D.

    2010-05-01

    The recently developed quantum-classical method has been applied to the study of dissipative dynamics in multidimensional systems. The method is designed to treat many-body systems consisting of a low dimensional quantum part coupled to a classical bath. Assuming the approximate zeroth order evolution rule, the corrections to the quantum propagator are defined in terms of the total Hamiltonian and the zeroth order propagator. Then the corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary part is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on two model systems coupled to a harmonic bath: (i) an anharmonic (Morse) oscillator and (ii) a double-well potential. The simulations have been performed at zero temperature. The results have been compared to the exact quantum simulations using the surrogate Hamiltonian approach.

  19. 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).

  20. An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach.

    PubMed

    Shakib, Farnaz A; Hanna, Gabriel

    2014-07-28

    The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.

  1. An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach

    SciTech Connect

    Shakib, Farnaz A.; Hanna, Gabriel

    2014-07-28

    The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.

  2. Comparing classical and quantum equilibration

    NASA Astrophysics Data System (ADS)

    Malabarba, Artur S. L.; Farrelly, Terry; Short, Anthony J.

    2016-09-01

    By using a physically relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial state of the system is completely known (a pure state). This shows that quantum equilibration is a fundamental aspect of many quantum systems, while classical equilibration relies on experimental ignorance. When the state is not completely known (a mixed state), this framework also shows that quantum equilibration requires weaker conditions.

  3. Rate constants calculation with a simple mixed quantum/classical implementation of the flux-flux correlation function method.

    PubMed

    Palma, Juliana

    2009-03-28

    A simple mixed quantum/classical (mixed-Q/C) implementation of the flux-flux correlation function method has been applied to evaluate rate constants for a two-dimensional model system. The model consists of an Eckart barrier resembling the collinear H + H(2) reaction, linearly coupled to a harmonic oscillator. Results are presented for a broad range of parameters for temperatures between 140 and 300 K. It is found that the mixed-Q/C method gives fairly accurate results as long as the reaction does not involve too many recrossings. This suggests that the methodology could be extended to treat direct polyatomic reactions in gas phase.

  4. Nonequilibrium statistical mechanics of mixed quantum classical ensembles: application to noncontact atomic force microscopy.

    PubMed

    Kantorovich, L N

    2002-08-26

    Using the nonequilibrium statistical operator method, we suggest a new general method of treating dynamics of a combined system consisting of interacting classical and quantum parts. The method is illustrated on the tip dynamics in the noncontact atomic force microscopy (NC-AFM) where a macroscopic tip interacts with a quantum microscopic system (the surface and the nanotip). The derived general equation of motion for the tip and the Fokker-Planck equation, applicable even at low temperatures, contain memory effects and a friction term which should (at least partially) be responsible for the observed energy dissipation in NC-AFM experiments.

  5. Classical-Quantum Limits

    NASA Astrophysics Data System (ADS)

    Oliynyk, Todd A.

    2016-12-01

    We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multi-particle Schrödinger equations. The limit equations obtained by this procedure, which we refer to as the classical-quantum limit, govern the interaction between classical and quantum systems, and they possess many desirable properties that are inherited in the limit from the multi-particle quantum system. As an application, we use the classical-quantum limit equations to identify the source of the non-local signalling that is known to occur in the classical-quantum hybrid scheme of Hall and Reginatto. We also derive the first order correction to the classical-quantum limit equation to obtain a fully consistent first order approximation to the Schrödinger equation that should be accurate for modeling the interaction between particles of disparate mass in the regime where the particles with the larger masses are effectively classical.

  6. Mixed quantum-classical molecular dynamics simulation of vibrational relaxation of ions in an electrostatic field.

    PubMed

    Koutselos, Andreas D

    2006-12-28

    The vibrational relaxation of ions in low-density gases under the action of an electrostatic field is reproduced through a molecular dynamics simulation method. The vibration is treated though quantum mechanics and the remaining degrees of freedom are considered classical. The procedure is tested through comparison against analytic results for a two-dimensional quantum model and by studying energy exchange during binary ion-atom collisions. Finally, the method has been applied successfully to the calculation of the mobility and the vibrational relaxation rate of O2+ in Kr as a function of the mean collision energy using a model interaction potential that reproduces the potential minimum of a previously known ab initio potential surface. The calculation of the steady mean vibrational motion of the ions in (flow) drift tubes seems straightforward, though at the expense of large amounts of computer time.

  7. 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.

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

    PubMed

    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.

  9. On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations

    SciTech Connect

    Valleau, Stephanie; Aspuru-Guzik, Alan; Eisfeld, Alexander

    2012-12-14

    We investigate on the procedure of extracting a 'spectral density' from mixed QM/MM calculations and employing it in open quantum systems models. In particular, we study the connection between the energy gap correlation function extracted from ground state QM/MM and the bath spectral density used as input in open quantum system approaches. We introduce a simple model which can give intuition on when the ground state QM/MM propagation will give the correct energy gap. We also discuss the role of higher order correlators of the energy-gap fluctuations which can provide useful information on the bath. Further, various semiclassical corrections to the spectral density, are applied and investigated. Finally, we apply our considerations to the photosynthetic Fenna-Matthews-Olson complex. For this system, our results suggest the use of the Harmonic prefactor for the spectral density rather than the Standard one, which was employed in the simulations of the system carried out to date.

  10. Mixed quantum/classical investigation of the photodissociation of NH3(A) and a practical method for maintaining zero-point energy in classical trajectories.

    PubMed

    Bonhommeau, David; Truhlar, Donald G

    2008-07-07

    The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode nu(2) with n(2)=0,[ellipsis (horizontal)],6 quanta of vibration) in the A electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTUSD+trajectory projection onto ZPE orbit (TRAPZ) and FSTUSD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH(2) internal energy distributions obtained for n(2)=0 and n(2)>1, as observed in experiments. Distributions obtained for n(2)=1 present an intermediate behavior between distributions obtained for smaller and larger n(2) values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH(2) internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n(2)=0 and n(2)=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.

  11. Mixed quantum-classical reaction path dynamics of C2H5F --> C2H4 + HF.

    PubMed

    Stopera, Christopher J; Bladow, Landon L; Thweatt, W David; Page, Michael

    2008-11-20

    A mixed quantum-classical method for calculating product energy partitioning based on a reaction path Hamiltonian is presented and applied to HF elimination from fluoroethane. The goal is to describe the effect of the potential energy release on the product energies using a simple model of quantized transverse vibrational modes coupled to a classical reaction path via the path curvature. Calculations of the minimum energy path were done at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G** levels of theory, followed by energy-partitioning dynamics calculations. The results for the final HF vibrational state distribution were found to be in good qualitative agreement with both experimental studies and quasiclassical trajectory simulations.

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

    NASA Astrophysics Data System (ADS)

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

    2010-05-01

    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.

  13. Plasmon enhanced molecular absorption: A mixed quantum-classical description of supramolecular complexes attached to a metal nanoparticle

    NASA Astrophysics Data System (ADS)

    Megow, Jörg; May, Volkhard

    2014-01-01

    The application of a mixed quantum-classical methodology for an investigation of single pheophorbide-a molecules (Pheos) and respective supramolecular complexes is continued to effects caused by a nearby placed metal nanoparticle (MNP). Therefore, the classical simulation of the molecular nuclear degrees of freedom is combined with a uniform quantum description of the molecular electronic excitations coupled to those of the MNP. To account for the short MNP plasmon life time the quantum dynamics of the electronic degrees of freedom is formulated in the framework of a system-bath theory. Linear absorption spectra are calculated for a spherical 14 nm diameter Au-MNP decorated with isolated Pheos or with P16 complexes formed by 16 Pheos. The spectra are analyzed with respect to the molecular orientation at the MNP surface. While all studies on P16 only account for the Pheo Qy-transition we also present data on the MNP induced change of the single Pheo Qx-absorption.

  14. Classical correlation and quantum entanglement in the mixed-spin Ising-XY model with Dzyaloshinskii-Moriya interaction

    NASA Astrophysics Data System (ADS)

    Zad, Hamid Arian; Movahhedian, Hossein

    2017-05-01

    In the present work, initially, a mixed-three-spin (1/2,1,1/2) cell of a mixed-N-spin chain with Ising-XY model is introduced, for which pair spins (1,1/2) have Ising-type interaction and pair spins (1/2,1/2) have both XY-type and Dzyaloshinskii-Moriya (DM) interactions together. An external homogeneous magnetic field B is considered for the system in thermal equilibrium. Integer-spins have a single-ion anisotropy property with coefficient ζ. Then, we investigate the quantum entanglement between half-spins (1/2,1/2), by means of the concurrence. Classical correlation (CC) for this pair of spins is investigated as well as the concurrence and some interesting temperature, the magnetic field and the DM interaction properties are expressed. Moreover, single-ion anisotropy effects on the correlation between half-spins is verified. According to the verifications based on the communication channels category by Rossini, Giovannetti and Fazio [D. Rossini, V. Giovannetti and R. Fazio, Int. J. Quantum Inf. 5, 439 (2007)], we theoretically consider such tripartite spin model as an ideal quantum channel, then calculate its information transmission rate and express some differences in behavior between this suggested model and introduced simple models in the previous works (chains without spin integer and DM interaction) from information transferring protocol point of view.

  15. 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.

    PubMed

    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(-1), which is about 2.5 times faster than that in vacuum, 0.27 ps(-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.

  16. 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.

  17. 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

    2016-06-09

    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.

  18. Mixed quantum-classical molecular dynamics analysis of the molecular-level mechanisms of vibrational frequency shifts.

    PubMed

    Morales, Christine M; Thompson, Ward H

    2007-06-28

    A detailed analysis of the origins of vibrational frequency shifts of diatomic molecules (I2 and ICl) in a rare gas (Xe) liquid is presented. Specifically, vibrationally adiabatic mixed quantum-classical molecular dynamics simulations are used to obtain the instantaneous frequency shifts and correlate the shifts to solvent configurations. With this approach, important mechanistic questions are addressed, including the following: How many solvent atoms determine the frequency shift? What solvent atom configurations lead to blue shifts, and which lead to red shifts? What is the effect of solute asymmetry? The mechanistic analysis can be generally applied and should be useful in understanding what information is provided by infrared and Raman spectra about the environment of the probed vibrational mode.

  19. Perspective: Quantum or classical coherence?

    PubMed

    Miller, William H

    2012-06-07

    Some coherence effects in chemical dynamics are described correctly by classical mechanics, while others only appear in a quantum treatment--and when these are observed experimentally it is not always immediately obvious whether their origin is classical or quantum. Semiclassical theory provides a systematic way of adding quantum coherence to classical molecular dynamics and thus provides a useful way to distinguish between classical and quantum coherence. Several examples are discussed which illustrate both cases. Particularly interesting is the situation with electronically non-adiabatic processes, where sometimes whether the coherence effects are classical or quantum depends on what specific aspects of the process are observed.

  20. Quantum backreaction on classical dynamics

    NASA Astrophysics Data System (ADS)

    Vachaspati, Tanmay

    2017-06-01

    Motivated by various systems in which quantum effects occur in classical backgrounds, we consider the dynamics of a classical particle as described by a coherent state that is coupled to a quantum bath via biquadratic interactions. We evaluate the resulting quantum dissipation of the motion of the classical particle. We also find classical initial conditions for the bath that effectively lead to the same dissipation as that due to quantum effects, possibly providing a way to approximately account for quantum backreaction within a classical analysis.

  1. Calculation of absorption spectra involving multiple excited states: approximate methods based on the mixed quantum classical Liouville equation.

    PubMed

    Bai, Shuming; Xie, Weiwei; Zhu, Lili; Shi, Qiang

    2014-02-28

    We investigate the calculation of absorption spectra based on the mixed quantum classical Liouville equation (MQCL) methods. It has been shown previously that, for a single excited state, the averaged classical dynamics approach to calculate the linear and nonlinear spectroscopy can be derived using the MQCL formalism. This work focuses on problems involving multiple coupled excited state surfaces, such as in molecular aggregates and in the cases of coupled electronic states. A new equation of motion to calculate the dipole-dipole correlation functions within the MQCL formalism is first presented. Two approximate methods are then proposed to solve the resulted equations of motion. The first approximation results in a mean field approach, where the nuclear dynamics is governed by averaged forces depending on the instantaneous electronic states. A modification to the mean field approach based on first order moment expansion is also proposed. Numerical examples including calculation of the absorption spectra of Frenkel exciton models of molecular aggregates, and the pyrazine molecule are presented.

  2. Calculation of absorption spectra involving multiple excited states: Approximate methods based on the mixed quantum classical Liouville equation

    SciTech Connect

    Bai, Shuming; Xie, Weiwei; Zhu, Lili; Shi, Qiang

    2014-02-28

    We investigate the calculation of absorption spectra based on the mixed quantum classical Liouville equation (MQCL) methods. It has been shown previously that, for a single excited state, the averaged classical dynamics approach to calculate the linear and nonlinear spectroscopy can be derived using the MQCL formalism. This work focuses on problems involving multiple coupled excited state surfaces, such as in molecular aggregates and in the cases of coupled electronic states. A new equation of motion to calculate the dipole-dipole correlation functions within the MQCL formalism is first presented. Two approximate methods are then proposed to solve the resulted equations of motion. The first approximation results in a mean field approach, where the nuclear dynamics is governed by averaged forces depending on the instantaneous electronic states. A modification to the mean field approach based on first order moment expansion is also proposed. Numerical examples including calculation of the absorption spectra of Frenkel exciton models of molecular aggregates, and the pyrazine molecule are presented.

  3. Self-Consistent Filtering Scheme for Efficient Calculations of Observables via the Mixed Quantum-Classical Liouville Approach.

    PubMed

    Dell'Angelo, David; Hanna, Gabriel

    2016-02-09

    Over the past decade, several algorithms have been developed for calculating observables using mixed quantum-classical Liouville dynamics, which differ in how accurately they solve the quantum-classical Liouville equation (QCLE). One of these algorithms, known as sequential short-time propagation (SSTP), is a surface-hopping algorithm that solves the QCLE almost exactly, but obtaining converged values of observables requires very large ensembles of trajectories due to the rapidly growing statistical errors inherent to this algorithm. To reduce the ensemble sizes, two filtering schemes (viz., observable cutting and transition filtering) have been previously developed and effectively applied to both simple and complex models. However, these schemes are either ad hoc in nature or require significant trial and error for them to work as intended. In this study, we present a self-consistent scheme, which, in combination with a soundly motivated probability function used for the Monte Carlo sampling of the nonadiabatic transitions, avoids the ad hoc observable cutting and reduces the amount of trial and error required for the transition filtering to work. This scheme is tested on the spin-boson model, in the weak, intermediate, and strong coupling regimes. Our transition filtered results obtained using a newly proposed probability function, which favors the sampling of nonadiabatic transitions with small energy gaps, show a significant improvement in accuracy and efficiency for all coupling regimes over the results obtained using observable cutting and the original implementation of transition filtering and are comparable to those obtained using the combination of these two techniques. It is therefore expected that this novel scheme will substantially reduce ensemble sizes and simplify the computation of observables in more complex systems.

  4. 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

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

    PubMed

    Fujii, Keisuke; Tamate, Shuhei

    2016-05-18

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

  6. 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.

  7. Classical versus quantum gravity

    SciTech Connect

    Drechsler, W. )

    1993-02-01

    Is Einstein's metric theory of gravitation to be quantized to yield a complete and logically consistent picture of the geometry of the real world in the presence of quantized material sources To answer this question, we give arguments that there is a consistent way to extent general relativity to small distances by incorporating further geometric quantities at the level of the connection into the theory and introducing corresponding field equations for their determination, allowing thereby the metric and the Levi-Civita connection to remain classical quantities. The dualism between matter and geometry is extended to quantized fields with the help of Hilbert bundle H raised over a Riemann-Cartan spacetime. Quantized subnuclear matter fields (generalized quantum mechanical wave functions) are sections on H which determine generalized bilinear currents acting as source currents for the bundle geometry at small distances. The established dualism between matter and the underling bundle geometry contains general relatively as a classical part.

  8. Quantum dynamics in open quantum-classical systems.

    PubMed

    Kapral, Raymond

    2015-02-25

    Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

  9. Photodynamics and time-resolved fluorescence of azobenzene in solution: a mixed quantum-classical simulation.

    PubMed

    Cusati, Teresa; Granucci, Giovanni; Persico, Maurizio

    2011-04-06

    We have simulated the photodynamics of azobenzene by means of the Surface Hopping method. We have considered both the trans → cis and the cis → trans processes, caused by excitation in the n → π* band (S(1) state). To bring out the solvent effects on the excited state dynamics, we have run simulations in four different environments: in vacuo, in n-hexane, in methanol, and in ethylene glycol. Our simulations reproduce very well the measured quantum yields and the time dependence of the intensity and anisotropy of the transient fluorescence. Both the photoisomerization and the S(1) → S(0) internal conversion require the torsion of the N═N double bond, but the N-C bond rotations and the NNC bending vibrations also play a role. In the trans → cis photoconversion the N═N torsional motion and the excited state decay are delayed by increasing the solvent viscosity, while the cis → trans processes are less affected. The analysis of the simulation results allows the experimental observations to be explained in detail, and in particular the counterintuitive increase of the trans → cis quantum yield with viscosity, as well as the relationship between the excited state dynamics and the solvent effects on the fluorescence lifetimes and depolarization.

  10. 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.

  11. 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.

  12. Solvent fluctuations drive the hole transfer in DNA: a mixed quantum-classical study.

    PubMed

    Kubar, Tomás; Kleinekathöfer, Ulrich; Elstner, Marcus

    2009-10-01

    We studied the hole transfer across adenine bridges in double-stranded DNA by means of a multiscale approach, propagating the hole in the framework of time-dependent DFT coupled to classical molecular dynamics simulation using a QM/MM scheme. The hole transfer in DNA is codetermined by the large fluctuations of site energies on the order of 0.4 eV, induced by the solvent degrees of freedom. These fluctuations lead to charge-transfer active conformations with large transfer efficiency, which are characterized by a favorable alignment of site energies along the DNA strand. This reduces the barrier for the hole transfer dramatically. Consequently, we find that a charge hopping mechanism is operative already for short bridges with fewer than four adenines, in contrast to the charge-transfer models assuming static DNA structures, where only tunneling occurs. The solvent fluctuations introduce a significant correlation between neighboring sites, enhancing the charge-transfer rate, while the fluctuation of electronic couplings has only a minor impact on the charge-transfer characteristics. Our results emphasize the importance of an accurate description of solvent effects as well as proper sampling, and it is suggested that charge transfer in DNA is gated by the dynamics of solvent.

  13. Quantum Inflation of Classical Shapes

    NASA Astrophysics Data System (ADS)

    Koslowski, Tim

    2017-03-01

    I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization.

  14. Quantum money with classical verification

    NASA Astrophysics Data System (ADS)

    Gavinsky, Dmitry

    2014-12-01

    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.

  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. Quantum transitions between classical histories

    NASA Astrophysics Data System (ADS)

    Hartle, James; Hertog, Thomas

    2015-09-01

    In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications. (a) Classical histories are generally available only in limited patches of the configuration space on which the state lives. (b) In a given patch, states generally predict relative probabilities for an ensemble of possible classical histories. (c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches. (d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion. We support and illustrate (a)-(d) by calculating the quantum transition across the de Sitter-like throat connecting asymptotically classical, inflating histories in the no-boundary quantum state. This supplies probabilities for how a classical history on one side transitions and branches into a range of classical histories on the opposite side. We also comment on the implications of (a)-(d) for the dynamics of black holes and eternal inflation.

  17. Classical and quantum ghosts

    NASA Astrophysics Data System (ADS)

    Sbisà, Fulvio

    2015-01-01

    The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated with a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we do not consider very ad hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz invariance or locality above the cut-off, in which case the cut-off has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz invariance spontaneously.

  18. 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.

  19. 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.

  20. Classical Physics and Quantum Loops

    SciTech Connect

    Barry R. Holstein; John F. Donoghue

    2004-05-01

    The standard picture of the loop expansion associates a factor of h-bar with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss examples wherein classical effects arise from loop contributions and display the relationship between the classical terms and the long range effects of massless particles.

