HighNOON states by mixing quantum and classical light.
Afek, Itai; Ambar, Oron; Silberberg, Yaron
20100514
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 highprecision phase measurements, becoming more and more advantageous as the number of photons grows. We generated "highNOON" states (N = 5) by multiphoton interference of quantum downconverted light with a classical coherent state in an approach that is inherently scalable. Superresolving phase measurements with up to five entangled photons were produced with a visibility higher than that obtainable using classical light only.
Mixed quantumclassical versus full quantum dynamics: Coupled quasiparticleoscillator system
NASA Astrophysics Data System (ADS)
Schanz, Holger; Esser, Bernd
19970501
The relation between the dynamical properties of a coupled quasiparticleoscillator system in the mixed quantumclassical 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 BornOppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
Mixed quantumclassical equilibrium in global flux surface hopping
Sifain, Andrew E.; Wang, Linjun; Prezhdo, Oleg V.
20150614
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 electronvibrational relaxation and phononassisted transport. By studying the dynamics in a threelevel 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.
Dynamically consistent method for mixed quantumclassical simulations: A semiclassical approach.
Antipov, Sergey V; Ye, Ziyu; Ananth, Nandini
20150514
We introduce a new semiclassical (SC) framework, the Mixed QuantumClassical Initial Value Representation (MQCIVR), that can be tuned to reproduce existing quantumlimit and classicallimit SC approximations to quantum realtime correlation functions. Applying a modified Filinov transformation to a quantumlimit 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 MQCIVR expression provides a consistent dynamic framework for mixed quantumclassical simulations and we demonstrate its numerical accuracy in the calculation of realtime correlation functions for a model 1D system and a model 2D system over the full range of quantum to classicallimit behaviors.
Dynamically consistent method for mixed quantumclassical simulations: A semiclassical approach
Antipov, Sergey V.; Ye, Ziyu; Ananth, Nandini
20150514
We introduce a new semiclassical (SC) framework, the Mixed QuantumClassical Initial Value Representation (MQCIVR), that can be tuned to reproduce existing quantumlimit and classicallimit SC approximations to quantum realtime correlation functions. Applying a modified Filinov transformation to a quantumlimit 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 MQCIVR expression provides a consistent dynamic framework for mixed quantumclassical simulations and we demonstrate its numerical accuracy in the calculation of realtime correlation functions for a model 1D system and a model 2D system over the full range of quantum to classicallimit behaviors.
Hsieh, ChangYu; Kapral, Raymond
20130407
Mixed quantumclassical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forwardbackward trajectory solution of the mixed quantumclassical 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 meanfield 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 forwardbackward trajectory solution, is analyzed and tested in detail and its various implementations are discussed.
Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantumclassical method
NASA Astrophysics Data System (ADS)
Gelman, David; Schwartz, Steven D.
20090401
The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantumclassical method. The method is suited to treat manybody 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.
Calculating twodimensional spectra with the mixed quantumclassical Ehrenfest method.
van der Vegte, C P; Dijkstra, A G; Knoester, J; Jansen, T L C
20130725
We present a mixed quantumclassical simulation approach to calculate twodimensional spectra of coupled twolevel 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 twodimensional 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 twodimensional 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 quantumclassical system however does obey a Boltzmann distribution, when coupled to a stochastic heat bath.
Shakib, Farnaz; Hanna, Gabriel
20160712
In this work, we derive a general mixed quantumclassical formula for calculating thermal protoncoupled electrontransfer (PCET) rate constants, starting from the time integral of the quantum fluxflux correlation function. This formula allows for the direct simulation of PCET reaction dynamics via the mixed quantumclassical 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 condensedphase 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.
Semenov, Alexander; Babikov, Dmitri
20140116
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 fullquantum 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 fullquantum framework.
Can Quantized Vibrational Effects Be Obtained from Ehrenfest Mixed QuantumClassical Dynamics?
Goings, Joshua J; Lingerfelt, David B; Li, Xiaosong
20161215
We explore the question of whether meanfield or "Ehrenfest" mixed quantumclassical dynamics is capable of capturing the quantized vibrational features in photoabsorption spectra that result from infrared and Ramanactive 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 timeevolving dipole in the presence of external fields and vibrational motion shows the origin of these features, demonstrating that mixed quantumclassical Ehrenfest dynamics is capable of producing infrared, Raman, and electronic absorption spectra from a single simulation.
Bai, Shuming; Xie, Weiwei; Shi, Qiang
20141002
Starting from the mixed quantumclassical 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 quantumclassical 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 onedimensional two surface problems and is shown to correctly solve the problem of the mean field approximation in several cases.