  1. Quantum vs. classical walks with memory two

    NASA Astrophysics Data System (ADS)

    Dimcovic, Zlatko; Kovchegov, Yevgeniy

    2010-03-01

    Quantum walks is an emerging field in quantum computing. It is expected to become the next most effective tool in speeding up quantum algorithms, possibly achieving the similar gain in speed as was the case with Gibbs sampling in classical computing. There already exist examples of super-exponential speed up using only quantum walks. Markov chains, or random walks on graphs, have many uses in physics; and walks with memory are standard models for a number of phenomena. We study persistent quantum walks, and compare them with equivalent classical Markov processes. The first question to ask is how the mixing time compares between persistent quantum and classical walks. Since quantum walks are generated by unitary matrices, they do not converge to a stationary state. The mixing time is then naturally introduced via a limiting distribution defined as the average of the probability distributions over time (Cesaro sum). We compare the mixing times, along with other properties, using numerical methods and spectral analysis. Our preliminary results indicate a significant speedup in some cases, and a number of other interesting aspects of quantum walks.

  2. On quantum vs. classical probability

    SciTech Connect

    Rau, Jochen

    2009-12-15

    Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry, probabilities, composition of systems, state preparation and reductionism. The essential distinction between classical and quantum theory, on the other hand, is shown to be joint decidability versus smoothness; for the latter in particular I supply ample explanation and motivation. Finally, I argue that beyond quantum theory there are no other generalisations of classical probability theory that are relevant to physics.

  3. Quantum reduplication of classical solitons

    NASA Astrophysics Data System (ADS)

    Sveshnikov, Konstantin

    1993-09-01

    The possible existence of a series of quantum copies of classical soliton solutions is discussed, which do not exist when the effective Planck constant of the theory γ tends to zero. Within the conventional weak-coupling expansion in √ γ such non-classical solitons are O(√ γ) in energy and therefore lie in between the true classical solutions and elementary quantum excitations. Analytic results concerning the shape functions, masses and characteristic scales of such quantum excitations are given for soliton models of a self-interacting scalar field. Stability properties and quantization of fluctuations in the neighborhood of these configurations are also discussed in detail.

  4. From Classical to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George

    2010-06-01

    Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.

  5. From Classical to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George

    2004-03-01

    Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.

  6. From classical to quantum criticality

    NASA Astrophysics Data System (ADS)

    Podolsky, Daniel; Shimshoni, Efrat; Silvi, Pietro; Montangero, Simone; Calarco, Tommaso; Morigi, Giovanna; Fishman, Shmuel

    2014-06-01

    We study the crossover from classical to quantum phase transitions at zero temperature within the framework of ϕ4 theory. The classical transition at zero temperature can be described by the Landau theory, turning into a quantum Ising transition with the addition of quantum fluctuations. We perform a calculation of the transition line in the regime where the quantum fluctuations are weak. The calculation is based on a renormalization group analysis of the crossover between classical and quantum transitions, and is well controlled even for space-time dimensionality D below 4. In particular, for D =2 we obtain an analytic expression for the transition line which is valid for a wide range of parameters, as confirmed by numerical calculations based on the density matrix renormalization group. This behavior could be tested by measuring the phase diagram of the linear-zigzag instability in systems of trapped ions or repulsively interacting dipoles.

  7. Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence

    NASA Astrophysics Data System (ADS)

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

    2005-12-01

    The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence—the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state—and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrödinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of

  8. Classical physics and quantum loops.

    PubMed

    Holstein, Barry R; Donoghue, John F

    2004-11-12

    The standard picture of the loop expansion associates a factor of variant Planck's over 2pi with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss counterexamples wherein classical effects arise from loop diagrams and display the relationship between the classical terms and the long range effects of massless particles.

  9. Classical and quantum Malus laws

    NASA Astrophysics Data System (ADS)

    Wódkiewicz, Krzysztof

    1995-04-01

    The classical and the quantum Malus laws for light and spin are discussed. It is shown that for spin 1/2, the quantum Malus law is equivalent in form to the classical Malus law provided the statistical average involves a quasidistribution function that can become negative. A generalization of Malus's law for arbitrary spin s is obtained in the form of a Feynman path-integral representation for the Malus amplitude. The classical limit of the Malus amplitude for s-->∞ is discussed.

  10. 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

  11. Recovering classical dynamics from coupled quantum systems through continuous measurement

    SciTech Connect

    Ghose, Shohini; Alsing, Paul; Deutsch, Ivan; Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

    2003-05-01

    We study the role of continuous measurement in the quantum to classical transition for a system with coupled internal (spin) and external (motional) degrees of freedom. Even when the measured motional degree of freedom can be treated classically, entanglement between spin and motion causes strong measurement back action on the quantum spin subsystem so that classical trajectories are not recovered in this mixed quantum-classical regime. The measurement can extract localized quantum trajectories that behave classically only when the internal action also becomes large relative to ({Dirac_h}/2{pi})

  12. Quantum teleportation without classical channel

    NASA Astrophysics Data System (ADS)

    Al Amri, M.; Li, Zheng-Hong; Zubairy, M. Suhail

    2016-11-01

    For the first time, we show how quantum teleportation can be achieved without the assistance of classical channels. Our protocol does not need any pre-established entangled photon pairs beforehand. Just by utilizing quantum Zeno effect and couterfactual communication idea, we can achieve two goals; entangling a photon and an atom and also disentangling them by non-local interaction. Information is completely transferred from atom to photon with controllable disentanglement processes. More importantly, there is no need to confirm teleportation results via classical channels.

  13. Nonequilibrium Mixed Quantum-Classical simulations of Hydrogen-bond Structure and Dynamics in Methanol-d Carbon tetrachloride liquid mixtures and its spectroscopic signature

    NASA Astrophysics Data System (ADS)

    Kwac, Kijeong; Geva, Eitan

    2011-03-01

    Liquid mixtures of methanol-d and carbon tetrachloride provide attractive model systems for investigating hydrogen-bond structure and dynamics. The hydrogen-bonded methanol oligomers in these mixtures give rise to a very broad hydroxyl stretch IR band (~ 150 cm-1). We have employed mixed quantum-classical molecular dynamics simulations to study the nature of hydrogen- bond structure and dynamics in this system and its spectroscopic signature. In our simulations, the hydroxyl stretch mode is treated quantum mechanically. We have found that the absorption spectrum is highly sensitive to the type of force fields used. Obtaining absorption spectra consistent with experiment required the use of corrected polarizabile force fields and a dipole damping scheme. We have established mapping relationships between the electric field along the hydroxyl bond and the hydrogen-stretch frequency and bond length thereby reducing the computational cost dramatically to simulate the complex nonequilibrium dynamics underlying pump-probe spectra.

  14. Why Do Mixed Quantum-Classical Methods Describe Short-Time Dynamics through Conical Intersections So Well? Analysis of Geometric Phase Effects.

    PubMed

    Gherib, Rami; Ryabinkin, Ilya G; Izmaylov, Artur F

    2015-04-14

    Adequate simulation of nonadiabatic dynamics through conical intersection requires accounting for a nontrivial geometric phase (GP) emerging in electronic and nuclear wave functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultrafast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: (1) compensation for repulsive diagonal second-order nonadiabatic couplings and (2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

  15. A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method

    SciTech Connect

    Shi Qiang; Geva, Eitan

    2009-07-21

    Electron transfer is investigated at the limit of strong friction. The analysis is based on the generic model of a two-state system bilinearly coupled to a harmonic bath. The dynamics is described within the framework of the mixed quantum classical Liouville (MQCL) equation, which is known to be exact for this model. In the case of zero electronic coupling, it is shown that while the dynamics of the electronic populations can be described by a Markovian quantum Smoluchowski equation, that of the electronic coherences are inherently non-Markovian. A non-Markovian modified Zusman equation is derived in the presence of electronic coupling and shown to be self-consistent in cases where the standard Zusman equation is not.

  16. A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method.

    PubMed

    Shi, Qiang; Geva, Eitan

    2009-07-21

    Electron transfer is investigated at the limit of strong friction. The analysis is based on the generic model of a two-state system bilinearly coupled to a harmonic bath. The dynamics is described within the framework of the mixed quantum classical Liouville (MQCL) equation, which is known to be exact for this model. In the case of zero electronic coupling, it is shown that while the dynamics of the electronic populations can be described by a Markovian quantum Smoluchowski equation, that of the electronic coherences are inherently non-Markovian. A non-Markovian modified Zusman equation is derived in the presence of electronic coupling and shown to be self-consistent in cases where the standard Zusman equation is not.

  17. 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.

  18. Quantum to classical randomness extractors

    NASA Astrophysics Data System (ADS)

    Wehner, Stephanie; Berta, Mario; Fawzi, Omar

    2013-03-01

    The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum system. To tackle this question we here introduce the notion of quantum-to-classical randomness extractors (QC-extractors). We identify an entropic quantity that determines exactly how much randomness can be obtained. Furthermore, we provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.

  19. Mixed classical-quantum simulation of vibro-rotational absorption spectra of HCl diluted in dense Ar: Anisotropic interaction and the Q-branch

    NASA Astrophysics Data System (ADS)

    Padilla, Antonio; Pérez, Justo

    2015-10-01

    We have developed a mixed classical-quantum dynamical simulation of HCl diluted in dense Ar in which both the rotation and vibration of the diatomic molecule are treated from a quantum point of view while the remaining translational degree of freedoms of the diatomic and solvent atoms, are treated classically. We have calculated the spectral density of the fundamental band and the rotational absorption coefficient of HCl in Ar at different thermodynamic conditions and we have compared them with the available experimental data. Unlike our previous simulation works on HCl in Ar, in this study we treat the diatomic vibration explicitly, so we can carry out a detailed theoretical-experimental comparative analysis of the spectral profiles. We have considered different models for the HCl-Ar binary anisotropic interaction, founding also different predictions for the absorption line shape, in one case with the presence of the central Q-branch observed in the experimental spectrum, and in another case with the absence of such spectral component. We have found that the theoretical Q-branch noticeably depends on the characteristic of the different anisotropic diatomic-solvent potentials proposed in the literature.

  20. Shear mixing in classical Novae

    NASA Astrophysics Data System (ADS)

    Alexakis, A.; Calder, A. C.; Dursi, L. J.; Times, F. X.; Truran, J. W.; Rosner, R.; Lamb, D. M.; Mignone, A.; Fryxel, B.; Zingale, M.; Olson, K.; Ricker, P.

    2003-03-01

    The mixing of white dwarf material with the accretion envelope in classical novae scenarios is essential for the later evolution and the outburst. One of the plausible mechanisms for the enrichment involves the coupling of large scale flows like convection or accretion with the breaking interfacial waves at the white dwarf surface. We examine how the interaction of accretion wind with a white dwarf surface can lead to a substantial C/O enrichment that can power a novae. We use the FLASH code to perform two and three dimensional simulations of wind driven gravity waves and investigate their growth and non-linear development for a variety of wind profiles. Our results show that even weak winds generate gravity waves through a resonant mechanism with the wind that grow nonlinear and break leading to spray formation and mixing. The total amount of white dwarf material mixed at late times, is shown to be proportional to the square of the maximum wind velocity, inversely proportional to gravity and independent of the functional form of the wind profile. This work has been supported by the DOE ASCI/Alliances program at the University of Chicago under grant No. B341495.

  1. Gaussian ensembles distributions from mixing quantum systems

    NASA Astrophysics Data System (ADS)

    Gomez, Ignacio S.; Portesi, M.

    2017-08-01

    In the context of dynamical systems we present a derivation of the Gaussian ensembles distributions from quantum systems having a classical analogue that is mixing. We find that factorization property is satisfied for the mixing quantum systems expressed as a factorization of quantum mean values. For the case of the kicked rotator and in its fully chaotic regime, the factorization property links decoherence by dephasing with Gaussian ensembles in terms of the weak limit, interpreted as a decohered state. Moreover, a discussion about the connection between random matrix theory and quantum chaotic systems, based on some attempts made in previous works and from the viewpoint of the mixing quantum systems, is presented.

  2. 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.

  3. Strong Analog Classical Simulation of Coherent Quantum Dynamics

    NASA Astrophysics Data System (ADS)

    Wang, Dong-Sheng

    2017-02-01

    A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational technique of quantum tomography, which applies broadly to cases of mixed states, nonunitary evolution, and infinite dimensional systems. The simulation provides an intriguing classical picture to probe quantum phenomena, namely, a coherent quantum dynamics can be viewed as a globally constrained classical Hamiltonian dynamics of a collection of coupled particles or strings. Efficiency analysis reveals a fundamental difference between the locality in real space and locality in Hilbert space, the latter enables efficient strong analog classical simulations. Examples are also studied to highlight the differences and gaps among various simulation methods. Funding support from NSERC of Canada and a research fellowship at Department of Physics and Astronomy, University of British Columbia are acknowledged

  4. Fundamental limits of classical and quantum imaging.

    PubMed

    Pérez-Delgado, Carlos A; Pearce, Mark E; Kok, Pieter

    2012-09-21

    Quantum imaging promises increased imaging performance over classical protocols. However, there are a number of aspects of quantum imaging that are not well understood. In particular, it has been unknown so far how to compare classical and quantum imaging procedures. Here, we consider classical and quantum imaging in a single theoretical framework and present general fundamental limits on the resolution and the deposition rate for classical and quantum imaging. The resolution can be estimated from the image itself. We present a utility function that allows us to compare imaging protocols in a wide range of applications.

  5. Reexamining the Quantum-Classical Relation

    NASA Astrophysics Data System (ADS)

    Bokulich, Alisa

    2008-10-01

    1. Intertheoretic relations: are imperialism and isolationism our only options?; 2. Heisenberg's closed theories and pluralistic realism; 3. Dirac's open theories and the reciprocal correspondence principle; 4. Bohr's generalization of classical mechanics; 5. Semiclassical mechanics: putting quantum flesh on classical bones; 6. Can classical structures explain quantum phenomena?; 7. A structural approach to intertheoretic relations; References; Index.

  6. 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.

  7. Exploring the role of decoherence in condensed-phase nonadiabatic dynamics: a comparison of different mixed quantum/classical simulation algorithms for the excited hydrated electron.

    PubMed

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

    2006-10-12

    Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensed-phase systems. There are many MQC algorithms available, however, and in cases where nonadiabatic coupling is important, different algorithms may lead to different results. Thus, it has been difficult to reach definitive conclusions about relaxation dynamics using nonadiabatic MQC methods because one is never certain whether any given algorithm includes enough of the necessary physics. In this paper, we explore the physics underlying different nonadiabatic MQC algorithms by comparing and contrasting the excited-state relaxation dynamics of the prototypical condensed-phase MQC system, the hydrated electron, calculated using different algorithms, including: fewest-switches surface hopping, stationary-phase surface hopping, and mean-field dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, mean-field dynamics with stochastic decoherence (MF-SD), is to be implemented for condensed-phase problems, and we apply MF-SD to the excited-state relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydrated-electron relaxation dynamics. We find that for three MQC methods that use Tully's fewest-switches criterion to determine surface hopping probabilities, the excited-state lifetime of the electron is the same. Moreover, the nonequilibrium solvent response function of the excited hydrated electron is the same with all of the nonadiabatic MQC algorithms discussed here, so that all of the algorithms would produce similar agreement with experiment. Despite the identical solvent response predicted by each MQC algorithm, we find that MF-SD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an

  8. 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.

  9. 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.

  10. Quantum Simulations of Classical Annealing Processes

    NASA Astrophysics Data System (ADS)

    Somma, R. D.; Boixo, S.; Barnum, H.; Knill, E.

    2008-09-01

    We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/δ steps to find an optimal solution with bounded error probability, where δ is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order 1/δ steps required by the latter.

  11. 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.

  12. Quantum simulation of classical thermal states.

    PubMed

    Dür, W; Van den Nest, M

    2011-10-21

    We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum state such that the reduced density operator behaves as the thermal state of the classical system. We show that all these quantum states are unique ground states of a universal 5-body local quantum Hamiltonian acting on a (polynomially enlarged) qubit system on a 2D lattice. The only free parameters of the quantum Hamiltonian are coupling strengths of two-body interactions, which allow one to choose the type and dimension of the classical model as well as the interaction strength and temperature. This opens the possibility to study and simulate classical spin models in arbitrary dimension using a 2D quantum system.

  13. 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.

  14. Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

    NASA Astrophysics Data System (ADS)

    Jeon, Kiyoung; Yang, Mino

    2017-02-01

    Three low-lying vibrational states of molecular systems are responsible for the signals of linear and third-order nonlinear vibrational spectroscopies. Theoretical studies based on mixed quantum/classical calculations provide a powerful way to analyze those experiments. A statistically meaningful result can be obtained from the calculations by solving the vibrational Schrödinger equation over many numbers of molecular configurations. The discrete variable representation (DVR) method is a useful technique to calculate vibrational eigenstates subject to an arbitrary anharmonic potential surface. Considering the large number of molecular configurations over which the DVR calculations are repeated, the calculations are desired to be optimized in balance between the cost and accuracy. We determine a dimension of the DVR method which appears to be optimum for the calculations of the three states of molecular vibrations with anharmonic strengths often found in realistic molecular systems. We apply the numerical technique to calculate the local OH stretching frequencies of liquid water, which are well known to be widely distributed due to the inhomogeneity in molecular configuration, and found that the frequencies of the 0-1 and 1-2 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.

  15. 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.

  16. 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

    2008-04-03

    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

  17. 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.

  18. First principles multielectron mixed quantum/classical simulations in the condensed phase. II. The charge-transfer-to-solvent states of sodium anions in liquid tetrahydrofuran.

    PubMed

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

    2010-04-14

    Gas-phase atomic anions lack bound electronic excited states, yet in solution many of these anions exhibit intense absorption bands due to the presence of excited states, referred to as charge-transfer-to-solvent (CTTS) states that are bound only by the presence of the solvent. CTTS spectra thus serve as delicate probes of solute-solvent interactions, but the fact that they are created by the interactions of a solute with many solvent molecules makes them a challenge to describe theoretically. In this paper, we use mixed quantum/classical molecular dynamics with the two-electron Fourier-grid (2EFG) electronic structure method presented in the previous paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144101 (2010)] to simulate the CTTS states of a sodium anion in liquid tetrahydrofuran, Na(-)/THF. Since our 2EFG method is based on configuration interaction with single and double excitations in a grid basis, it allows for an exact treatment of the two valence electrons of the sodium anion. To simulate Na(-)/THF, we first develop a new electron-THF pseudopotential, and we verify the accuracy of this potential by reproducing the experimental absorption spectrum of an excess electron in liquid THF with near quantitative accuracy. We also are able to reproduce the CTTS spectrum of Na(-)/THF and find that the CTTS states of Na(-) exhibit a Rydberg-like progression due to the pre-existing long-range solvent polarization around the anion. We also find that the CTTS states are highly mixed with the disjoint electronic states supported by naturally occurring solvent cavities that exist in liquid THF. This mixing explains why the solvated electrons that are ejected following CTTS excitation appear with their equilibrium absorption spectrum. The mixing of the CTTS and solvent-cavity states also explains why the recombination of the electron and its geminate Na(0) partner occurs on slower time scales when photoexciting in the blue compared to in the red

  19. Coherent quantum states from classical oscillator amplitudes

    NASA Astrophysics Data System (ADS)

    Briggs, John S.; Eisfeld, Alexander

    2012-05-01

    In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schrödinger equation and the classical position and momentum variables solving Hamilton's equations. Here it is shown that the analogy can be made an equivalence in that, in principle, systems of classical oscillators can be constructed whose position and momenta variables form time-dependent amplitudes which are identical to the complex quantum amplitudes of the coupled wave function of an N-level quantum system with real coupling matrix elements. Hence classical motion can reproduce quantum coherence.

  20. New insights into the nonadiabatic state population dynamics of model proton-coupled electron transfer reactions from the mixed quantum-classical Liouville approach

    SciTech Connect

    Shakib, Farnaz A.; Hanna, Gabriel

    2016-01-14

    In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model proton-coupled electron transfer (PCET) reaction via the mixed quantum-classical Liouville (MQCL) approach and found that the trajectories spend the majority of their time on the mean of two coherently coupled adiabatic potential energy surfaces. This suggested a need for mean surface evolution to accurately simulate observables related to ultrafast PCET processes. In this study, we simulate the time-dependent populations of the three lowest adiabatic states in the ET-PT (i.e., electron transfer preceding proton transfer) version of the same PCET model via the MQCL approach and compare them to the exact quantum results and those obtained via the fewest switches surface hopping (FSSH) approach. We find that the MQCL population profiles are in good agreement with the exact quantum results and show a significant improvement over the FSSH results. All of the mean surfaces are shown to play a direct role in the dynamics of the state populations. Interestingly, our results indicate that the population transfer to the second-excited state can be mediated by dynamics on the mean of the ground and second-excited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the first-excited state surface altogether. This is made possible through nonadiabatic transitions between different mean surfaces, which is the manifestation of coherence transfer in MQCL dynamics. We also investigate the effect of the strength of the coupling between the proton/electron and the solvent coordinate on the state population dynamics. Drastic changes in the population dynamics are observed, which can be understood in terms of the changes in the potential energy surfaces and the nonadiabatic couplings. Finally, we investigate the state population dynamics in the PT-ET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT

  1. New insights into the nonadiabatic state population dynamics of model proton-coupled electron transfer reactions from the mixed quantum-classical Liouville approach.

    PubMed

    Shakib, Farnaz A; Hanna, Gabriel

    2016-01-14

    In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model proton-coupled electron transfer (PCET) reaction via the mixed quantum-classical Liouville (MQCL) approach and found that the trajectories spend the majority of their time on the mean of two coherently coupled adiabatic potential energy surfaces. This suggested a need for mean surface evolution to accurately simulate observables related to ultrafast PCET processes. In this study, we simulate the time-dependent populations of the three lowest adiabatic states in the ET-PT (i.e., electron transfer preceding proton transfer) version of the same PCET model via the MQCL approach and compare them to the exact quantum results and those obtained via the fewest switches surface hopping (FSSH) approach. We find that the MQCL population profiles are in good agreement with the exact quantum results and show a significant improvement over the FSSH results. All of the mean surfaces are shown to play a direct role in the dynamics of the state populations. Interestingly, our results indicate that the population transfer to the second-excited state can be mediated by dynamics on the mean of the ground and second-excited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the first-excited state surface altogether. This is made possible through nonadiabatic transitions between different mean surfaces, which is the manifestation of coherence transfer in MQCL dynamics. We also investigate the effect of the strength of the coupling between the proton/electron and the solvent coordinate on the state population dynamics. Drastic changes in the population dynamics are observed, which can be understood in terms of the changes in the potential energy surfaces and the nonadiabatic couplings. Finally, we investigate the state population dynamics in the PT-ET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT

  2. Continuous quantum measurement and the quantum to classical transition

    SciTech Connect

    Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

    2003-04-01

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

  3. 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

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

    PubMed

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

    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

  5. 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.

  6. 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

  7. Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

    NASA Astrophysics Data System (ADS)

    Fathi, M.; Jalalzadeh, S.

    2017-07-01

    How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.

  8. Hybrid Quantum-Classical Approach to Quantum Optimal Control.

    PubMed

    Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

    2017-04-14

    A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

  9. Hybrid Quantum-Classical Approach to Quantum Optimal Control

    NASA Astrophysics Data System (ADS)

    Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

    2017-04-01

    A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

  10. 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.

  11. Thermodynamic integration from classical to quantum mechanics.

    PubMed

    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. © 2011 American Institute of Physics

  12. 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.``

  13. 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

  14. 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.

  15. Mixed quantum/classical calculations of total and differential elastic and rotationally inelastic scattering cross sections for light and heavy reduced masses in a broad range of collision energies

    SciTech Connect

    Semenov, Alexander; Babikov, Dmitri

    2014-01-28

    The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H{sub 2} and Na + N{sub 2}. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.

  16. 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)

  17. 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)

  18. Unraveling Quantum Annealers using Classical Hardness

    NASA Astrophysics Data System (ADS)

    Martin-Mayor, Victor; Hen, Itay

    2015-10-01

    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.

  19. Unraveling Quantum Annealers using Classical Hardness

    PubMed Central

    Martin-Mayor, Victor; Hen, Itay

    2015-01-01

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

  20. Finding quantum effects in strong classical potentials

    NASA Astrophysics Data System (ADS)

    Hegelich, B. Manuel; Labun, Lance; Labun, Ou Z.

    2017-06-01

    The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe the dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron-hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. They must therefore be improved and adapted for the description of laser-plasma experiments that typically involve the acceleration of electrons. Theory developed from quantum electrodynamics, together with dedicated experimental efforts, offer the best controllable context to establish a robust, experimentally validated foundation for the fundamental theory of quantum effects in strong classical potentials.

  1. Classical field approach to quantum weak measurements.

    PubMed

    Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco

    2014-03-21

    By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.

  2. Quantum approach to classical statistical mechanics.

    PubMed

    Somma, R D; Batista, C D; Ortiz, G

    2007-07-20

    We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

  3. 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.

  4. Quantum feedback control and classical control theory

    SciTech Connect

    Doherty, Andrew C.; Habib, Salman; Jacobs, Kurt; Mabuchi, Hideo; Tan, Sze M.

    2000-07-01

    We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential. (c) 2000 The American Physical Society.

  5. 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.

  6. 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…

  7. 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…

  8. 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.

  9. Quantum phase uncertainties in the classical limit

    NASA Technical Reports Server (NTRS)

    Franson, James D.

    1994-01-01

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

  10. Classical underpinnings of gravitationally induced quantum interference

    SciTech Connect

    Mannheim, P.D.

    1998-02-01

    We show that the gravitational modification of the phase of a neutron beam [the Colella-Overhauser-Werner (COW) experiment] has a classical origin, being due to the time delay that classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics. {copyright} {ital 1998} {ital The American Physical Society}

  11. Classical underpinnings of gravitationally induced quantum interference

    NASA Astrophysics Data System (ADS)

    Mannheim, Philip D.

    1998-02-01

    We show that the gravitational modification of the phase of a neutron beam [the Colella-Overhauser-Werner (COW) experiment] has a classical origin, being due to the time delay that classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics.

  12. Classical noise, quantum noise and secure communication

    NASA Astrophysics Data System (ADS)

    Tannous, C.; Langlois, J.

    2016-01-01

    Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudo-noise) as performed in spread-spectrum communication used presently in Wi-Fi and smartphone telecommunication systems. Quantum communication based on entanglement is another route for securing communications as demonstrated by several important experiments described in this work. The central role played by the photon in unifying the description of classical and quantum noise as major ingredients of secure communication systems is highlighted and described on the basis of the classical and quantum fluctuation dissipation theorems.

  13. Quantum-classical Liouville dynamics of nonadiabatic proton transfer.

    PubMed

    Hanna, Gabriel; Kapral, Raymond

    2005-06-22

    A proton transfer reaction in a linear hydrogen-bonded complex dissolved in a polar solvent is studied using mixed quantum-classical Liouville dynamics. In this system, the proton is treated quantum mechanically and the remainder of the degrees of freedom is treated classically. The rates and mechanisms of the reaction are investigated using both adiabatic and nonadiabatic molecular dynamics. We use a nonadiabatic dynamics algorithm which allows the system to evolve on single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Reactive-flux correlation function expressions are used to compute the rate coefficients and the role of the dynamics on the coherently coupled surfaces is elucidated.

  14. Macroscopic quantum mechanics in a classical spacetime.

    PubMed

    Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei

    2013-04-26

    We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.

  15. Quantum and classical phases in optomechanics

    NASA Astrophysics Data System (ADS)

    Armata, Federico; Latmiral, Ludovico; Pikovski, Igor; Vanner, Michael R.; Brukner, Časlav; Kim, M. S.

    2016-06-01

    The control of quantum systems requires the ability to change and read-out the phase of a system. The noncommutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase gates and for precision measurements. Here we study the phase acquired by a radiation field after its radiation pressure interaction with a mechanical oscillator, and compare the classical and quantum contributions. The classical description can reproduce the nonlinearity induced by the mechanical oscillator and the loss of correlations between mechanics and optical field at certain interaction times. Such features alone are therefore insufficient for probing the quantum nature of the interaction. Our results thus isolate genuine quantum contributions of the optomechanical interaction that could be probed in current experiments.

  16. 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.

  17. 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.

  18. Quantum cryptography: a view from classical cryptography

    NASA Astrophysics Data System (ADS)

    Buchmann, Johannes; Braun, Johannes; Demirel, Denise; Geihs, Matthias

    2017-06-01

    Much of digital data requires long-term protection of confidentiality, for example, medical health records. Cryptography provides such protection. However, currently used cryptographic techniques such as Diffe-Hellman key exchange may not provide long-term security. Such techniques rely on certain computational assumptions, such as the hardness of the discrete logarithm problem that may turn out to be incorrect. On the other hand, quantum cryptography---in particular quantum random number generation and quantum key distribution---offers information theoretic protection. In this paper, we explore the challenge of providing long-term confidentiality and we argue that a combination of quantum cryptography and classical cryptography can provide such protection.

  19. Classical and Quantum Thermal Physics

    NASA Astrophysics Data System (ADS)

    Prasad, R.

    2016-11-01

    List of figures; List of tables; Preface; Acknowledgement; Dedication; 1. The kinetic theory of gases; 2. Ideal to real gas, viscosity, conductivity and diffusion; 3. Thermodynamics: definitions and Zeroth law; 4. First Law of Thermodynamics and some of its applications; 5. Second Law of Thermodynamics and some of its applications; 6. TdS equations and their applications; 7. Thermodynamic functions, potentials, Maxwell equations, the Third Law and equilibrium; 8. Some applications of thermodynamics to problems of physics and engineering; 9. Application of thermodynamics to chemical reactions; 10. Quantum thermodynamics; 11. Some applications of quantum thermodynamics; 12. Introduction to the thermodynamics of irreversible processes; Index.

  20. 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.

  1. 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.

  2. A mixed quantum-classical molecular dynamics study of the hydroxyl stretch in methanol/carbon tetrachloride mixtures: equilibrium hydrogen-bond structure and dynamics at the ground state and the infrared absorption spectrum.

    PubMed

    Kwac, Kijeong; Geva, Eitan

    2011-07-28

    We present a mixed quantum-classical molecular dynamics study of the structure and dynamics of the hydroxyl stretch in methanol/carbon tetrachloride mixtures. One of the methanol molecules is tagged, and its hydroxyl stretch is treated quantum-mechanically, while the remaining degrees of freedom are treated classically. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the corresponding adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are in turn affected by the quantum-mechanical state of the tagged hydroxyl stretch via the corresponding Hellmann-Feynman forces. The ability of five different force-field combinations to reproduce the experimental absorption infrared spectrum of the hydroxyl stretch is examined for different isotopomers and on a wide range of compositions. It is found that, in addition to accounting for the anharmonic nature of the hydroxyl stretch, one also has to employ polarizable force fields and account for the damping of the polarizability at short distances. The equilibrium ground-state hydrogen-bonding structure and dynamics is analyzed, and its signature on the absorption infrared spectrum of the hydroxyl stretch is investigated in detail. Five different hydroxyl stretch subpopulations are identified and spectrally assigned: monomers (α), hydrogen-bond acceptors (β), hydrogen-bond donors (γ), simultaneous hydrogen-bond donors and acceptors (δ), and simultaneous hydrogen-bond donors and double-acceptors (ε). The fundamental transition frequencies of the α and β subpopulations are found to be narrowly distributed and to overlap, thereby giving rise to a single narrow band whose intensity is significantly diminished by rotational relaxation. The fundamental transition frequency distributions of the γ, δ, and ε subpopulations are found to be

  3. 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.

  4. Classical Ising model test for quantum circuits

    NASA Astrophysics Data System (ADS)

    Geraci, Joseph; Lidar, Daniel A.

    2010-07-01

    We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.

  5. 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.

  6. 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.

  7. Communication: quantum dynamics in classical spin baths.

    PubMed

    Sergi, Alessandro

    2013-07-21

    A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.

  8. Communication: Quantum dynamics in classical spin baths

    NASA Astrophysics Data System (ADS)

    Sergi, Alessandro

    2013-07-01

    A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.

  9. Classical enhancement of quantum vacuum fluctuations

    NASA Astrophysics Data System (ADS)

    De Lorenci, V. A.; Ford, L. H.

    2017-01-01

    We propose a mechanism for the enhancement of vacuum fluctuations by means of a classical field. The basic idea is that if an observable quantity depends quadratically upon a quantum field, such as the electric field, then the application of a classical field produces a cross term between the classical and quantum fields. This cross term may be significantly larger than the purely quantum part, but also undergoes fluctuations driven by the quantum field. We illustrate this effect in a model for light-cone fluctuations involving pulses in a nonlinear dielectric. Vacuum electric field fluctuations produce fluctuations in the speed of a probe pulse, and form an analog model for quantum gravity effects. If the material has a nonzero third-order susceptibility, then the fractional light speed fluctuations are proportional to the square of the fluctuating electric field. Hence the application of a classical electric field can enhance the speed fluctuations. We give an example where this enhancement can be an increase of 1 order of magnitude, increasing the possibility of observing the effect.

  10. 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.

  11. Uniform Additivity in Classical and Quantum Information

    NASA Astrophysics Data System (ADS)

    Cross, Andrew; Li, Ke; Smith, Graeme

    2017-01-01

    Information theory quantifies the optimal rates of resource interconversions, usually in terms of entropies. However, nonadditivity often makes evaluating entropic formulas intractable. In a few auspicious cases, additivity allows a full characterization of optimal rates. We study uniform additivity of formulas, which is easily evaluated and captures all known additive quantum formulas. Our complete characterization of uniform additivity exposes an intriguing new additive quantity and identifies a remarkable coincidence—the classical and quantum uniformly additive functions with one auxiliary variable are identical.

  12. Study of the redox properties of singlet and triplet Tris(2,2'-bipyridine)ruthenium(II) ([Ru(bpy)3]2+) in aqueous solution by full quantum and mixed quantum/classical molecular dynamics simulations.

    PubMed

    Diamantis, Polydefkis; Gonthier, Jérôme Florian; Tavernelli, Ivano; Rothlisberger, Ursula

    2014-04-10

    The oxidation of ground-state (singlet) and triplet [Ru(bpy)3](2+) were studied by full quantum-mechanical (QM) and mixed quantum/classical (QM/MM) molecular dynamics simulations. Both approaches provide reliable results for the redox potentials of the two spin states. The two redox reactions closely obey Marcus theory for electron transfer. The free energy difference between the two [Ru(bpy)3](2+) states amounts to 1.78 eV from both QM and QM/MM simulations. The two methods also provide similar results for the reorganization free energy associated with the transition from singlet to triplet [Ru(bpy)3](2+) (0.06 eV for QM and 0.07 eV for QM/MM). On the basis of single-point calculations, we estimate the entropic contribution to the free energy difference between singlet and triplet [Ru(bpy)3](2+) to be 0.27 eV, which is significantly greater than previously assumed (0.03 eV) and in contradiction with the assumption that the transition between these two states can be accurately described using purely energetic considerations. Employing a thermodynamic cycle involving singlet [Ru(bpy)3](2+), triplet [Ru(bpy)3](2+), and [Ru(bpy)3](3+), we calculated the triplet oxidation potential to be -0.62 V vs the standard hydrogen electrode, which is significantly different from a previous experimental estimate based on energetic considerations only (-0.86 V).

  13. 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.

  14. A mixed quantum-classical molecular dynamics study of anti-tetrol and syn-tetrol dissolved in liquid chloroform: hydrogen-bond structure and its signature on the infrared absorption spectrum.

    PubMed

    Kwac, Kijeong; Geva, Eitan

    2013-12-27

    The intramolecular hydrogen-bond structure of stereoselectively synthesized syn-tetrol and anti-tetrol dissolved in deuterated chloroform is investigated via a mixed quantum-classical molecular dynamics simulation. An extensive conformational analysis is performed in order to determine the dominant conformations, the distributions among them, and their sensitivity to the method for assigning partial charges (RESP vs AM1-BCC). The signature of the conformational distribution and method of assigning partial charges on the infrared absorption spectra is analyzed in detail. The relationship between the spectra and the underlying hydrogen-bond structure is elucidated.

  15. 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.

  16. 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.

  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. 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

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

    PubMed

    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) ∈ [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.

  20. 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.

  1. Noisy Quantum Cellular Automata for Quantum versus Classical Excitation Transfer

    NASA Astrophysics Data System (ADS)

    Avalle, Michele; Serafini, Alessio

    2014-05-01

    We introduce a class of noisy quantum cellular automata on a qubit lattice that includes all classical Markov chains, as well as maps where quantum coherence between sites is allowed to build up over time. We apply such a construction to the problem of excitation transfer through 1D lattices, and compare the performance of classical and quantum dynamics with equal local transition probabilities. Our discrete approach has the merits of stripping down the complications of the open system dynamics, of clearly isolating coherent effects, and of allowing for an exact treatment of conditional dynamics, all while capturing a rich variety of dynamical behaviors.

  2. Noisy quantum cellular automata for quantum versus classical excitation transfer.

    PubMed

    Avalle, Michele; Serafini, Alessio

    2014-05-02

    We introduce a class of noisy quantum cellular automata on a qubit lattice that includes all classical Markov chains, as well as maps where quantum coherence between sites is allowed to build up over time. We apply such a construction to the problem of excitation transfer through 1D lattices, and compare the performance of classical and quantum dynamics with equal local transition probabilities. Our discrete approach has the merits of stripping down the complications of the open system dynamics, of clearly isolating coherent effects, and of allowing for an exact treatment of conditional dynamics, all while capturing a rich variety of dynamical behaviors.

  3. Comparing classical and quantum PageRanks

    NASA Astrophysics Data System (ADS)

    Loke, T.; Tang, J. W.; Rodriguez, J.; Small, M.; Wang, J. B.

    2017-01-01

    Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for all networks we studied in this paper. For the discrete-time case, we investigated the periodic nature of the walker's probability distribution for a wide range of networks and found that the dominant period does not grow with the size of these networks. Based on this observation, we introduce a new quantum measure using the maximum probabilities of the associated walker during the first couple of periods. This is particularly important, since it leads to a quantum PageRanking scheme that is scalable with respect to network size.

  4. 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.

  5. 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.

  6. 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)

  7. 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

  8. 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)

  9. Isoperiodic classical systems and their quantum counterparts

    NASA Astrophysics Data System (ADS)

    Asorey, M.; Cariñena, J. F.; Marmo, G.; Perelomov, A.

    2007-06-01

    One-dimensional isoperiodic classical systems have been first analyzed by Abel. Abel's characterization can be extended for singular potentials and potentials which are not defined on the whole real line. The standard shear equivalence of isoperiodic potentials can also be extended by using reflection and inversion transformations. We provide a full characterization of isoperiodic rational potentials showing that they are connected by translations, reflections or Joukowski transformations. Upon quantization many of these isoperiodic systems fail to exhibit identical quantum energy spectra. This anomaly occurs at order O( ℏ2) because semiclassical corrections of energy levels of order O( ℏ) are identical for all isoperiodic systems. We analyze families of systems where this quantum anomaly occurs and some special systems where the spectral identity is preserved by quantization. Conversely, we point out the existence of isospectral quantum systems which do not correspond to isoperiodic classical systems.

  10. Classical simulation of quantum fields I

    NASA Astrophysics Data System (ADS)

    Hirayama, T.; Holdom, B.

    2006-10-01

    We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler-Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In lambda phi(4) theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously.

  11. Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems

    NASA Astrophysics Data System (ADS)

    Cárdenas-López, F. A.; Allende, S.; Retamal, J. C.

    2017-03-01

    Classical to quantum decoherence transition, an issue existing for incoherent superposition of Bell-diagonal states is studied for three dimensional bipartite AB mixed quantum systems. Depending on the initial conditions, the dynamics of classical and quantum correlations can exhibit a sudden transition between classical to quantum decoherence. This result is calculated numerically by using entropic and geometric measures of correlations. An alternative explanation for this effect could be obtained by extending the bipartite A ⊗ B qutrit system to a pure tripartite A ⊗ B ⊗ C system. The freezing of classical correlations in AB is related to a freezing of the entanglement in the AC bipartition.

  12. Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems.

    PubMed

    Cárdenas-López, F A; Allende, S; Retamal, J C

    2017-03-20

    Classical to quantum decoherence transition, an issue existing for incoherent superposition of Bell-diagonal states is studied for three dimensional bipartite AB mixed quantum systems. Depending on the initial conditions, the dynamics of classical and quantum correlations can exhibit a sudden transition between classical to quantum decoherence. This result is calculated numerically by using entropic and geometric measures of correlations. An alternative explanation for this effect could be obtained by extending the bipartite A ⊗ B qutrit system to a pure tripartite A ⊗ B ⊗ C system. The freezing of classical correlations in AB is related to a freezing of the entanglement in the AC bipartition.