Schubert, Alexander; Falvo, Cyril; Meier, Christoph
20160807
We present mixed quantumclassical 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 nonadiabatic 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.
NASA Astrophysics Data System (ADS)
Schubert, Alexander; Falvo, Cyril; Meier, Christoph
20160801
We present mixed quantumclassical 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 nonadiabatic 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.
Semenov, Alexander; Babikov, Dmitri
20150521
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 asymmetrictop 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 selfconsistent 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 fullquantum approach. Theoretical prediction of inelastic cross sections for a number of complex organic molecules observed in space becomes feasible using this new computational tool.
NASA Astrophysics Data System (ADS)
Dzegilenko, Fedor N.
19950101
Both classical and mixed quantumclassical approaches have been used to study the nonthermal 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 selfconsistently using the discrete variable representation method for the propagation of the quantum wave function. Nonthermal 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 nonmonotonic function of the Debye frequency of the solid in the range 285000 cm^{1}, and is larger for "nonrigid" 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
NASA Astrophysics Data System (ADS)
Gelman, David; Schwartz, Steven D.
20080701
The recently developed mixed quantumclassical 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 zerothorder propagators. The method is applied to a model system of a doublewell 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 doublewell potential.
Babikov, Dmitri; Semenov, Alexander
20160128
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, symmetrictop rotors, and asymmetrictop 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 fullquantum calculations. At low collision energies and for lowmass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with fullquantum calculations at low energies.
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
20151105
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the timederivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantumclassical 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 finitedifference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive severalorderofmagnitude speedups of the TDNAC calculation step for midsize molecules.
Multipartite quantum and classical correlations in symmetric nqubit mixed states
NASA Astrophysics Data System (ADS)
Giorgi, Gian Luca; Campbell, Steve
20161101
We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed nqubit 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 nonlocal and genuine quantum features of these states and note some interesting properties.
NASA Astrophysics Data System (ADS)
Megow, Jörg; Kulesza, Alexander; May, Volkhard
20160101
The groundstate classical path approximation is utilized to compute molecular absorption spectra in a mixed quantumclassical frame. To improve the description for highfrequency vibrational satellites, related quantum correction factors are introduced. The improved method is demonstrated for the Qy and Qxbands of pheophorbide a.
Megow, Jörg; Röder, Beate; Kulesza, Alexander; BonačićKoutecký, Vlasta; May, Volkhard
20110225
Electronic excitation energy transfer (EET) is described theoretically for the chromophore complex P(4) formed by a butanediamine dendrimer to which four pheophorbidea molecules are covalently linked. To achieve a description with atomic resolution, and to account for the effect of an ethanol solvent, a mixed quantumclassical methodology is utilized. Roomtemperature molecular dynamics simulations are used to describe the nuclear dynamics, and EET is accounted for in utilizing a mixed quantumclassical formulation of the transition rates. Therefore, the full quantum expression of the EET rates is given and the change to a mixed quantumclassical 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 timedependent Schrödinger equation entering the mixed quantumclassical 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.
Ryabinkin, Ilya G; Izmaylov, Artur F
20170119
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 quantumclassical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic blockdiagonalization applied to the timedependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with a simplified Ehrenfest approach and with a fullmemory electronic friction model on a 1D "adatom + atomic chain" model. Our simulations demonstrate that collectivemode 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.
Ivanov, Mikhail; Dubernet, MarieLise; Babikov, Dmitri
20140407
The mixed quantum/classical theory (MQCT) formulated in the spacefixed 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 fullquantum 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 statetostate transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the averagevelocity 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 bodyfixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the fullquantum results almost everywhere through fourordersofmagnitude range of collision energies, except near resonances, where the errors are somewhat larger.
Nonadiabatic mixed quantumclassical dynamic simulation of pistacked oligophenylenevinylenes.
Sterpone, Fabio; BedardHearn, Michael J; Rossky, Peter J
20090416
We present results from the first nonadiabatic (NA), nonequilibrium mixed quantumclassical molecular dynamics simulations of pistacked oligophenylvinylene (OPV) chains with a quantum electronic Hamiltonian (PariserParrPople with excited states given by configuration interaction) that goes beyond the tightbinding 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.
Mixed quantumclassical studies of energy partitioning in unimolecular chemical reactions
NASA Astrophysics Data System (ADS)
Bladow, Landon Lowell
A mixed quantumclassical 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 exitchannel 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, 1,1difluoroethane, 1,1difluoroethene, 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 1,1difluoroethene 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 exitchannel potential energy in unimolecular reactions.