  13. 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

    NASA Astrophysics Data System (ADS)

    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.

  14. Convection and Mixing in Classical Novae Precursors

    NASA Astrophysics Data System (ADS)

    Dursi, L. J.; Calder, A. C.; Alexakis, A.; Truran, J. W.; Zingale, M.; Times, F. X.; Ricker, P. M.; Fryxell, B.; Olson, K.; Rosner, R.; MacNeice, P.

    2002-06-01

    To explain observed abundances from classical nova outbursts, and to help explain their energetics, nova models must incorporate a mechanism that will dredge up the heavier white dwarf material into the lighter accreted atmosphere. One proposed mechanism relies on the fluid motions from an early convective phase to do the mixing. We present recent work investigating two aspects of this mechanism. We examine results from two-dimensional simulations of classical nova precursor models that demonstrate the beginning of a convective phase during the `simmering' of a nova precursor. We use a new hydrostatic equilibrium hydrodynamics module recently developed for the adaptive-mesh code FLASH. The two-dimensional models are based on the one-dimensional models of Ami Glasner (Glasner et al. 1997), and were evolved with FLASH from a pre-convective state to the onset of convection. The onset of convection induces a velocity field near the C,O/H,He interface, which can then cause mixing through interactions with gravity waves. We show results from simulations of these wind-wave interactions, and estimate whether the `wind' caused by the convection could induce sufficient dredge-up to power a classical novae. This research has been supported by the US. Department of Energy under grant no. B341495 to the ASCI Flash Center at the University of Chicago

  15. Classical billiards and quantum fluids

    NASA Astrophysics Data System (ADS)

    Araújo Lima, T.; de Aguiar, F. M.

    2015-01-01

    The dynamics of a particle confined in the elliptical stadium billiard with rectangular thickness 2 t , major axis 2 a , and minor axis 2 b =2 is numerically investigated in a reduced phase space with discrete time n . Both relative measure r (n ) , with asymptotic value r (n →∞ ) =r∞ and Shannon entropy s , are calculated in the vicinity of a particular line in the a ×t parameter space, namely tc=t0(a ) =√{a2-1 } , with a ∈(1 ,√{4 /3 }) . If t mixed phase space (regular and chaotic regions). As the line tc is crossed upwards by increasing t with fixed a , we observe that the function ψ (t ) =√{1 -r∞(t ) } critically vanishes at t =tc . In addition, we show that the function c (t )=t (d s /d t ) displays a pronounced peak at t =tc . In the vicinity of tc (t

  16. Quantum vertex model for reversible classical computing

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

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

  17. Quantum vertex model for reversible classical computing.

    PubMed

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

    2017-05-12

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

  18. Quantum vertex model for reversible classical computing

    PubMed Central

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

    2017-01-01

    Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without ‘learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing. PMID:28497790

  19. Monogamy properties of quantum and classical correlations

    SciTech Connect

    Giorgi, Gian Luca

    2011-11-15

    In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy; that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure three-qubit states belonging to the subclass of W states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 two-qubit states, discord and classical correlations are bounded from above by single-qubit von Neumann entropies.

  20. Classical and quantum-mechanical state reconstruction

    NASA Astrophysics Data System (ADS)

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

    2012-07-01

    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 used in medical imaging known as computer-aided tomography. It is remarkable that this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although it may take on negative values, plays the role of the probability density in phase space in classical physics. We then present another approach to quantum state reconstruction based on the notion of mutually unbiased bases—a notion of current research interest, for which we give explanatory remarks—and indicate the relation between these two approaches. Since the subject of state reconstruction is rarely considered at the level of textbooks, the presentation in this paper is aimed at graduate-level readers.

  1. The classical-quantum boundary for correlations: Discord and related measures

    NASA Astrophysics Data System (ADS)

    Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko

    2012-10-01

    One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

  2. Categories of quantum and classical channels

    NASA Astrophysics Data System (ADS)

    Coecke, Bob; Heunen, Chris; Kissinger, Aleks

    2016-12-01

    We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantum and classical channels, providing elegant abstract notions of preparation and measurement. We also consider nonstandard models that can be used to investigate which notions from algebraic quantum information theory are operationally justifiable.

  3. Nonadiabatic dynamics in open quantum-classical systems: forward-backward trajectory solution.

    PubMed

    Hsieh, Chang-Yu; Kapral, Raymond

    2012-12-14

    A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation is obtained in a coherent state basis using the mapping representation, which expresses N quantum degrees of freedom in a 2N-dimensional phase space. The solution yields a simple dynamics in which a set of N coherent state coordinates evolves in forward and backward trajectories, while the bath coordinates evolve under the influence of the mean potential that depends on these forward and backward trajectories. It is shown that the solution satisfies the differential form of the quantum-classical Liouville equation exactly. Relations to other mixed quantum-classical and semi-classical schemes are discussed.

  4. Geometric uncertainty relation for mixed quantum states

    SciTech Connect

    Andersson, Ole Heydari, Hoshang

    2014-04-15

    In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrödinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrödinger, and vice versa.

  5. 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.

  6. 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.

  7. Mesoscopic systems: classical irreversibility and quantum coherence.

    PubMed

    Barbara, Bernard

    2012-09-28

    Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like

  8. 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.

  9. 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.

  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. 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.

  12. Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

    NASA Astrophysics Data System (ADS)

    Zhuang, Quntao; Zhu, Elton Yechao; Shor, Peter W.

    2017-05-01

    We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness." Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender's signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack's information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.

  13. Quantum-classical path integral. I. Classical memory and weak quantum nonlocality.

    PubMed

    Lambert, Roberto; Makri, Nancy

    2012-12-14

    We consider rigorous path integral descriptions of the dynamics of a quantum system coupled to a polyatomic environment, assuming that the latter is well approximated by classical trajectories. Earlier work has derived semiclassical or purely classical expressions for the influence functional from the environment, which should be sufficiently accurate for many situations, but the evaluation of quantum-(semi)classical path integral (QCPI) expressions has not been practical for large-scale simulation because the interaction with the environment introduces couplings nonlocal in time. In this work, we analyze the nature of the effects on a system from its environment in light of the observation [N. Makri, J. Chem. Phys. 109, 2994 (1998)] that true nonlocality in the path integral is a strictly quantum mechanical phenomenon. If the environment is classical, the path integral becomes local and can be evaluated in a stepwise fashion along classical trajectories of the free solvent. This simple "classical path" limit of QCPI captures fully the decoherence of the system via a classical mechanism. Small corrections to the classical path QCPI approximation may be obtained via an inexpensive random hop QCPI model, which accounts for some "back reaction" effects. Exploiting the finite length of nonlocality, we argue that further inclusion of quantum decoherence is possible via an iterative evaluation of the path integral. Finally, we show that the sum of the quantum amplitude factors with respect to the system paths leads to a smooth integrand as a function of trajectory initial conditions, allowing the use of Monte Carlo methods for the multidimensional phase space integral.

  14. Statistical mechanics of quantum-classical systems with holonomic constraints.

    PubMed

    Sergi, Alessandro

    2006-01-14

    The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.

  15. 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.

  16. 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).

  17. Classical and quantum routes to linear magnetoresistance

    NASA Astrophysics Data System (ADS)

    Hu, Jingshi

    The transverse, positive magnetoresistance of suitably doped silver chalcogenides and indium antimonides changes linearly with magnetic field by thousands of percent, with no sign of saturation up to MegaGauss. A precise characterization of these unexpected observations has led to two very different, yet equally interesting magnetotransport mechanisms: the classical inhomogeneity-induced current jetting, and quantum linear magnetoresistance. The inhomogeneous distribution of excess/deficient silver atoms lies behind the anomalous magnetoresistive response of silver chalcogenides, introducing spatial conductivity fluctuations with length scales independent of the cyclotron radius. We show that a systematic investigation of the resistivity tensor in longitudinal field could be used to identify the spatial inhomogeneities and determine the associated length scale of the current distortion. By contrast, the linear magnetoresistance observed in single-crystalline InSb presents a spectacular manifestation of magnetotransport in the extreme quantum limit, when only one Landau band is partially filled. Harnessing both the classical and quantum effects opens the gate to artificial fabrication of conducting networks with micron scale unit size for enhanced magnetoresistive sensitivity.

  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 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).

  20. On quantum coding for ensembles of mixed states

    NASA Astrophysics Data System (ADS)

    Barnum, Howard; Caves, Carlton M.; Fuchs, Christopher A.; Jozsa, Richard; Schumacher, Benjamin

    2001-09-01

    We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.

  1. Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.

    2015-08-01

    Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

  2. Fully adaptive propagation of the quantum-classical Liouville equation.

    PubMed

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

    2004-05-15

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

  3. Exploring Classically Chaotic Potentials with a Matter Wave Quantum Probe

    SciTech Connect

    Gattobigio, G. L.; Couvert, A.; Georgeot, B.; Guery-Odelin, D.

    2011-12-16

    We study an experimental setup in which a quantum probe, provided by a quasimonomode guided atom laser, interacts with a static localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling between the different degrees of freedom. Our experimental results display a clear signature of this transition. On the basis of extensive numerical simulations, we discuss the quantum versus classical physics predictions in this context. This system opens new possibilities for investigating quantum scattering, provides a new testing ground for classical and quantum chaos, and enables us to revisit the quantum-classical correspondence.

  4. Classical and nonclassical randomness in quantum measurements

    NASA Astrophysics Data System (ADS)

    Farenick, Douglas; Plosker, Sarah; Smith, Jerrod

    2011-12-01

    The space POVM_H(X) of positive operator-valued probability measures on the Borel sets of a compact (or even locally compact) Hausdorff space X with values in B(H), the algebra of linear operators acting on a d-dimensional Hilbert space H, is studied from the perspectives of classical and nonclassical convexity through a transform Γ that associates any positive operator-valued measure ν with a certain completely positive linear map Γ(ν) of the homogeneous C*-algebra C(X)⊗ B(H) into B(H). This association is achieved by using an operator-valued integral in which nonclassical random variables (that is, operator-valued functions) are integrated with respect to positive operator-valued measures and which has the feature that the integral of a random quantum effect is itself a quantum effect. A left inverse Ω for Γ yields an integral representation, along the lines of the classical Riesz representation theorem for linear functionals on C(X), of certain (but not all) unital completely positive linear maps φ :C(X)⊗ B(H)rArr B(H). The extremal and C*-extremal points of POVM_H(X) are determined.

  5. 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

  6. 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.

  7. Classical simulation of quantum energy flow in biomolecules.

    PubMed

    Stock, Gerhard

    2009-03-20

    Based on a comparison of classical and quantum-mechanical perturbation theory, the validity of classical nonequilibrium molecular dynamics simulations to describe vibrational energy redistribution in biomolecules is studied. Adopting a small model peptide in aqueous solution as an example, the theory correctly predicts quantum correction factors that need to be applied to the results of classical simulations in order to match the correct quantum results.

  8. 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.

  9. Coarsening Measurement References and the Quantum-to-Classical Transition

    NASA Astrophysics Data System (ADS)

    Jeong, Hyunseok; Lim, Youngrong; Kim, M. S.

    2014-01-01

    We investigate the role of inefficiency in quantum measurements in the quantum-to-classical transition, and consistently observe the quantum-to-classical transition by coarsening the references of the measurements (e.g., when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer's ability to precisely control the measurement references.

  10. Coarsening measurement references and the quantum-to-classical transition.

    PubMed

    Jeong, Hyunseok; Lim, Youngrong; Kim, M S

    2014-01-10

    We investigate the role of inefficiency in quantum measurements in the quantum-to-classical transition, and consistently observe the quantum-to-classical transition by coarsening the references of the measurements (e.g., when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer's ability to precisely control the measurement references.

  11. 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.

  12. Mixed quantum states with variable Planck constant

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.

    2017-09-01

    Recent cosmological measurements tend to confirm that the fine structure constant α is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's constant h. The aim of this Letter is to explore some consequences of such a possible change of h for the pure and mixed states of quantum mechanics. Surprisingly enough it is found that not only is the purity of a state extremely sensitive to such changes, but that quantum states can evolve into classical states, and vice versa. A complete classification of such transitions is however not possible for the moment being because of yet unsolved mathematical difficulties related to the study of positivity properties of trace class operators.

  13. Transition to classical chaos in a coupled quantum system through continuous measurement

    SciTech Connect

    Ghose, Shohini; Alsing, Paul; Deutsch, Ivan; Bhattacharya, Tanmoy; Habib, Salman

    2004-05-01

    Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via a continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling, we find that classical dynamics emerges only when the position and spin actions are both large compared to ({Dirac_h}/2{pi}). These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result, it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin-(1/2) particle. When the conditions for classicality are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence, we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.

  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. Excited State Quantum-Classical Molecular Dynamics

    NASA Astrophysics Data System (ADS)

    Krstic, Predrag

    2005-05-01

    The development of a new theoretical, algorithmic, and computational framework is reported describing the corresponding excited state many-body dynamics by applying multiphysics described by classical equations of motion for nuclei and Hartree-Fock/Multi-Configuration Hartree-Fock and multiresolution techniques for solving the quantum part of the problem (i.e. the motion of the electrons). We primarily have in mind reactive and electron-transition dynamics which involves molecular clusters, containing hundreds of atoms, perturbed by a slow ionic/atomic/molecular projectile, with possible applications in plasma-surface interactions, cluster physics, chemistry and biotechnology. The validation of the developed technique is performed at three-body systems. Application to the transition dynamics in small carbon clusters and hydrocarbons perturbed by slow carbon ions resolves some long-standing issues in the ion-surface interactions in fusion tokamaks.

  16. 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

  17. Trotter-based simulation of quantum-classical dynamics.

    PubMed

    Kernan, Dónal Mac; Ciccotti, Giovanni; Kapral, Raymond

    2008-01-17

    Quantum rate processes in condensed phase systems are often computed by combining quantum and classical descriptions of the dynamics. An algorithm for simulating the quantum-classical Liouville equation, which describes the dynamics of a quantum subsystem coupled to a classical bath, is presented in this paper. The algorithm is based on a Trotter decomposition of the quantum-classical propagator, in conjunction with Monte Carlo sampling of quantum transitions, to yield a surface-hopping representation of the dynamics. An expression for the nonadiabatic propagator that is responsible for quantum transitions and associated bath momentum changes is derived in a form that is convenient for Monte Carlo sampling and exactly conserves the total energy of the system in individual trajectories. The expectation values of operators or quantum correlation functions can be evaluated by initial sampling of quantum states and use of quantum-classical Liouville dynamics for the time evolution. The algorithm is tested by calculations on the spin-boson model, for which exact quantum results are available, and is shown to reproduce the exact results for stronger nonadiabatic coupling and much longer times using fewer trajectories than other schemes for simulating quantum-classical Liouville dynamics.

  18. Quantum evaporation of flavor-mixed particles

    NASA Astrophysics Data System (ADS)

    Medvedev, Mikhail V.

    2014-03-01

    Particles whose propagation (mass) and interaction (flavor) bases are misaligned are mixed, e.g., neutrinos, quarks, Kaons, etc. We show that interactions (elastic scattering) of individual mass-eigenstates can result in their inter-conversions. Most intriguing and counter-intuitive implication of this process is a new process, which we refer to as the ``quantum evaporation.'' Consider a mixed particle trapped in a gravitational potential. If such a particle scatters off something (e.g., from another mixed particle) elastically from time to time, this particle (or both particles, respectively) can eventually escape to infinity with no extra energy supplied. That is as if a ``flavor-mixed satellite'' hauled along a bumpy road puts itself in space without a rocket, fuel, etc. Of course, the process at hand is entirely quantum and has no counterpart in classical mechanics. It also has nothing to do with tunneling or other known processes. We discuss some implications to the dark matter physics, cosmology and cosmic neutrino background. Supported by grant DOE grant DE-FG02-07ER54940 and NSF grant AST-1209665.

  19. Improved classical and quantum random access codes

    NASA Astrophysics Data System (ADS)

    Liabøtrø, O.

    2017-05-01

    A (quantum) random access code ((Q)RAC) is a scheme that encodes n bits into m (qu)bits such that any of the n bits can be recovered with a worst case probability p >1/2 . We generalize (Q)RACs to a scheme encoding n d -levels into m (quantum) d -levels such that any d -level can be recovered with the probability for every wrong outcome value being less than 1/d . We construct explicit solutions for all n ≤d/2m-1 d -1 . For d =2 , the constructions coincide with those previously known. We show that the (Q)RACs are d -parity oblivious, generalizing ordinary parity obliviousness. We further investigate optimization of the success probabilities. For d =2 , we use the measure operators of the previously best-known solutions, but improve the encoding states to give a higher success probability. We conjecture that for maximal (n =4m-1 ,m ,p ) QRACs, p =1/2 {1 +[(√{3}+1)m-1 ] -1} is possible, and show that it is an upper bound for the measure operators that we use. We then compare (n ,m ,pq) QRACs with classical (n ,2 m ,pc) RACs. We can always find pq≥pc , but the classical code gives information about every input bit simultaneously, while the QRAC only gives information about a subset. For several different (n ,2 ,p ) QRACs, we see the same trade-off, as the best p values are obtained when the number of bits that can be obtained simultaneously is as small as possible. The trade-off is connected to parity obliviousness, since high certainty information about several bits can be used to calculate probabilities for parities of subsets.

  20. 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.

  1. Proliferation of Observables and Measurement in Quantum-Classical Hybrids

    NASA Astrophysics Data System (ADS)

    Elze, Hans-Thomas

    2012-01-01

    Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM-CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

  2. 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.

  3. Clean Quantum and Classical Communication Protocols.

    PubMed

    Buhrman, Harry; Christandl, Matthias; Perry, Christopher; Zuiddam, Jeroen

    2016-12-02

    By how much must the communication complexity of a function increase if we demand that the parties not only correctly compute the function but also return all registers (other than the one containing the answer) to their initial states at the end of the communication protocol? Protocols that achieve this are referred to as clean and the associated cost as the clean communication complexity. Here we present clean protocols for calculating the inner product of two n-bit strings, showing that (in the absence of preshared entanglement) at most n+3 qubits or n+O(sqrt[n]) bits of communication are required. The quantum protocol provides inspiration for obtaining the optimal method to implement distributed cnot gates in parallel while minimizing the amount of quantum communication. For more general functions, we show that nearly all Boolean functions require close to 2n bits of classical communication to compute and close to n qubits if the parties have access to preshared entanglement. Both of these values are maximal for their respective paradigms.

  4. Clean Quantum and Classical Communication Protocols

    NASA Astrophysics Data System (ADS)

    Buhrman, Harry; Christandl, Matthias; Perry, Christopher; Zuiddam, Jeroen

    2016-12-01

    By how much must the communication complexity of a function increase if we demand that the parties not only correctly compute the function but also return all registers (other than the one containing the answer) to their initial states at the end of the communication protocol? Protocols that achieve this are referred to as clean and the associated cost as the clean communication complexity. Here we present clean protocols for calculating the inner product of two n -bit strings, showing that (in the absence of preshared entanglement) at most n +3 qubits or n +O (√{n }) bits of communication are required. The quantum protocol provides inspiration for obtaining the optimal method to implement distributed cnot gates in parallel while minimizing the amount of quantum communication. For more general functions, we show that nearly all Boolean functions require close to 2 n bits of classical communication to compute and close to n qubits if the parties have access to preshared entanglement. Both of these values are maximal for their respective paradigms.

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. 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

  10. Simulation of Pake doublet with classical spins and correspondence between the quantum and classical approaches

    NASA Astrophysics Data System (ADS)

    Henner, Victor K.; Klots, Andrey; Belozerova, Tatyana

    2016-12-01

    Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used to model spin systems. In this paper we show that a classical spins based approach can be used to describe the phenomena essentially quantum in nature such as of the Pake doublet.

  11. Experimental Blind Quantum Computing for a Classical Client

    NASA Astrophysics Data System (ADS)

    Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C.; Lu, Chao-Yang; Pan, Jian-Wei

    2017-08-01

    To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

  12. 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.

  13. Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems

    PubMed Central

    Cárdenas-López, F. A.; Allende, S.; Retamal, J. C.

    2017-01-01

    Classical to quantum decoherence transition, an issue existing for incoherent superposition of Bell-diagonal states is studied for three dimensional bipartite AB mixed quantum systems. Depending on the initial conditions, the dynamics of classical and quantum correlations can exhibit a sudden transition between classical to quantum decoherence. This result is calculated numerically by using entropic and geometric measures of correlations. An alternative explanation for this effect could be obtained by extending the bipartite A ⊗ B qutrit system to a pure tripartite A ⊗ B ⊗ C system. The freezing of classical correlations in AB is related to a freezing of the entanglement in the AC bipartition. PMID:28317916

  14. 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.

  15. Quantum and classical behavior in interacting bosonic systems

    SciTech Connect

    Hertzberg, Mark P.

    2016-11-21

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

  16. Quantum and classical behavior in interacting bosonic systems

    NASA Astrophysics Data System (ADS)

    Hertzberg, Mark P.

    2016-11-01

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

  17. On the correspondence between quantum and classical variational principles

    DOE PAGES

    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.

  18. Classical synchronization indicates persistent entanglement in isolated quantum systems.

    PubMed

    Witthaut, Dirk; Wimberger, Sandro; Burioni, Raffaella; Timme, Marc

    2017-04-12

    Synchronization and entanglement constitute fundamental collective phenomena in multi-unit classical and quantum systems, respectively, both equally implying coordinated system states. Here, we present a direct link for a class of isolated quantum many-body systems, demonstrating that synchronization emerges as an intrinsic system feature. Intriguingly, quantum coherence and entanglement arise persistently through the same transition as synchronization. This direct link between classical and quantum cooperative phenomena may further our understanding of strongly correlated quantum systems and can be readily observed in state-of-the-art experiments, for example, with ultracold atoms.

  19. Classical synchronization indicates persistent entanglement in isolated quantum systems

    NASA Astrophysics Data System (ADS)

    Witthaut, Dirk; Wimberger, Sandro; Burioni, Raffaella; Timme, Marc

    2017-04-01

    Synchronization and entanglement constitute fundamental collective phenomena in multi-unit classical and quantum systems, respectively, both equally implying coordinated system states. Here, we present a direct link for a class of isolated quantum many-body systems, demonstrating that synchronization emerges as an intrinsic system feature. Intriguingly, quantum coherence and entanglement arise persistently through the same transition as synchronization. This direct link between classical and quantum cooperative phenomena may further our understanding of strongly correlated quantum systems and can be readily observed in state-of-the-art experiments, for example, with ultracold atoms.

  20. Noise-enhanced classical and quantum capacities in communication networks.

    PubMed

    Caruso, Filippo; Huelga, Susana F; Plenio, Martin B

    2010-11-05

    The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. In particular, we find analytically and numerically the quantum and classical capacities for a large family of quantum channels and show that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics.

  1. 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.

  2. Quantum and classical parallelism in parity algorithms for ensemble quantum computers

    SciTech Connect

    Stadelhofer, Ralf; Suter, Dieter; Banzhaf, Wolfgang

    2005-03-01

    The determination of the parity of a string of N binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least N/2 oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor 2{sup k}, with k is a member of {l_brace}{l_brace}1,2,...,log{sub 2}(N/2{r_brace}{r_brace}, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.

  3. Embedding quantum into classical: contextualization vs conditionalization.

    PubMed

    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.

  4. Classical and quantum stability in putative landscapes

    NASA Astrophysics Data System (ADS)

    Dine, Michael

    2017-01-01

    Landscape analyses often assume the existence of large numbers of fields, N , with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N , eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N ; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. We consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.

  5. Classical and quantum stability in putative landscapes

    DOE PAGES

    Dine, Michael

    2017-01-18

    Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity.more » We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.« less

  6. Using Hilbert transform and classical chains to simulate quantum walks

    NASA Astrophysics Data System (ADS)

    Xiong, Daxing; Thiel, Felix; Barkai, Eli

    2017-08-01

    We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.

  7. 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.

  8. Functional methods underlying classical mechanics, relativity and quantum theory

    NASA Astrophysics Data System (ADS)

    Kryukov, A.

    2013-04-01

    The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.

  9. Studies in classical and quantum gravity

    NASA Astrophysics Data System (ADS)

    Maran, Suresh Kumar

    Advancing physics beyond its present status requires the unification of quantum field theory and gravity, This thesis focuses on non-perturbative approaches to the quantization of gravity. We explore generalizations, discover relationships between various ideas, develop problem solving methods, address the various issues that arise. The new ideas in this thesis are as follows. (1) In chapter nine we lay the foundation for the (n - 1) + 1 formulation of spin foam models in n dimensions. This work was motivated by a desire to relate spin foams to their canonical formulation. By foliating the underlying n-dimensional simplicial manifold using (n - 1)-dimensional simplicial hypersurfaces, the spin foam models are reformulated. We believe our work brings the spin foam models as close as possible to the canonical quantum formulation without introducing any approximations. (2) In chapter nine we present our progress in developing a rigorous 4D Lorentzian spin foam model starting from the 4D Lorentzian BF spin foam model and imposing the relevant constraints. We use the Gelfand-Naimarck theory of the unitary representations of the Lorentz group. We discuss the implementation of the Barrett-Crane constraints in this model. We derive an equation that the general Lorentzian spin foam model has to satisfy. (3) In chapter eleven we propose a canonical formulation of gravity with arbitrary foliations, discuss motivations behind it, and ideas related to it. We propose a generalization of the Ashtekar formalism in which the type of the foliation is included in the initial conditions. (4) In chapter seven we introduce a 3 + 1 formulation of Regge Calculus. We identify some of the geometrical structures associated with the Regge-Einstein equations. (5) In chapters three and four we have investigated generalizations of classical canonical theories to higher dimensions and to extended gauge groups aiming at unification. We heuristically analyze the associated constraints. In the

  10. Generic emergence of classical features in quantum Darwinism.

    PubMed

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

    2015-08-12

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

  11. 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.

  12. Quantum-classical Liouville dynamics in the mapping basis

    SciTech Connect

    Kim, Hyojoon; Nassimi, Ali; Kapral, Raymond

    2008-08-28

    The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in the mapping Hamiltonian basis for the quantum subsystem is derived. The resulting equation of motion, in conjunction with expressions for quantum expectation values in the mapping basis, provides another route to the computation of the nonadiabatic dynamics of observables that does not involve surface-hopping dynamics. The quantum-classical Liouville equation is exact for the spin-boson system. This well-known model is simulated using an approximation to the evolution equation in the mapping basis, and close agreement with exact quantum results is found.

  13. Quantum-classical Liouville dynamics in the mapping basis.

    PubMed

    Kim, Hyojoon; Nassimi, Ali; Kapral, Raymond

    2008-08-28

    The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in the mapping Hamiltonian basis for the quantum subsystem is derived. The resulting equation of motion, in conjunction with expressions for quantum expectation values in the mapping basis, provides another route to the computation of the nonadiabatic dynamics of observables that does not involve surface-hopping dynamics. The quantum-classical Liouville equation is exact for the spin-boson system. This well-known model is simulated using an approximation to the evolution equation in the mapping basis, and close agreement with exact quantum results is found.

  14. Fokker-Planck quantum master equation for mixed quantum-semiclassical dynamics.

    PubMed

    Ding, Jin-Jin; Wang, Yao; Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

    2017-01-14

    We revisit Caldeira-Leggett's quantum master equation representing mixed quantum-classical theory, but with limited applications. Proposed is a Fokker-Planck quantum master equation theory, with a generic bi-exponential correlation function description on semiclassical Brownian oscillators' environments. The new theory has caustic terms that bridge between the quantum description on primary systems and the semiclassical or quasi-classical description on environments. Various parametrization schemes, both analytical and numerical, for the generic bi-exponential environment bath correlation functions are proposed and scrutinized. The Fokker-Planck quantum master equation theory is of the same numerical cost as the original Caldeira-Leggett's approach but acquires a significantly broadened validity and accuracy range, as illustrated against the exact dynamics on model systems in quantum Brownian oscillators' environments, at moderately low temperatures.

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

    PubMed

    Hooft, Gerard 't

    2015-08-06

    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.

  16. 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).

  17. Quantum physics of classical waves in plasma

    NASA Astrophysics Data System (ADS)

    Dodin, I. Y.

    2012-10-01

    The Lagrangian approach to plasma wave physics is extended to a universal nonlinear theory which yields generic equations invariant with respect to the wave nature. The traditional understanding of waves as solutions of the Maxwell-Vlasov system is abandoned. Oscillations are rather treated as physical entities, namely, abstract vectors |ψ> in a specific Hilbert space. The invariant product <ψ|ψ> is the total action and has the sign of the oscillation energy. The action density is then an operator. Projections of the corresponding operator equation generate assorted wave kinetic equations; the nonlinear Wigner-Moyal equation is just one example and, in fact, may be more delicate than commonly assumed. The linear adiabatic limit of this classical theory leads to quantum mechanics in its general form. The action conservation theorem, together with its avatars such as Manley-Rowe relations, then becomes manifest and in partial equilibrium can modify statistical properties of plasma fluctuations. In the quasi-monochromatic limit geometrical optics (GO) is recovered and can as well be understood as a particular field theory in its own right. For linear waves, the energy-momentum equations, in both canonical and (often) kinetic form, then follow automatically, even without a reference to electromagnetism. Yet for waves in plasma the general GO Lagrangian is also derived explicitly, in terms of single-particle oscillation-center Hamiltonians. Applications to various plasma waves are then discussed with an emphasis on the advantages of an abstract theory. Specifically covered are nonlinear dispersion, dynamics, and stability of BGK modes, and also other wave transformations in laboratory and cosmological plasmas.

  18. 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.

  19. Hybrid annealing: Coupling a quantum simulator to a classical computer

    NASA Astrophysics Data System (ADS)

    Graß, Tobias; Lewenstein, Maciej

    2017-05-01

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

  20. 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.

  1. 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.

  2. Classical and quantum distinctions between weak and strong coupling

    NASA Astrophysics Data System (ADS)

    Rahimzadeh-Kalaleh Rodriguez, Said

    2016-03-01

    Coupled systems subject to dissipation exhibit two different regimes known as weak coupling and strong coupling. Two damped coupled harmonic oscillators (CHOs) constitute a model system where the key features of weak and strong coupling can be identified. Several of these features are common to classical and quantum systems, as a number of quantum-classical correspondences have shown. However, the condition defining the boundary between weak and strong coupling is distinct in classical and quantum formalisms. Here we describe the origin of two widely used definitions of strong coupling. Using a classical CHO model, we show that energy exchange cycles and avoided resonance crossings signal the onset of strong coupling according to one criterion. From the classical CHO model we derive a non-Hermitian Hamiltonian describing open quantum systems. Based on the analytic properties of the Hamiltonian, we identify the boundary between weak and strong coupling with a different feature: a non-Hermitian degeneracy known as the exceptional point. For certain parameter ranges the classical and quantum criterion for strong coupling coincide; for other ranges they do not. Examples of systems in strong coupling according to one or another criterion, but not both, are illustrated. The framework here presented is suitable for introducing graduate or advanced undegraduate students to the basic properties of strongly coupled systems, as well as to the similarities and subtle differences between classical and quantum descriptions of coupled dissipative systems.

  3. Classical to quantum correspondence in dissipative directed transport.

    PubMed

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

    2015-11-01

    We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏ(eff) values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results-obtained for the mean currents and asymptotic distributions only-and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

  4. Classical to quantum correspondence in dissipative directed transport

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

    We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏeff values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results—obtained for the mean currents and asymptotic distributions only—and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

  5. Comparisons of classical chemical dynamics simulations of the unimolecular decomposition of classical and quantum microcanonical ensembles.

    PubMed

    Manikandan, Paranjothy; Hase, William L

    2012-05-14

    Previous studies have shown that classical trajectory simulations often give accurate results for short-time intramolecular and unimolecular dynamics, particularly for initial non-random energy distributions. To obtain such agreement between experiment and simulation, the appropriate distributions must be sampled to choose initial coordinates and momenta for the ensemble of trajectories. If a molecule's classical phase space is sampled randomly, its initial decomposition will give the classical anharmonic microcanonical (RRKM) unimolecular rate constant for its decomposition. For the work presented here, classical trajectory simulations of the unimolecular decomposition of quantum and classical microcanonical ensembles, at the same fixed total energy, are compared. In contrast to the classical microcanonical ensemble, the quantum microcanonical ensemble does not sample the phase space randomly. The simulations were performed for CH(4), C(2)H(5), and Cl(-)---CH(3)Br using both analytic potential energy surfaces and direct dynamics methods. Previous studies identified intrinsic RRKM dynamics for CH(4) and C(2)H(5), but intrinsic non-RRKM dynamics for Cl(-)---CH(3)Br. Rate constants calculated from trajectories obtained by the time propagation of the classical and quantum microcanonical ensembles are compared with the corresponding harmonic RRKM estimates to obtain anharmonic corrections to the RRKM rate constants. The relevance and accuracy of the classical trajectory simulation of the quantum microcanonical ensemble, for obtaining the quantum anharmonic RRKM rate constant, is discussed.

  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. Surface hopping from the perspective of quantum-classical Liouville dynamics

    NASA Astrophysics Data System (ADS)

    Kapral, Raymond

    2016-12-01

    Fewest-switches surface hopping is studied in the context of quantum-classical Liouville dynamics. Both approaches are mixed quantum-classical theories that provide a way to describe and simulate the nonadiabatic quantum dynamics of many-body systems. Starting from a surface-hopping solution of the quantum-classical Liouville equation, it is shown how fewest-switches dynamics can be obtained by dropping terms that are responsible for decoherence and restricting the nuclear momentum changes that accompany electronic transitions to those events that occur between population states. The analysis provides information on some of the elements that are essential for the construction of accurate and computationally tractable algorithms for nonadiabatic processes.

  8. Experimental device-independent tests of classical and quantum dimensions

    NASA Astrophysics Data System (ADS)

    Ahrens, Johan; Badziag, Piotr; Cabello, Adán; Bourennane, Mohamed

    2012-08-01

    A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. The classical information encoded in a set of states is limited by the number of distinguishable states or classical dimension dc of the set. The sets used in quantum communication and information processing contain states that are neither identical nor distinguishable, and the quantum dimension dq of the set is the dimension of the Hilbert space spanned by these states. An important challenge is to assess the (classical or quantum) dimension of a set of states in a device-independent way, that is, without referring to the internal working of the device generating the states. Here we experimentally test dimension witnesses designed to efficiently determine the minimum dimension of sets of (three or four) photonic states from the correlations originated from measurements on them, and distinguish between classical and quantum sets of states.

  9. Quantum and classical operational complementarity for single systems

    SciTech Connect

    Luis, Alfredo

    2005-07-15

    We investigate duality relations between conjugate observables after measurements performed on a single realization of the system. The application of standard inference methods implies the existence of duality relations for single systems when using classical as well as quantum physics.

  10. Simulating all nonsignaling correlations via classical or quantum theory with negative probabilities.

    PubMed

    Al-Safi, Sabri W; Short, Anthony J

    2013-10-25

    Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the nonsignaling condition. We show that any such distribution can be obtained from classical or quantum theory by relaxing positivity constraints on either the mixed state shared by the parties or the local functions that generate measurement outcomes. Our results apply to generic nonsignaling correlations, but in particular they yield two distinct quasiclassical models for quantum correlations.

  11. Quantum nonlocality and the end of classical spacetime

    NASA Astrophysics Data System (ADS)

    Banerjee, Shreya; Bera, Sayantani; Singh, Tejinder P.

    2016-07-01

    Quantum nonlocal correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that spacetime is fundamentally noncommutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying noncommutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary spacetime geometry. However, measurement on an entangled state can be correctly described only in the underlying noncommutative spacetime, where there is no causality violation, nor a spooky action at a distance.

  12. Line mixing effects in isotropic Raman spectra of pure N2: a classical trajectory study.

    PubMed

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

    2014-11-14

    Line mixing effects in the Q branch of pure N2 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 N2 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.

  13. Line mixing effects in isotropic Raman spectra of pure N2: A classical trajectory study

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

    Line mixing effects in the Q branch of pure N2 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 N2 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. Genuine quantum and classical correlations in multipartite systems.

    PubMed

    Giorgi, Gian Luca; Bellomo, Bruno; Galve, Fernando; Zambrini, Roberta

    2011-11-04

    Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.

  15. 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.

  16. The Classical Scattering of Waves: Some Analogies with Quantum Scattering

    DTIC Science & Technology

    1992-01-01

    Code . Approved for public release; distribution is unlimited. 13. Abstract (Maximum 200 words). The scattering of waves in classical physics and quantum...both areas. 92-235222’ 14. Subject Terms. IS. Number of Page. Acoustic scattering , shallow water, waveguide propagation . 27 16. Price Code . 17. Security...Numbers. The Classical Scattering of Waves: Some Analogies with Quantum Scattering Contract ,~~ ~ -V ,~Pom Element NO- 0601153N 6. Author(s). t

  17. Efficient classical simulation of optical quantum information circuits.

    PubMed

    Bartlett, Stephen D; Sanders, Barry C

    2002-11-11

    We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This simulatability result places powerful constraints on the capability to realize exponential quantum speedups as well as on inducing an optical nonlinear transformation via linear optics, photodetection-based measurement, and classical feedforward of measurement results, optimal cloning, and a wide range of other processes.

  18. 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.

    PubMed

    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 Schrodinger 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

  19. 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.

  20. Isochronous classical systems and quantum systems with equally spaced spectra

    NASA Astrophysics Data System (ADS)

    Cariñena, J. F.; Perelomov, A. M.; Rañada, M. F.

    2007-11-01

    We study isoperiodic classical systems, what allows us to find the classical isochronous systems, i.e. having a period independent of the energy. The corresponding quantum analog, systems with an equally spaced spectrum are analysed by looking for possible creation-like differential operators. The harmonic oscillator and the isotonic oscillator are the two main essentially unique examples of such situation.

  1. Chaos and the Classical Limit of Quantum Systems

    NASA Astrophysics Data System (ADS)

    Hogg, T.; Huberman, B. A.

    1984-10-01

    We discuss the question of whether experiments can be designed to test the existence of quantum chaos. In particular, we show that high energies are not sufficient to guarantee that an initially localized wave packet will behave classically for long times. We present computer simulations illustrating these ideas, and comment on whether experiments can be designed to observe quantum chaos.

  2. Reversing quantum dynamics with near-optimal quantum and classical fidelity

    NASA Astrophysics Data System (ADS)

    Barnum, H.; Knill, E.

    2002-05-01

    We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the "noise" dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.

  3. Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

    NASA Astrophysics Data System (ADS)

    Mantri, Atul; Demarie, Tommaso F.; Menicucci, Nicolas C.; Fitzsimons, Joseph F.

    2017-07-01

    Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

  4. 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.

  5. Quantum-Classical Correspondence of Shortcuts to Adiabaticity

    NASA Astrophysics Data System (ADS)

    Okuyama, Manaka; Takahashi, Kazutaka

    2017-04-01

    We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.

  6. 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.

  7. Faithful actions of locally compact quantum groups on classical spaces

    NASA Astrophysics Data System (ADS)

    Goswami, Debashish; Roy, Sutanu

    2017-03-01

    We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

  8. Faithful actions of locally compact quantum groups on classical spaces

    NASA Astrophysics Data System (ADS)

    Goswami, Debashish; Roy, Sutanu

    2017-07-01

    We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

  9. Quantum versus classical dynamics in the optical centrifuge

    NASA Astrophysics Data System (ADS)

    Armon, Tsafrir; Friedland, Lazar

    2017-09-01

    The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

  10. Efficient classical simulation of continuous variable quantum information processes.

    PubMed

    Bartlett, Stephen D; Sanders, Barry C; Braunstein, Samuel L; Nemoto, Kae

    2002-03-04

    We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

  11. Classical-quantum arbitrarily varying wiretap channel: common randomness assisted code and continuity

    NASA Astrophysics Data System (ADS)

    Boche, Holger; Cai, Minglai; Deppe, Christian; Nötzel, Janis

    2017-01-01

    We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels. Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legitimate receiver and varies arbitrarily from the sender to the eavesdropper. We examine when the secrecy capacity is a continuous function of the system parameters as an application and show that resources, e.g., having access to a perfect copy of the outcome of a random experiment, can guarantee continuity of the capacity function of arbitrarily varying classical-quantum wiretap channels.

  12. 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.

  13. 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.

  14. The ambiguity of simplicity in quantum and classical simulation

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

    A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the ;elegance; of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

  15. 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.

  16. 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.

  17. 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.