On the equivalence between nonfactorizable mixedstrategy classical games and quantum games
Iqbal, Azhar; Chappell, James M.; Abbott, Derek
20160101
A gametheoretic 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 gametheoretic 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 nonfactorizable probabilities. We discuss two approaches for obtaining a nonfactorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a nonfactorizable game and determine the limitations of our approach. PMID:26909174
NASA Astrophysics Data System (ADS)
Gelman, David; Schwartz, Steven D.
20100501
The recently developed quantumclassical method has been applied to the study of dissipative dynamics in multidimensional systems. The method is designed to treat manybody 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 doublewell potential. The simulations have been performed at zero temperature. The results have been compared to the exact quantum simulations using the surrogate Hamiltonian approach.
Shakib, Farnaz A; Hanna, Gabriel
20140728
The nonadiabatic dynamics of model protoncoupled electron transfer (PCET) reactions is investigated for the first time using a surfacehopping algorithm based on the solution of the mixed quantumclassical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantumclassical systems, which is lacking in the molecular dynamics with quantum transitions surfacehopping 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 subsystembath 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 QCLEbased surfacehopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.
Randomness: Quantum versus classical
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
20160501
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).
Comparing classical and quantum equilibration
NASA Astrophysics Data System (ADS)
Malabarba, Artur S. L.; Farrelly, Terry; Short, Anthony J.
20160901
By using a physically relevant and theory independent definition of measurementbased 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.
Kantorovich, L N
20020826
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 (NCAFM) 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 FokkerPlanck 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 NCAFM experiments.
Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang
20140507
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 nonadiabatic 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 nonadiabatic transmission coefficients. It is found that the twosurface LandauZener 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 LandauZener formula.
Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang
20140507
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 nonadiabatic 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 nonadiabatic transmission coefficients. It is found that the twosurface LandauZener 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 LandauZener formula.
NASA Astrophysics Data System (ADS)
Oliynyk, Todd A.
20161201
We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multiparticle Schrödinger equations. The limit equations obtained by this procedure, which we refer to as the classicalquantum limit, govern the interaction between classical and quantum systems, and they possess many desirable properties that are inherited in the limit from the multiparticle quantum system. As an application, we use the classicalquantum limit equations to identify the source of the nonlocal signalling that is known to occur in the classicalquantum hybrid scheme of Hall and Reginatto. We also derive the first order correction to the classicalquantum 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.
Valleau, Stephanie; AspuruGuzik, Alan; Eisfeld, Alexander
20121214
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 energygap 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 FennaMatthewsOlson 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.
Bonhommeau, David; Truhlar, Donald G
20080707
The photodissociation dynamics of ammonia upon excitation of the outofplane 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 finalstate properties are compared to experiments. Five mixed quantum/classical methods are tested: one meanfield approach (the coherent switching with decay of mixing method), two surfacehopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surfacehopping methods with zeropoint 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 singlesurface 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.
Mixed quantumclassical reaction path dynamics of C2H5F > C2H4 + HF.
Stopera, Christopher J; Bladow, Landon L; Thweatt, W David; Page, Michael
20081120
A mixed quantumclassical 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/6311++G(2d,2p) and MP2/6311++G** levels of theory, followed by energypartitioning 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.
NASA Astrophysics Data System (ADS)
Megow, Jörg; May, Volkhard
20140101
The application of a mixed quantumclassical methodology for an investigation of single pheophorbidea 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 systembath theory. Linear absorption spectra are calculated for a spherical 14 nm diameter AuMNP 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 Qytransition we also present data on the MNP induced change of the single Pheo Qxabsorption.
Morales, Christine M; Thompson, Ward H
20070628
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 quantumclassical 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.
Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu
20140828
In order to investigate proton transfer reaction in solution, mixed quantumclassical 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 quantumclassical 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 quantumclassical calculations. This clearly shows that the tunneling effect is important in the reaction.
Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu
20140828
In order to investigate proton transfer reaction in solution, mixed quantumclassical 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 quantumclassical 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 quantumclassical calculations. This clearly shows that the tunneling effect is important in the reaction.
Semenov, Alexander; Babikov, Dmitri
20160609
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 quantummechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the statetostate transition cross sections are compared versus those obtained from the fullquantum 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 fullquantum 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.
Perspective: Quantum or classical coherence?
Miller, William H
20120607
Some coherence effects in chemical dynamics are described correctly by classical mechanics, while others only appear in a quantum treatmentand 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 nonadiabatic processes, where sometimes whether the coherence effects are classical or quantum depends on what specific aspects of the process are observed.