  18. Information security: from classical to quantum

    NASA Astrophysics Data System (ADS)

    Barnett, Stephen M.; Brougham, Thomas

    2012-09-01

    Quantum cryptography was designed to provide a new approach to the problem of distributing keys for private-key cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon.

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

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

  20. 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.

  1. 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.

  2. Quantum correction to classical gravitational interaction between two polarizable objects

    NASA Astrophysics Data System (ADS)

    Wu, Puxun; Hu, Jiawei; Yu, Hongwei

    2016-12-01

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

  3. Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit

    SciTech Connect

    Takeoka, Masahiro; Fujiwara, Mikio; Mizuno, Jun; Sasaki, Masahide

    2004-05-01

    Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques.

  4. Quantum Mechanics as a Statistical Description of Classical Electrodynamics

    NASA Astrophysics Data System (ADS)

    Knoll, Yehonatan

    2017-07-01

    It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a classical ontology, can be traced to the fact that classical electrodynamics of interacting particles has never been given a consistent definition. Once this is done, our conjecture follows rather naturally, including a purely classical explanation of photon related phenomena. Our analysis entirely rests on the block-universe view entailed by relativity theory.

  5. Classical and quantum dynamics of the sphere

    NASA Astrophysics Data System (ADS)

    Lasukov, Vladimir; Moldovanova, Evgeniia; Abdrashitova, Maria; Malik, Hitendra; Gorbacheva, Ekaterina

    2016-07-01

    In Minkowski space, there has been developed the mathematic quantum model of the real particle located on the sphere evolving owing to the negative pressure inside the sphere. The developed model is analogous to the geometrodynamic model of the Lemaitre-Friedmann primordial atom in superspace-time, whose spatial coordinate is the scale factor functioning as a radial coordinate. There is a formulation of quantum geometrodynamics in which the spatial coordinate is an offset of the scale factor and wave function at the same time. With the help of the Dirac procedure for extracting the root from the Hamiltonian operator we have constructed a Dirac quantum dynamics of the sphere with fractional spin.

  6. Quantum transition probabilities and classical Fourier harmonics

    NASA Astrophysics Data System (ADS)

    Fedak, William

    2002-03-01

    A quantum dot is an atomic-like system consisting of a semiconductor nanoparticle surrounded by an insulator. When an electron in the valence band of the semiconductor becomes excited, the electron-hole pair that is created (called an exiton) acts much like a hydrogen atom. Investigations have demonstrated the potential application of quantum dots for optical switching and optical memory. A model of a truncated pyramidal InAs quantum dot in an InP matrix will be presented and described. The model uses a single band envelope theory that accurately describes the truncated pyramidal shape of the dot. The matrix representation of the Hamiltonian is calculated in a basis consisting of kinetic energy eigenfunctions that vanish on the surface of a cube containing the dot. The eigenvalues of this matrix are the energy levels. These results will then be compared with photoluminescence measurements of energy levels conducted at the Microelectronics-Photonics Center at the University of Arkansas - Fayetteville

  7. A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. I. A test of IBC model for the relaxation of a nonpolar solute in nonpolar solvent at high density.

    PubMed

    Sato, Masahiro; Okazaki, Susumu

    2005-09-22

    In order to investigate vibrational relaxation mechanism in condensed phase, a series of mixed quantum-classical molecular dynamics calculations have been executed for nonpolar solute in nonpolar solvent and polar solute in polar solvent. In the first paper (Paper I), relaxation mechanism of I2 in Ar, where Lennard-Jones force is predominant in the interaction, is investigated as a function of density and temperature, focusing our attention on the isolated binary collision (IBC) model. The model was originally established for the relaxation in gas phase. A key question, here, is "can we apply the IBC model to the relaxation in the high-density fluid?" Analyzing the trajectory of solvent molecule as well as its interaction with the solute, we found that collisions between them may be defined clearly even in the high-density fluid. Change of the survival probability of the vibrationally first excited state on collision was traced. The change caused by collisions with a particular solvent molecule was also traced together with the interaction between them. Each collision makes a contribution to the relaxation by a stepwise change in the probability. The analysis clearly shows that the relaxation is caused by collisions even in the high-density fluid. The difference between stepwise relaxation and the continuous one found for the total relaxation in the low-density fluid and in the high-density one, respectively, was clarified to come from just the difference in frequency of the collision. The stronger the intensity of the collision is, the greater the relaxation caused by the collision is. Further, the shorter the collision time is, the greater the resultant relaxation is. The discussion is followed by the succeeding paper (Paper II), where we report that molecular mechanism of the relaxation of a polar molecule in supercritical water is significantly different from that assumed in the IBC model despite that the density dependence of the relaxation rate showed a

  8. 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.

  9. Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston.

    PubMed

    Patra, Ayoti; Jarzynski, Christopher

    2017-04-20

    Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian, ĤCD, is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian, HCD, ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions, or translations of the system. Here we investigate an example of a non-scale-invariant system, a tilted piston. We solve exactly for the classical counterdiabatic Hamiltonian, HCD(q, p, t), which we then quantize to obtain a Hermitian operator, ĤCD(t). Using numerical simulations, we find that ĤCD effectively suppresses nonadiabatic excitations under rapid driving. These results offer a proof of principle, beyond the special case of scale-invariant driving, that quantum shortcuts to adiabaticity can successfully be constructed from their classical counterparts.

  10. Quantum models as classical cellular automata

    NASA Astrophysics Data System (ADS)

    Elze, Hans-Thomas

    2017-05-01

    A synopsis is offered of the properties of discrete and integer-valued, hence “natural”, cellular automata (CA). A particular class comprises the “Hamiltonian CA” with discrete updating rules that resemble Hamilton’s equations. The resulting dynamics is linear like the unitary evolution described by the Schrödinger equation. Employing Shannon’s Sampling Theorem, we construct an invertible map between such CA and continuous quantum mechanical models which incorporate a fundamental discreteness scale l. Consequently, there is a one-to-one correspondence of quantum mechanical and CA conservation laws. We discuss the important issue of linearity, recalling that nonlinearities imply nonlocal effects in the continuous quantum mechanical description of intrinsically local discrete CA - requiring locality entails linearity. The admissible CA observables and the existence of solutions of the l-dependent dispersion relation for stationary states are mentioned, besides the construction of multipartite CA obeying the Superposition Principle. We point out problems when trying to match the deterministic CA here to those envisioned in ‘t Hooft’s CA Interpretation of Quantum Mechanics.

  11. 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.

  12. 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.

  13. Quantum-classical transition and quantum activation of ratchet currents in the parameter space.

    PubMed

    Beims, M W; Schlesinger, M; Manchein, C; Celestino, A; Pernice, A; Strunz, W T

    2015-05-01

    The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero-temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed based on quantum, semiclassical, and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

  14. Quantum mechanics can reduce the complexity of classical models.

    PubMed

    Gu, Mile; Wiesner, Karoline; Rieper, Elisabeth; Vedral, Vlatko

    2012-03-27

    Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. Here we show how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.

  15. 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.

  16. Quantum and classical dynamics of Langmuir wave packets.

    PubMed

    Haas, F; Shukla, P K

    2009-06-01

    The quantum Zakharov system in three spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws, are derived. In the adiabatic and semiclassical cases, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schrödinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time dependence of the Gaussian-shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation. The possibility of laboratory tests in the next generation intense laser-solid plasma compression experiment is discussed.

  17. Electromagnetically induced classical and quantum Lau effect

    NASA Astrophysics Data System (ADS)

    Qiu, Tianhui; Yang, Guojian; Xiong, Jun; Xu, Deqin

    2016-07-01

    We present two schemes of Lau effect for an object, an electromagnetically induced grating generated based on the electromagnetically induced effect. The Lau interference pattern is detected either directly in the way of the traditional Lau effect measurement with a classical thermal light being the imaging light, or indirectly and nonlocally in the way of two-photon coincidence measurement with a pair of entangled photons being the imaging light.

  18. 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

  19. Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

    NASA Astrophysics Data System (ADS)

    Malpetti, Daniele; Roscilde, Tommaso

    2017-02-01

    The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical

  20. New mixed quantum/semiclassical propagation method

    NASA Astrophysics Data System (ADS)

    Antoniou, Dimitri; Gelman, David; Schwartz, Steven D.

    2007-05-01

    The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.

    1. Experimental device-independent tests of classical and quantum entropy

      NASA Astrophysics Data System (ADS)

      Zhu, Feng; Zhang, Wei; Chen, Sijing; You, Lixing; Wang, Zhen; Huang, Yidong

      2016-12-01

      In quantum information processing, it is important to witness the entropy of the message in the device-independent way which was proposed recently [R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015), 10.1103/PhysRevLett.115.110501]. In this paper, we theoretically obtain the minimal quantum entropy for three widely used linear dimension witnesses, which is considered "a difficult question." Then we experimentally test the classical and quantum entropy in a device-independent manner. The experimental results agree well with the theoretical analysis, demonstrating that entropy is needed in quantum systems that is lower than the entropy needed in classical systems with the given value of the dimension witness.

    2. Classical counterparts of quantum attractors in generic dissipative systems.

      PubMed

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

      2017-06-01

      In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.

    3. Gating Classical Information Flow via Equilibrium Quantum Phase Transitions.

      PubMed

      Banchi, Leonardo; Fernández-Rossier, Joaquín; Hirjibehedin, Cyrus F; Bose, Sougato

      2017-04-07

      The development of communication channels at the ultimate size limit of atomic scale physical dimensions will make the use of quantum entities an imperative. In this regime, quantum fluctuations naturally become prominent and are generally considered to be detrimental. Here, we show that for spin-based information processing, these fluctuations can be uniquely exploited to gate the flow of classical binary information across a magnetic chain in thermal equilibrium. Moreover, this information flow can be controlled with a modest external magnetic field that drives the system through different many-body quantum phases in which the orientation of the final spin does or does not reflect the orientation of the initial input. Our results are general for a wide class of anisotropic spin chains that act as magnetic cellular automata and suggest that quantum phase transitions play a unique role in driving classical information flow at the atomic scale.

    4. Classical hallmarks of macroscopic quantum wave function propagation

      NASA Astrophysics Data System (ADS)

      Feagin, James M.; Briggs, John S.

      2017-08-01

      The precise connection between quantum wave functions and the underlying classical trajectories often is presented rather vaguely by practitioners of quantum mechanics. Here we demonstrate, with simple examples, that the imaging theorem (IT) based on the semiclassical propagator provides a precise connection. Wave functions are preserved out to macroscopic distances but the variables, position and momentum of these functions describe classical trajectories. We show that the IT, based on an overtly time-dependent picture, provides a strategy alternative to standard scattering theory with which to compare experimental results to theory.

    5. Revivals and classical-motion bases of quantum wave packets

      NASA Astrophysics Data System (ADS)

      Aronstein, David L.

      This thesis explores the boundary between classical and quantum mechanics by studying wave packets, coherent superpositions of the stationary states of a quantum system. Such wave packets travel as localized entities along the trajectories predicted by classical mechanics for small windows of time before they spread out and decay away. Our investigations focus on two central issues---the revivals of the shape and classical motion of these wave packets that occur long after their initial decay, and the classical-motion bases that describe the quantum wavefunction in terms of constitutive objects that move classically. We study the infinite square-well potential, a simple model of complete confinement in a one-dimensional interval. The quantum motion seen in this potential is compared with classical models of a particle bouncing between two walls and of a wave traveling along a stretched string with both ends secured. We uncover a remarkable wave-motion basis, with which the wavefunction at any moment in time can be decomposed into a sum of distinct wave propagations of the initial quantum wavefunction in the classical wave equation. These results are extended to the finite square-well potential and we show how the wave-motion basis can be reconciled with the seemingly disparate theory of revivals for highly excited quantum wave packets. We explore the commonalities of the quantum revivals seen in a wide variety of systems by developing a mathematical formalism called phase-difference equations. These equations connect physical models for revivals with the subsequent prediction of revival times in a general way and offer a comprehensive "calculus" for understanding revival phenomena. We apply this calculus to several examples to demonstrate its power and versatility. Using a recently developed semiclassical basis for quantum states, we explore the radial wave packets of the hydrogen atom. Viewed in the semiclassical basis, the revivals of these wave packets are shown

    6. 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.

    7. Classical Fractals and Quantum Chaos in Ultracold Dipolar Collisions.

      PubMed

      Yang, B C; Pérez-Ríos, Jesús; Robicheaux, F

      2017-04-14

      We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix. The nearest-eigenphase-spacing statistics have an intermediate behavior between the Poisson and the Wigner-Dyson distributions. The character of the distribution can be controlled by changing an effective Planck constant or the dipole moment. The degree of quantum chaos shows a good correspondence with the overall average of the classical scattering function. The results presented here also provide helpful insights for understanding the role of the inherent dipole-dipole interaction in the currently ongoing experiments on ultracold collisions of highly magnetic atoms.

    8. Interpretation of quantum and classical angular momentum polarization moments.

      PubMed

      de Miranda, Marcelo P; Aoiz, F Javier

      2004-08-20

      This Letter presents a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization. The results involve an "uncertainty broadening" term that directly expresses the restrictions imposed by the uncertainty principle. It is argued that neglect of this term can lead to error in the interpretation of theoretical or experimental angular momentum polarization data. Functions that take the uncertainty broadening into account, appropriate for use in quantum or quasiclassical descriptions of spatial distributions of angular momenta, are defined.

    9. 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?

    10. Quantum-classical path integral. II. Numerical methodology

      NASA Astrophysics Data System (ADS)

      Lambert, Roberto; Makri, Nancy

      2012-12-01

      We present a quantum-classical methodology for propagating the density matrix of a system coupled to a polyatomic (large molecular or solvent) environment. The system is treated via a full path integral, while the dynamics of the environment is approximated in terms of classical trajectories. We obtain quantum-classical path integral (QCPI) expressions in which the trajectories can undergo transitions to other quantum states at regular time intervals, but the cumulative probability of these transitions is governed by the local strength of the state-to-state coupling as well as the magnitude of the solvent reorganization energy. If quantum effects in the coordinates of the environment are relatively weak, an inexpensive random hop approximation leads to accurate descriptions of the dynamics. We describe a systematic iterative scheme for including quantum mechanical corrections for the solvent by gradually accounting for nonlocal "quantum memory" effects. As the length of the included memory approaches the decoherence time of the environment, the iterative QCPI procedure converges to the full QCPI result. The methodology is illustrated with application to dissipative symmetric and asymmetric two-level systems.

    11. Smoothed quantum-classical states in time-irreversible hybrid dynamics

      NASA Astrophysics Data System (ADS)

      Budini, Adrián A.

      2017-09-01

      We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

    12. On the singular limit of the quantum-classical molecular dynamics model

      SciTech Connect

      Bornemann, F.A. . Center of Mathematical Sciences); Schuette, C. )

      1999-05-01

      In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by means of classical mechanics but describe an important, small portion of the system by means of quantum mechanics. A particularly extensively used model, the quantum-classical molecular dynamics (WCMD) model, consists of a singularity perturbed Schroedinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born-Oppenheimer model of quantum theory--provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. The authors will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a funnel consisting of infinitely many trajectories.

    13. Coulomb crystallization in classical and quantum systems

      NASA Astrophysics Data System (ADS)

      Bonitz, Michael

      2007-11-01

      Coulomb crystallization occurs in one-component plasmas when the average interaction energy exceeds the kinetic energy by about two orders of magnitude. A simple road to reach such strong coupling consists in using external confinement potentials the strength of which controls the density. This has been succsessfully realized with ions in traps and storage rings and also in dusty plasma. Recently a three-dimensional spherical confinement could be created [1] which allows to produce spherical dust crystals containing concentric shells. I will give an overview on our recent results for these ``Yukawa balls'' and compare them to experiments. The shell structure of these systems can be very well explained by using an isotropic statically screened pair interaction. Further, the thermodynamic properties of these systems, such as the radial density distribution are discussed based on an analytical theory [3]. I then will discuss Coulomb crystallization in trapped quantum systems, such as mesoscopic electron and electron hole plasmas in coupled layers [4,5]. These systems show a very rich correlation behavior, including liquid and solid like states and bound states (excitons, biexcitons) and their crystals. On the other hand, also collective quantum and spin effects are observed, including Bose-Einstein condensation and superfluidity of bound electron-hole pairs [4]. Finally, I consider Coulomb crystallization in two-component neutral plasmas in three dimensions. I discuss the necessary conditions for crystals of heavy charges to exist in the presence of a light component which typically is in the Fermi gas or liquid state. It can be shown that their exists a critical ratio of the masses of the species of the order of 80 [5] which is confirmed by Quantum Monte Carlo simulations [6]. Familiar examples are crystals of nuclei in the core of White dwarf stars, but the results also suggest the existence of other crystals, including proton or α-particle crystals in dense matter

    14. Simultaneous classical communication and quantum key distribution using continuous variables*

      NASA Astrophysics Data System (ADS)

      Qi, Bing

      2016-10-01

      Presently, 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 show 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.

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

      SciTech Connect

      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 show 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.

    16. 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.

    17. Quantum density fluctuations in classical liquids.

      PubMed

      Ford, L H; Svaiter, N F

      2009-01-23

      We discuss the density fluctuations of a fluid due to zero point motion, assuming a linear dispersion relation. We argue that density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We calculate the differential cross section for light scattering by the zero point density fluctuations, and find a result proportional to the fifth power of the light frequency. We give some estimates of the relative magnitude of this effect compared to the scattering by thermal density fluctuations, and find that it can be of the order 13% for liquid neon at optical frequencies. This relative magnitude is proportional to frequency and inversely proportional to temperature. Although the scattering by zero point density fluctuation is small, it may be observable.

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

      PubMed

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

      2012-05-08

      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. Nilpotent representations of classical quantum groups at roots of unity

      SciTech Connect

      Abe, Yuuki; Nakashima, Toshiki

      2005-11-01

      Properly specializing the parameters in 'Schnizer modules', for types A,B,C, and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.

    20. 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…

    1. Equivalent emergence of time dependence in classical and quantum mechanics

      NASA Astrophysics Data System (ADS)

      Briggs, John S.

      2015-05-01

      Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes another part. Translating this scenario into both classical and quantum mechanics allows a transition to be made from a time-independent mechanics for the closed composite to a time-dependent description of the observed part alone. The use of Hamilton-Jacobi theory yields a very close parallel between the derivations in classical and quantum mechanics. The time-dependent equations, Hamilton-Jacobi or Schrödinger, appear as approximations since no observed system is truly closed. The quantum case has an additional feature in the condition that the observing environment must become classical in order to define a real classical time variable. This condition leads to a removal of entanglement engendered by the interaction between the observed system and the observing environment. Comparison is made to the similar emergence of time in quantum gravity theory.

    2. Spectral properties of circulant positive maps: classical versus quantum

      NASA Astrophysics Data System (ADS)

      Chruściński, Dariusz

      2015-06-01

      A class of circulant stochastic matrices and positive maps in matrix algebras displaying circulant structure is analyzed. It is shown how the spectral properties of matrices and linear maps are related to positivity conditions. An interesting interplay between the classical and quantum case is revealed. Dedicated to Margarita and Volodia Man’ko for their 150th birthday.

    3. 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…

    4. On the classical capacity of quantum Gaussian channels

      NASA Astrophysics Data System (ADS)

      Lupo, Cosmo; Pirandola, Stefano; Aniello, Paolo; Mancini, Stefano

      2011-02-01

      The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.

    5. Autonomous quantum to classical transitions and the generalized imaging theorem

      SciTech Connect

      Briggs, John S.; Feagin, James M.

      2016-03-16

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

    6. Quantum and classical limits in a potential step

      NASA Astrophysics Data System (ADS)

      Dib, Claudio O.; Orellana, Oscar

      2017-07-01

      We have often found among many of our students and colleagues the common idea that the mathematical expression for a physical quantity that is essentially of quantum nature must contain a dependence on ℏ. Conversely, a phenomenon described by classical physics should contain no explicit reference to ℏ. However, the problem of a particle encountering a discontinuous potential step, which is one of the simplest examples in quantum mechanics, contradicts this common thought: even when the particle carries enough kinetic energy to go across the step, the resulting expression for the reflection probability is non-zero—a purely quantum phenomenon—and yet it contains no reference to ℏ. We show that the absence of ℏ in this purely quantum expression is due to the idealised limit in which the potential rises sharply at a single position, thus losing any reference to a length dimension in the problem. To address the correct classical limit of the phenomenon we first regularise the discontinuity in the potential by taking a continuous linearly rising function over a distance a. We show that the correct classical limit, which is when no reflection occurs, is obtained for large values of a, not for vanishing a. The latter actually corresponds to a purely quantum case, albeit in a limiting case of a discontinuously abrupt change in the potential at a single point in space.

    7. 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.

    8. Positive Wigner functions render classical simulation of quantum computation efficient.

      PubMed

      Mari, A; Eisert, J

      2012-12-07

      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.

    9. Minimal classical communication and measurement complexity for quantum information splitting

      NASA Astrophysics Data System (ADS)

      Zhang, Zhan-jun; Cheung, Chi-Yee

      2008-01-01

      We present two quantum information splitting schemes using respectively tripartite GHZ and asymmetric W states as quantum channels. We show that if the secret state is chosen from a special ensemble and known to the sender (Alice), then she can split and distribute it to the receivers Bob and Charlie by performing only a single-qubit measurement and broadcasting a one-cbit message. It is clear that no other schemes could possibly achieve the same goal with simpler measurement and less classical communication. In comparison, existing schemes work for arbitrary quantum states which need not be known to Alice; however she is required to perform a two-qubit Bell measurement and communicate a two-cbit message. Hence there is a trade-off between flexibility and measurement complexity plus classical resource. In situations where our schemes are applicable, they will greatly reduce the measurement complexity and at the same time cut the communication overhead by one half.

    10. The simplified Fermi accelerator in classical and quantum mechanics

      NASA Astrophysics Data System (ADS)

      Karner, Gunther

      1994-11-01

      We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the "free" Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth "wall oscillations" (typically of C 2 type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that "random boundary conditions" are necessary to model a quantum analog to the chaotic regime of the classical accelerator.

    11. Can fluctuations of classical random field produce quantum averages?

      NASA Astrophysics Data System (ADS)

      Khrennikov, Andrei

      2009-08-01

      Albert Einstein did not believe in completeness of QM. He dreamed of creation of prequantum classical statistical mechanics such that QM will be reproduced as its approximation. He also dreamed of total exclusion of corpuscules from the future model. Reality of Einstein's dream was pure fields' reality. Recently I made his dream come true in the form of so called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., electromagnetic field (instead of photon), electron field or neutron field. In this paper we generalize PCSFT to composite quantum system. It is well known that in QM, unlike classical mechanics, the state of a composite system is described by the tensor product of state spaces for its subsystems. In PCSFT one can still use Cartesian product, but state spaces are spaces of classical fields (not particles). In particular, entanglement is nothing else than correlation of classical random fields, cf. again Einstein. Thus entanglement was finally demystified.

    12. Decoherence control in open quantum systems via classical feedback

      NASA Astrophysics Data System (ADS)

      Ganesan, Narayan; Tarn, Tzyh-Jong

      2007-03-01

      In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations.

    13. Quantum probes for the spectral properties of a classical environment

      NASA Astrophysics Data System (ADS)

      Benedetti, Claudia; Buscemi, Fabrizio; Bordone, Paolo; Paris, Matteo G. A.

      2014-03-01

      We address the use of simple quantum probes for the spectral characterization of classical noisy environments. In our scheme a qubit interacts with a classical stochastic field describing environmental noise and is then measured after a given interaction time in order to estimate the characteristic parameters of the noise. In particular, we address estimation of the spectral parameters of two relevant kinds of non-Gaussian noise: random telegraph noise with a Lorentzian spectrum and colored noise with a 1/fα spectrum. We analyze in detail the estimation precision achievable by quantum probes and prove that population measurement on the qubit is optimal for noise estimation in both cases. We also evaluate the optimal interaction times for the quantum probe, i.e., the values maximizing the quantum Fisher information (QFI) and the quantum signal-to-noise ratio. For random telegraph noise the QFI is inversely proportional to the square of the switching rate, meaning that the quantum signal-to-noise ratio is constant and thus the switching rate may be uniformly estimated with the same precision in its whole range of variation. For colored noise, the precision achievable in the estimation of "color," i.e., of the exponent α, strongly depends on the structure of the environment, i.e., on the number of fluctuators describing the classical environment. For an environment modeled by a single random fluctuator estimation is more precise for pink noise, i.e., for α =1, whereas by increasing the number of fluctuators, the quantum signal-to-noise ratio has two local maxima, with the largest one drifting towards α =2, i.e., brown noise.

    14. 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.

    15. Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

      NASA Astrophysics Data System (ADS)

      Khrennikov, Andrei

      2017-02-01

      The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.

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

      NASA Astrophysics Data System (ADS)

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

      2016-02-01

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

    17. Autonomous quantum to classical transitions and the generalized imaging theorem

      DOE PAGES

      Briggs, John S.; Feagin, James M.

      2016-03-16

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

    18. 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.

    19. 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.

    20. 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.

    1. 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

    2. 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.

    3. 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

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

      PubMed Central

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

      2015-01-01

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

    5. 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.

    6. 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.

    7. Observing quantum chaos with noisy measurements and highly mixed states

      NASA Astrophysics Data System (ADS)

      Ralph, Jason F.; Jacobs, Kurt; Everitt, Mark J.

      2017-01-01

      A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to ℏ . While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system.

    8. Classical and quantum mechanics of diatomic molecules in tilted fields

      NASA Astrophysics Data System (ADS)

      Arango, Carlos A.; Kennerly, William W.; Ezra, Gregory S.

      2005-05-01

      We investigate the classical and quantum mechanics of diatomic molecules in noncollinear (tilted) static electric and nonresonant linearly polarized laser fields. The classical diatomic in tilted fields is a nonintegrable system, and we study the phase space structure for physically relevant parameter regimes for the molecule KCl. While exhibiting low-energy (pendular) and high-energy (free-rotor) integrable limits, the rotor in tilted fields shows chaotic dynamics at intermediate energies, and the degree of classical chaos can be tuned by changing the tilt angle. We examine the quantum mechanics of rotors in tilted fields. Energy-level correlation diagrams are computed, and the presence of avoided crossings quantified by the study of nearest-neighbor spacing distributions as a function of energy and tilting angle. Finally, we examine the influence of classical periodic orbits on rotor wave functions. Many wave functions in the tilted field case are found to be highly nonseparable in spherical polar coordinates. Localization of wave functions in the vicinity of classical periodic orbits, both stable and unstable, is observed for many states.

    9. Classical and quantum mechanics of diatomic molecules in tilted fields.

      PubMed

      Arango, Carlos A; Kennerly, William W; Ezra, Gregory S

      2005-05-08

      We investigate the classical and quantum mechanics of diatomic molecules in noncollinear (tilted) static electric and nonresonant linearly polarized laser fields. The classical diatomic in tilted fields is a nonintegrable system, and we study the phase space structure for physically relevant parameter regimes for the molecule KCl. While exhibiting low-energy (pendular) and high-energy (free-rotor) integrable limits, the rotor in tilted fields shows chaotic dynamics at intermediate energies, and the degree of classical chaos can be tuned by changing the tilt angle. We examine the quantum mechanics of rotors in tilted fields. Energy-level correlation diagrams are computed, and the presence of avoided crossings quantified by the study of nearest-neighbor spacing distributions as a function of energy and tilting angle. Finally, we examine the influence of classical periodic orbits on rotor wave functions. Many wave functions in the tilted field case are found to be highly nonseparable in spherical polar coordinates. Localization of wave functions in the vicinity of classical periodic orbits, both stable and unstable, is observed for many states.

    10. Measurable signatures of quantum mechanics in a classical spacetime

      NASA Astrophysics Data System (ADS)

      Helou, Bassam; Luo, Jun; Yeh, Hsien-Chi; Shao, Cheng-gang; Slagmolen, B. J. J.; McClelland, David E.; Chen, Yanbei

      2017-08-01

      We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013), 10.1103/PhysRevLett.110.170401]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.

    11. 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.

    12. 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.

    13. Statistical origin of classical mechanics and quantum mechanics

      NASA Astrophysics Data System (ADS)

      Chu, Shu-Yuan

      1993-11-01

      The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.

    14. Alternative routes to equivalent classical models of a quantum system

      NASA Astrophysics Data System (ADS)

      Radonjić, M.; Slobodan, Prvanović; Nikola, Burić

      2012-12-01

      Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechanical behavior from the quantum formalism. We utilize the two-mode Bose—Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dynamical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.

    15. 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.

    16. Quantum conductance fluctuations and classical short-path dynamics

      SciTech Connect

      Ishio, H.; Burgdoerfer, J. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6377 )

      1995-01-15

      We present numerical results for ballistic-electron quantum transport through weakly open integrable circle and chaotic stadium billiards. The geometry of the pair of conducting leads is chosen in accordance with recent experiments for semiconductor microstructures [Marcus [ital et] [ital al]., Phys. Rev. Lett. [bold 69], 506 (1992)]. The conductance as a function of the Fermi wave number displays characteristic noisy fluctuations for both the integrable and the chaotic systems. We show that structures in the conductance autocorrelation function as a function of the Fermi wave number are related to short-length classical orbits. This correspondence permits incorporation of effects of phase decoherence due to incoherent scattering into the quantum calculation.

    17. 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.

    18. Implementation of quantum and classical discrete fractional Fourier transforms.

      PubMed

      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

      2016-03-23

      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.

    19. Quantum simulation of frustrated classical magnetism in triangular optical lattices.

      PubMed

      Struck, J; Ölschläger, C; Le Targat, R; Soltan-Panahi, P; Eckardt, A; Lewenstein, M; Windpassinger, P; Sengstock, K

      2011-08-19

      Magnetism plays a key role in modern technology and stimulates research in several branches of condensed matter physics. Although the theory of classical magnetism is well developed, the demonstration of a widely tunable experimental system has remained an elusive goal. Here, we present the realization of a large-scale simulator for classical magnetism on a triangular lattice by exploiting the particular properties of a quantum system. We use the motional degrees of freedom of atoms trapped in an optical lattice to simulate a large variety of magnetic phases: ferromagnetic, antiferromagnetic, and even frustrated spin configurations. A rich phase diagram is revealed with different types of phase transitions. Our results provide a route to study highly debated phases like spin-liquids as well as the dynamics of quantum phase transitions.

    20. 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

    1. Parameter scaling in the decoherent quantum-classical transition for chaotic rf superconducting quantum interference devices.

      PubMed

      Mao, Ting; Yu, Yang

      2010-01-01

      We numerically investigated the quantum-classical transition in rf-superconducting quantum interference device (SQUID) systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent lambda(m), exhibits nonmonotonic behavior as a function of the coupling strength D. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of lambda(m)/D. In addition, the scaling holds in SQUID systems to a relatively smaller variant Planck's over [symbol: see text], suggesting the universality for this scaling.

    2. Classical and quantum magnetism in giant Keplerate magnetic molecules.

      PubMed

      Müller, A; Luban, M; Schröder, C; Modler, R; Kögerler, P; Axenovich, M; Schnack, J; Canfield, P; Bud'ko, S; Harrison, N

      2001-09-17

      Complementary theoretical modeling methods are presented for the classical and quantum Heisenberg model to explain the magnetic properties of nanometer-sized magnetic molecules. Excellent quantitative agreement is achieved between our experimental data down to 0.1 K and for fields up to 60 Tesla and our theoretical results for the giant Keplerate species {Mo72Fe30}, by far the largest paramagnetic molecule synthesized to date.

    3. 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.

    4. 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.

    5. 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.

    6. 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.

    7. 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.

    8. Coevolution of Quantum and Classical Strategies on Evolving Random Networks

      PubMed Central

      Li, Qiang; Iqbal, Azhar; Perc, Matjaž; Chen, Minyou; Abbott, Derek

      2013-01-01

      We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner’s dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient. PMID:23874622

    9. 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)

    10. Classical simulation of quantum entanglement without local hidden variables

      NASA Astrophysics Data System (ADS)

      Massar, Serge; Bacon, Dave; Cerf, Nicolas J.; Cleve, Richard

      2001-05-01

      Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of possibilities and the goal is to find a classical scheme that reproduces exactly the correlations that arise when an actual quantum system is measured. Previous results have shown that, using local hidden variables, a finite amount of communication suffices to simulate the correlations for a Bell state. We extend this in a number of ways. First, we show that, when the communication is merely required to be finite on average, Bell states can be simulated without any local hidden variables. More generally, we show that arbitrary positive operator valued measurements on systems of n Bell states can be simulated with O(n2n) bits of communication on average (again, without local hidden variables). On the other hand, when the communication is required to be absolutely bounded, we show that a finite number of bits of local hidden variables is insufficient to simulate a Bell state. This latter result is based on an analysis of the nondeterministic communication complexity of the NOT-EQUAL function, which is constant in the quantum model and logarithmic in the classical model.

    11. Quantum Versus Classical Advantages in Secret Key Distillation (and Their Links to Quantum Entanglement

      NASA Astrophysics Data System (ADS)

      Chitambar, Eric; Fortescue, Benjamin; Hsieh, Min-Hsiu

      We consider the extraction of shared secret key from correlations that are generated by either a classical or quantum source. In the classical setting, two honest parties (Alice and Bob) use public discussion and local operations to distill secret key from some distribution pXYZ that is shared with an unwanted eavesdropper (Eve). In the quantum settings, the correlations pXYZ are delivered to the parties as either an incoherent mixture of orthogonal quantum states or as coherent superposition of such states. Here we demonstrate that the classical and quantum key rates are equivalent when the correlations are generated incoherently in the quantum setting. For coherent sources, we next show that the rates are incomparable, and in fact, their difference can be arbitrarily large in either direction. However, we identify a large class of non-trivial distributions that possess the following properties: (i) Eve's advantage is always greater in the quantum source than classically, and (ii) for the entanglement shared in the coherent source, the so-called entanglement cost/squashed entanglement/relative entropy of entanglement can all be computed. We thus present a rare instance in which various entropic entanglement measures of a quantum state can be explicitly computed.

    12. 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.

    13. Representational Realism, Closed Theories and the Quantum to Classical Limit

      NASA Astrophysics Data System (ADS)

      de Ronde, Christian

      In this chapter, we discuss the representational realist stance as a pluralistontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two (Bohrian) metaphysical presuppositions - accepted in the present as dogmas that all interpretations must follow. We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the chapter, we revisit, from representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence.

    14. Reduction of Classical Measurement Noise via Quantum-Dense Metrology

      NASA Astrophysics Data System (ADS)

      Ast, Melanie; Steinlechner, Sebastian; Schnabel, Roman

      2016-10-01

      Quantum-dense metrology constitutes a special case of quantum metrology in which two orthogonal phase space projections of a signal are simultaneously sensed beyond the shot-noise limit. Previously, it was shown that the additional sensing channel that is provided by quantum-dense metrology contains information that can be used to identify and to discard corrupted segments from the measurement data. Here, we propose and demonstrate a new method in which this information is used for improving the sensitivity without discarding any measurement segments. Our measurement reached sub-shot-noise performance, although initially strong classical noise polluted the data. The new method has high potential for improving the noise spectral density of gravitational-wave detectors at signal frequencies of high astrophysical relevance.

    15. Large Quantum Gravity Effects: Unforeseen Limitations of the Classical Theory

      NASA Astrophysics Data System (ADS)

      Ashtekar, Abhay

      1996-12-01

      Three-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axisymmetry. The solution is used to probe several quantum gravity issues. In particular, it is found that if there is an electromagnetic wave of Planckian frequency even with such low amplitude that the curvature of the classical solution is small, the uncertainty in the quantum metric can be very large. More generally, the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality N\\(ħGω\\)2<<1. Results hold also for a sector of the four-dimensional theory (consisting of Einstein-Rosen gravitational waves).

    16. Reduction of Classical Measurement Noise via Quantum-Dense Metrology.

      PubMed

      Ast, Melanie; Steinlechner, Sebastian; Schnabel, Roman

      2016-10-28

      Quantum-dense metrology constitutes a special case of quantum metrology in which two orthogonal phase space projections of a signal are simultaneously sensed beyond the shot-noise limit. Previously, it was shown that the additional sensing channel that is provided by quantum-dense metrology contains information that can be used to identify and to discard corrupted segments from the measurement data. Here, we propose and demonstrate a new method in which this information is used for improving the sensitivity without discarding any measurement segments. Our measurement reached sub-shot-noise performance, although initially strong classical noise polluted the data. The new method has high potential for improving the noise spectral density of gravitational-wave detectors at signal frequencies of high astrophysical relevance.

    17. The search for quantum critical scaling in a classical system

      NASA Astrophysics Data System (ADS)

      Lamsal, Jagat; Gaddy, John; Petrovic, Marcus; Montfrooij, Wouter; Vojta, Thomas

      2009-04-01

      Order-disorder phase transitions in magnetic metals that occur at zero temperature have been studied in great detail. Theorists have advanced scenarios for these quantum critical systems in which the unusual response can be seen to evolve from a competition between ordering and disordering tendencies, driven by quantum fluctuations. Unfortunately, there is a potential disconnect between the real systems that are being studied experimentally, and the idealized systems that theoretical scenarios are based upon. Here we discuss how disorder introduces a change in morphology from a three-dimensional system to a collection of magnetic clusters, and we present neutron scattering data on a classical system, Li[Mn1.96Li0.04]O4, that show how magnetic clusters by themselves can lead to scaling laws that mimic those observed in quantum critical systems.

    18. Classical and quantum emitters near a metal surface

      NASA Astrophysics Data System (ADS)

      Mohammadi, Zahra; Kheirandish, Fardin

      2017-04-01

      The propagation of surface plasmon polaritons in an attenuating medium is investigated. The analytical calculations of the total electric-field Green’s tensor of a metal–dielectric interface structure are provided and novel explicit expressions for the Green’s tensor of a metal–dielectric interface are presented. The contribution of plasmons is obtained by evaluating the poles of the reflection coefficient for p-polarized waves incident on the metal interface. The emission pattern of a classical dipole located above the air/silver interface is studied. The relative intensity of the field to the field intensity in free space is studied for both normal and parallel orientations of the dipole. The quantum optical properties of a quantum emitter coupled to a metal surface are studied. Single photon emission is demonstrated for a quantum dot near a metal surface using second-order correlation functions.

    19. 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.

    20. Security of quantum digital signatures for classical messages

      PubMed Central

      Wang, Tian-Yin; Cai, Xiao-Qiu; Ren, Yan-Li; Zhang, Rui-Ling

      2015-01-01

      Quantum digital signatures can be used to authenticate classical messages in an information-theoretically secure way. Previously, a novel quantum digital signature for classical messages has been proposed and gave an experimental demonstration of distributing quantum digital signatures from one sender to two receivers. Some improvement versions were subsequently presented, which made it more feasible with present technology. These proposals for quantum digital signatures are basic building blocks which only deal with the problem of sending single bit messages while no-forging and non-repudiation are guaranteed. For a multi-bit message, it is only mentioned that the basic building blocks must be iterated, but the iteration of the basic building block still does not suffice to define the entire protocol. In this paper, we show that it is necessary to define the entire protocol because some attacks will arise if these building blocks are used in a naive way of iteration. Therefore, we give a way of defining an entire protocol to deal with the problem of sending multi-bit messages based on the basic building blocks and analyse its security. PMID:25782417

    1. Security of quantum digital signatures for classical messages

      NASA Astrophysics Data System (ADS)

      Wang, Tian-Yin; Cai, Xiao-Qiu; Ren, Yan-Li; Zhang, Rui-Ling

      2015-03-01

      Quantum digital signatures can be used to authenticate classical messages in an information-theoretically secure way. Previously, a novel quantum digital signature for classical messages has been proposed and gave an experimental demonstration of distributing quantum digital signatures from one sender to two receivers. Some improvement versions were subsequently presented, which made it more feasible with present technology. These proposals for quantum digital signatures are basic building blocks which only deal with the problem of sending single bit messages while no-forging and non-repudiation are guaranteed. For a multi-bit message, it is only mentioned that the basic building blocks must be iterated, but the iteration of the basic building block still does not suffice to define the entire protocol. In this paper, we show that it is necessary to define the entire protocol because some attacks will arise if these building blocks are used in a naive way of iteration. Therefore, we give a way of defining an entire protocol to deal with the problem of sending multi-bit messages based on the basic building blocks and analyse its security.

    2. 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.

    3. 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.

    4. Performance comparison between classical and quantum control for a simple quantum system

      NASA Astrophysics Data System (ADS)

      Xi, Zairong; Jin, Guangsheng

      2008-02-01

      Brańczyk et al. pointed out that the quantum control scheme is superior to the classical control scheme for a simple quantum system using simulation [A.M. Brańczyk, P.E.M.F. Mendonca, A. Gilchrist, A.C. Doherty, S.D. Barlett, Quantum control theory of a single qubit, Physical Review A 75 (2007) 012329 or arXiv e-print quant-ph/0608037]. Here we rigorously prove the result. Furthermore we will show that any quantum operation does not universally “correct” the dephasing noise.

    5. Emergence of order in quantum extensions of the classical quasispecies evolution

      NASA Astrophysics Data System (ADS)

      Narnhofer, Heide; Posch, Harald A.; Thirring, Walter

      2007-10-01

      We study evolution equations which model selection and mutation within the framework of quantum mechanics. The main question is to what extent order is achieved for an ensemble of typical systems. As an indicator for mixing or purification, a quadratic entropy is used which assumes values between zero for pure states and (d-1)/d for fully mixed states. Here, d is the dimension. Whereas the classical counterpart, the quasispecies dynamics, has previously been found to be predominantly mixing, the quantum quasispecies (QS) evolution surprisingly is found to be strictly purifying for all dimensions. This is also typically true for an alternative formulation (AQS) of this quantum mechanical flow. We compare this also to analogous results for the Lindblad evolution. Although the latter may be viewed as a simple linear superposition of the purifying QS and AQS evolutions, it is found to be predominantly mixing. The reason for this behavior may be explained by the fact that the two subprocesses by themselves converge to different pure states, such that the combined process is mixing. These results also apply to high-dimensional systems.

    6. 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

    7. Classical and quantum cosmology of the little rip abrupt event

      NASA Astrophysics Data System (ADS)

      Albarran, Imanol; Bouhmadi-López, Mariam; Kiefer, Claus; Marto, João; Vargas Moniz, Paulo

      2016-09-01

      We analyze from a classical and quantum point of view the behavior of the Universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structures in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.

    8. Geometric control of quantum mechanical and nonlinear classical systems

      NASA Astrophysics Data System (ADS)

      Nelson, Richard Joseph

      1999-10-01

      Geometric control refers to the judicious use of the non- commuting nature of inputs and natural dynamics as the basis for control. The last few decades in control system theory have seen the application of differential geometry in proving several important properties of systems, including controllability and observability. Until recently, however, the results of this mathematical geometry have rarely been used as the basis for designing and implementing an actual controller. This thesis demonstrates the application of a judicious selection of inputs, so that if the system is proven to be controllable using geometric methods, one can design input sequences using the same geometry. A demonstration of this method is shown in simulating the attitude control of a satellite: a highly non-linear, non- holonomic control problem. Although not a practical method for large re-orientations of a typical satellite, the approach can be applied to other nonlinear systems. The method is also applied to the closed-loop performance of a quantum mechanical system to demonstrate the feasibility of coherent quantum feedback-something impossible using a conventional controller. Finally, the method is applied in the open-loop control of a quantum mechanical system: in this case, the creation of Greenberger-Horne-Zeilinger correlations among the nuclei of an ensemble of alanine molecules in a nuclear magnetic resonance spectrometer. In each case, the data demonstrate the usefulness of a geometric approach to control. In addition to demonstrations of geometric control in practice, the quantum mechanical experiments also demonstrate for the first time peculiar quantum correlations, including GHZ correlations, that have no classical analog. The quantum experiments further establish nuclear magnetic resonance as a viable and accessible testbed of quantum predictions and processes. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax

    9. 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.

    10. Quantum to classical transition induced by gravitational time dilation

      NASA Astrophysics Data System (ADS)

      Sokolov, Boris; Vilja, Iiro; Maniscalco, Sabrina

      2017-07-01

      We study the loss of quantumness caused by time dilation [I. Pikovski, M. Zych, F. Costa, and Č. Brukner, Nat. Phys. 11, 668 (2015), 10.1038/nphys3366] for a Schrödinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion, and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely, on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [J. Trapani, M. Bina, S. Maniscalco, and M. G. A. Paris, Phys. Rev. A 91, 022113 (2015), 10.1103/PhysRevA.91.022113]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.

    11. Decoherence and quantum-classical master equation dynamics.

      PubMed

      Grunwald, Robbie; Kapral, Raymond

      2007-03-21

      The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.

    12. PT symmetry in classical and quantum statistical mechanics.

      PubMed

      Meisinger, Peter N; Ogilvie, Michael C

      2013-04-28

      PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.

    13. Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord

      SciTech Connect

      He Qiliang; Xu Jingbo; Zhang Yeqi; Yao Daoxin

      2011-08-15

      We investigate the phenomenon of sudden transition between classical and quantum decoherence in the study of quantum discord for a dissipative cavity QED system, which consists of two noninteracting two-level atoms, each trapped in a dissipative cavity. It is found that the quantum discord between the two atoms, which are prepared initially in the X-type quantum states, is not destroyed by the dissipation of the cavities for a finite time interval, and the stationary quantum discord can arise in the interaction of atoms with cavities as the time approaches infinity. The transition time is sensitive to the initial state parameter of the two atoms and the mean photon number of the coherent field. Interestingly, the quantum discord between the two atoms is completely unaffected by the dissipation of the cavities if we choose the suitable value of the ratio, which depends on the decay rate of the two cavities and the atom-field coupling constant.

    14. 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…

    15. 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…

    16. Numerical evidence of quantum melting of spin ice: quantum-classical crossover

      NASA Astrophysics Data System (ADS)

      Kato, Yasuyuki; Onoda, Shigeki

      2015-03-01

      Unbiased quantum Monte-Carlo simulations are performed on the simplest case of the quantum spin ice model, namely, the nearest-neighbor spin-1/2 XXZ model on the pyrochlore lattice with an antiferromagnetic longitudinal and a weak ferromagnetic transverse exchange couplings, J and J⊥. On cooling across TCSI ~ 0 . 2 J , the specific heat shows a broad peak associated with a crossover to a classical Coulomb liquid regime characterized by a remnant of the pinch-point singularity in longitudinal spin correlations as well as the Pauling ice entropy for | J⊥ | << J , as in classical spin ice. On further cooling, the entropy restarts gradually decaying to zero for J⊥ >J⊥ c ~ - 0 . 104 J , as expected for bosonic quantum Coulomb liquids. With negatively increasing J⊥ across J⊥ c, a first-order transition occurs at a nonzero temperature from the quantum Coulomb liquid to an XY ferromagnet. Relevance to magnetic rare-earth pyrochlore oxides is discussed.

    17. 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.

    18. 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.

    19. 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.

    20. Operational dynamic modeling transcending quantum and classical mechanics.

      PubMed

      Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A

      2012-11-09

      We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

    1. 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.

    2. Quantum walk classical simulation with slot waveguide array for sensing

      NASA Astrophysics Data System (ADS)

      Ma, Qingyan; Wang, Yufei; Qi, Fan; Liu, Zhishuang; Zheng, Wanhua

      2017-10-01

      A quantum walk (QW) classical simulation with a slot waveguide array is first proposed for sensing. The waveguide array is designed on a silicon-on-insulator, with the electric field mainly confined in the cladding region to enhance the interaction between the light and medium. The intensity distribution, i.e. the possibilities of QW, at the end of the array changes with the refractive index of the sensing area (surrounding region). Simulation results show good sensing characteristics with compact footprint and refractive index resolution of 1E-11 RIU.

    3. Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

      NASA Astrophysics Data System (ADS)

      Bondar, Denys I.; Cabrera, Renan; Lompay, Robert R.; Ivanov, Misha Yu.; Rabitz, Herschel A.

      2012-11-01

      We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

    4. 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

    5. 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

      2015-11-20

      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.

    6. Quantum secret sharing via local operations and classical communication

      NASA Astrophysics Data System (ADS)

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

      2015-11-01

      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. Exact Classical and Quantum Dynamics in Background Electromagnetic Fields

      NASA Astrophysics Data System (ADS)

      Heinzl, Tom; Ilderton, Anton

      2017-03-01

      Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focusing of intense laser fields implies a need to go beyond the plane wave model. By exploiting Poincaré symmetry and superintegrability we show how to construct, and solve without approximation, new models of laser-matter interactions. We illustrate the method with a model of a radially polarized (TM) laser beam, for which we exactly determine the classical orbits and quantum wave functions. Including in this way the effects of transverse field structure should improve predictions and analyses for experiments at intense laser facilities.

    8. 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

    9. 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.

    10. 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.

    11. Unitary Qubit Representation of Quantum and Classical Turbulence

      NASA Astrophysics Data System (ADS)

      Vahala, George; Zhang, Bo; Vahala, Linda; Soe, Min

      2011-10-01

      A unitary qubit lattice algorithm, which scales almost perfectly to the full number of cores available (216000 cores on a CRAY XT5), is used to examine quantum turbulence and its interrelationship to classical turbulence with production runs on grids up to 57603. The maximal grids achievable by conventional CFD for quantum turbulence is just 20483, and artificial dissipation had to be introduced. Our unitary algorithms preserve the Hamiltonian structure of the Gross-Pitaevskii equation which describes quantum turbulence in a zero-temperature (BEC). As a result, parameter regimes have been uncovered which exhibit very short Poincare recurrence time, as well as a strong triple cascade structure in the kinetic energy spectrum, with small k-region obeying a Kolmogorov k - 5 / 3 spectrum The incompressible energy spectrum shows a k-3 spectrum for large-k, but a Saffman-like k-4 for smaller-k which is attributed to vorticity discontinuities. 2D and 3D turbulence is considered. These unitary qubit lattice algorithms are directly applicable to quantum computers.

    12. Many-body formalism for thermally excited wave packets: A way to connect the quantum regime to the classical regime

      NASA Astrophysics Data System (ADS)

      Chenu, Aurélia; Combescot, Monique

      2017-06-01

      Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet operators that connects these two limits, the thermal energy being distributed between the state spatial extension and its thermal excitation. The corresponding mixed quantum-classical states, which render the Boltzmann operator diagonal, are the physically relevant states when the temperature is finite. The formulation of many-body Hamiltonians in terms of these thermally excited wave packets and the resulting effective scatterings is provided.

    13. A classical approach to the graph isomorphism problem using quantum walks

      NASA Astrophysics Data System (ADS)

      Douglas, Brendan L.; Wang, Jingbo B.

      2008-02-01

      Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such algorithms have been scarce. In this work, we enumerate some important differences between quantum and classical walks, leading to their markedly different properties. We show that for many practical purposes, the implementation of quantum walks can be efficiently achieved using a classical computer. We then develop both classical and quantum graph isomorphism algorithms based on discrete-time quantum walks. We show that they are effective in identifying isomorphism classes of large databases of graphs, in particular groups of strongly regular graphs. We consider this approach to represent a promising candidate for an efficient solution to the graph isomorphism problem, and believe that similar methods employing quantum walks, or derivatives of these walks, may prove beneficial in constructing other algorithms for a variety of purposes.

    14. The quantum state of the universe from deformation quantization and classical-quantum correlation

      NASA Astrophysics Data System (ADS)

      Rashki, M.; Jalalzadeh, S.

      2017-02-01

      In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-Wigner-Groenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is described by the Moyal-Wheeler-DeWitt equation which has exact solutions in Moyal phase space, resulting in Wigner quasiprobability distribution functions peaking around the classical paths for large values of scale factor. We show that the Wigner functions of these models are peaked around the non-singular universes with quantum modified density parameter of radiation.

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

      NASA Astrophysics Data System (ADS)

      Biswas, Shyamal

      2015-05-01

      We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He 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. 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.

    17. 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.

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

      NASA Astrophysics Data System (ADS)

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

      2016-02-01

      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.

    19. Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel.

      PubMed

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

      2016-02-15

      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.

    20. 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.

    1. Classical transients and the support of open quantum maps.

      PubMed

      Carlo, Gabriel G; Wisniacki, D A; Ermann, Leonardo; Benito, R M; Borondo, F

      2013-01-01

      The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller-the set of nonescaping orbits in the future and past evolution-is the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps [L. Ermann, G. G. Carlo, J. M. Pedrosa, and M. Saraceno, Phys. Rev. E 85, 066204 (2012)], which share the same asymptotic properties but differ in their short-time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems. We provide an interpretation of the results in order to have hints about them.

    2. 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.

    3. Classical transients and the support of open quantum maps

      NASA Astrophysics Data System (ADS)

      Carlo, Gabriel G.; Wisniacki, D. A.; Ermann, Leonardo; Benito, R. M.; Borondo, F.

      2013-01-01

      The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller—the set of nonescaping orbits in the future and past evolution—is the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps [L. Ermann, G. G. Carlo, J. M. Pedrosa, and M. Saraceno, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.066204 85, 066204 (2012)], which share the same asymptotic properties but differ in their short-time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems. We provide an interpretation of the results in order to have hints about them.

    4. 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

    5. 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.

    6. Parts and Wholes. An Inquiry into Quantum and Classical Correlations

      NASA Astrophysics Data System (ADS)

      Seevinck, M. P.

      2008-10-01

      The primary topic of this dissertation is, firstly, the study of the correlations between outcomes of measurements on the subsystems of a composed system as predicted by a particular physical theory; secondly, the study of what this physical theory predicts for the relationships these subsystems can have to the composed system they are a part of; and thirdly, the comparison of different physical theories with respect to these two aspects. The physical theories investigated and compared are generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. The motivation for these enquiries is that a comparison of the relationships between parts and whole as described by each theory, and of the correlations predicted by each theory between separated subsystems yields a fruitful method to investigate what these physical theories say about the world. One then finds, independent of any physical model, relationships and constraints that capture the essential physical assumptions and structural aspects of the theory in question. As such one gains a larger and deeper understanding of the different physical theories under investigation and of what they say about the world. A large part of this dissertation is devoted to understanding different aspects of different kinds of correlations that can exist between the outcomes of measurement on subsystems of a larger system. Four different kinds of correlation have been investigated: local, partially-local, no-signaling and quantum mechanical. Novel characteristics of these correlations have been used to study how they are related and how they can be discerned. The main tool of this investigation has been the usage of Bell-type inequalities that give non-trivial bounds on the strength of the correlations. The study of quantum correlations has also prompted us to study the multi-partite qubit state space with respect to its entanglement and separability characteristics, and the differing

    7. Quantum ergodicity breaking in semi-classical electron transfer dynamics.

      PubMed

      Goychuk, Igor

      2017-01-25

      Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.

    8. 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

    9. 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.

    10. 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.

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

      NASA Astrophysics Data System (ADS)

      Kamenshchik, A. Yu.; Manti, S.

      2013-02-01

      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.

    12. Classical and quantum big brake cosmology for scalar field and tachyonic models

      NASA Astrophysics Data System (ADS)

      Kamenshchik, Alexander Y.; Manti, Serena

      2012-06-01

      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.

    13. Classical and Quantum Big Brake Cosmology for Scalar Field and Tachyonic Models

      NASA Astrophysics Data System (ADS)

      Kamenshchik, Alexander; Manti, Serena

      2015-01-01

      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.

    14. 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.

    15. 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.

    16. 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.

    17. Polynomial-Time Classical Simulation of Quantum Ferromagnets

      NASA Astrophysics Data System (ADS)

      Bravyi, Sergey; Gosset, David

      2017-09-01

      We consider a family of quantum spin systems which includes, as special cases, the ferromagnetic X Y model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any model in this family can be efficiently approximated to a given relative error ɛ using a classical randomized algorithm with runtime polynomial in ɛ-1, system size, and inverse temperature. As a consequence, we obtain a polynomial time algorithm which approximates the free energy or ground energy to a given additive error. We first show how to approximate the partition function by the perfect matching sum of a finite graph with positive edge weights. Although the perfect matching sum is not known to be efficiently approximable in general, the graphs obtained by our method have a special structure which facilitates efficient approximation via a randomized algorithm due to Jerrum and Sinclair.

    18. 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

    19. Hidden symmetries of dynamics in classical and quantum physics

      NASA Astrophysics Data System (ADS)

      Cariglia, Marco

      2014-10-01

      This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as nonrelativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of nontrivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher-dimensional black holes, the Dirac equation, and supergravity with and without fluxes, providing a tool to probe the dynamics of nonlinear systems.

    20. 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.

    1. 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.

    2. 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.

    3. Strong Converse Exponent for Classical-Quantum Channel Coding

      NASA Astrophysics Data System (ADS)

      Mosonyi, Milán; Ogawa, Tomohiro

      2017-10-01

      We determine the exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity. Our form of the exponent is an exact analogue of Arimoto's, given as a transform of the Rényi capacities with parameters {α > 1}. It is important to note that, unlike in the classical case, there are many inequivalent ways to define the Rényi divergence of states, and hence the Rényi capacities of channels. Our exponent is in terms of the Rényi capacities corresponding to a version of the Rényi divergences that has been introduced recently in Müller-Lennert et al. (J Math Phys 54(12):122203, 2013. arXiv:1306.3142), and Wilde et al. (Commun Math Phys 331(2):593-622, 2014. arXiv:1306.1586). Our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems.

    4. Correlated electron-nuclear dissociation dynamics: classical versus quantum motion

      NASA Astrophysics Data System (ADS)

      Schaupp, Thomas; Albert, Julian; Engel, Volker

      2017-01-01

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

    5. 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.

    6. Analytical examples, measurement models, and classical limit of quantum backflow

      NASA Astrophysics Data System (ADS)

      Yearsley, J. M.; Halliwell, J. J.; Hartshorn, R.; Whitby, A.

      2012-10-01

      We investigate the backflow effect in elementary quantum mechanics—the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz [Penz, Grübl, Kreidl, and Wagner, J. Phys. AJPHAC50305-447010.1088/0305-4470/39/2/012 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70% of the maximum possible backflow, a dimensionless number cbm≈0.04, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. AJPHAC50305-447010.1088/0305-4470/27/6/040 27, 2197 (1994)]. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.

    7. 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.

    8. 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.

    9. Characterizing quantum channels with non-separable states of classical light

      NASA Astrophysics Data System (ADS)

      Ndagano, Bienvenu; Perez-Garcia, Benjamin; Roux, Filippus S.; McLaren, Melanie; Rosales-Guzman, Carmelo; Zhang, Yingwen; Mouane, Othmane; Hernandez-Aranda, Raul I.; Konrad, Thomas; Forbes, Andrew

      2017-04-01

      High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

    10. Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

      NASA Astrophysics Data System (ADS)

      Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.

      2017-01-01

      A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

    11. Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards.

      PubMed

      Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F

      2017-01-01

      A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

    12. 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

    13. 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.

    14. 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…

    15. 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…

    16. Numerical Evidence of Quantum Melting of Spin Ice: Quantum-to-Classical Crossover

      NASA Astrophysics Data System (ADS)

      Kato, Yasuyuki; Onoda, Shigeki

      2015-08-01

      Unbiased quantum Monte Carlo simulations are performed on the nearest-neighbor spin-1/2 pyrochlore X X Z model with an antiferromagnetic longitudinal and the weak ferromagnetic transverse exchange couplings, J and J⊥ . The specific heat exhibits a broad peak at TCSI˜0.2 J associated with a crossover to a classical Coulomb liquid regime showing a suppressed spin-ice monopole density, a broadened pinch-point singularity, and the Pauling entropy for |J⊥|≪J , as in classical spin ice. On further cooling, the entropy restarts decaying for J⊥>J⊥c˜-0.104 J , producing another broad specific heat peak for a crossover to a bosonic quantum Coulomb liquid, where the spin correlation contains both photon and quantum spin-ice monopole contributions. With negatively increasing J⊥ across J⊥c, a first-order thermal phase transition occurs from the quantum Coulomb liquid to an X Y ferromagnet. Relevance to magnetic rare-earth pyrochlore oxides is discussed.

    17. Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

      NASA Astrophysics Data System (ADS)

      Boche, Holger; Janßen, Gisbert; Kaltenstadler, Stephan

      2017-04-01

      We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entanglement-assisted classical capacities does hold for each arbitrarily varying quantum channel.

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

      PubMed

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

      2015-03-17

      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.

    19. 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

    20. Extreme Quantum Advantage when Simulating Classical Systems with Long-Range Interaction.

      PubMed

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

      2017-07-27

      Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators has recently come to the fore: they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems-in particular, the Dyson one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction range increases. In particular, simulating Dyson's original spin chain with the most memory-efficient classical algorithm known requires infinite memory, while a quantum simulator requires only finite memory. Thus, quantum systems can very efficiently simulate strongly coupled one-dimensional classical spin systems.