Computational quantumclassical boundary of noisy commuting quantum circuits
NASA Astrophysics Data System (ADS)
Fujii, Keisuke; Tamate, Shuhei
20160501
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 quantumclassical 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 measurementbased 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 projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Computational quantumclassical boundary of noisy commuting quantum circuits
Fujii, Keisuke; Tamate, Shuhei
20160101
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 quantumclassical 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 measurementbased 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 projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
Computational quantumclassical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
20160518
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 quantumclassical 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 measurementbased 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 projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical 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.
Cusati, Teresa; Granucci, Giovanni; Persico, Maurizio
20110406
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 nhexane, 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 NC 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.
Quantum dynamics in open quantumclassical systems.
Kapral, Raymond
20150225
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 wellapproximated by classical mechanics, so that one is led to consider the dynamics of open quantumclassical systems. Since a full quantum dynamical description of large manybody systems is not currently feasible, mixed quantumclassical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantumclassical Liouville dynamics, one of several quantumclassical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantumclassical systems, nonadiabatic dynamics, surfacehopping and meanfield theories and their relation to quantumclassical Liouville dynamics, as well as methods for simulating the dynamics.
Solvent fluctuations drive the hole transfer in DNA: a mixed quantumclassical study.
Kubar, Tomás; Kleinekathöfer, Ulrich; Elstner, Marcus
20091001
We studied the hole transfer across adenine bridges in doublestranded DNA by means of a multiscale approach, propagating the hole in the framework of timedependent 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 chargetransfer 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 chargetransfer models assuming static DNA structures, where only tunneling occurs. The solvent fluctuations introduce a significant correlation between neighboring sites, enhancing the chargetransfer rate, while the fluctuation of electronic couplings has only a minor impact on the chargetransfer 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.
Semenov, Alexander; Ivanov, Mikhail; Babikov, Dmitri
20130821
The mixed quantum/classical approach is applied to the problem of rovibrational 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 averagevelocity 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 semiquantitative 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.
Quantum money with classical verification
Gavinsky, Dmitry
20141204
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.
Quantum money with classical verification
NASA Astrophysics Data System (ADS)
Gavinsky, Dmitry
20141201
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.
NASA Astrophysics Data System (ADS)
Sbisà, Fulvio
20150101
The aim of these notes is to provide a selfcontained 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 cutoff, in which case the cutoff 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.
Semenov, Alexander; Babikov, Dmitri
20151217
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 moleculemolecule 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 meanfield potential. Numerical tests of this theory are carried out for several most important rotational statetostate transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with fullquantum 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 fullquantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetrictop rotor (polyatomic) molecules are relatively straightforward.
Quantum vs. classical walks with memory two
NASA Astrophysics Data System (ADS)
Dimcovic, Zlatko; Kovchegov, Yevgeniy
20100301
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 superexponential 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.
Quantum reduplication of classical solitons
NASA Astrophysics Data System (ADS)
Sveshnikov, Konstantin
19930901
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 weakcoupling expansion in √ γ such nonclassical 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 selfinteracting scalar field. Stability properties and quantization of fluctuations in the neighborhood of these configurations are also discussed in detail.
NASA Astrophysics Data System (ADS)
BedardHearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.
20051201
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 quantummechanical phase information (e.g., the decay of the offdiagonal 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 nuclearinduced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC moleculardynamics (MD) algorithm, which we call meanfield dynamics with stochastic decoherence (MFSD). MFSD begins by evolving the quantum subsystem according to the timedependent Schrödinger equation, leading to meanfield dynamics. MFSD then uses the nuclearinduced 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 wavefunction collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MFSD combines surface hops and decoherence into a single idea: decoherence in MFSD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MFSD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of
From classical to quantum criticality
NASA Astrophysics Data System (ADS)
Podolsky, Daniel; Shimshoni, Efrat; Silvi, Pietro; Montangero, Simone; Calarco, Tommaso; Morigi, Giovanna; Fishman, Shmuel
20140601
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 spacetime 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 linearzigzag instability in systems of trapped ions or repulsively interacting dipoles.
Classical and quantum Malus laws
NASA Astrophysics Data System (ADS)
Wódkiewicz, Krzysztof
19950401
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 pathintegral representation for the Malus amplitude. The classical limit of the Malus amplitude for s>∞ is discussed.
Gherib, Rami; Ryabinkin, Ilya G; Izmaylov, Artur F
20150414
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 quantumclassical (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 twodimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: (1) compensation for repulsive diagonal secondorder nonadiabatic couplings and (2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.
NASA Astrophysics Data System (ADS)
Kwac, Kijeong; Geva, Eitan
20110301
Liquid mixtures of methanold and carbon tetrachloride provide attractive model systems for investigating hydrogenbond structure and dynamics. The hydrogenbonded methanol oligomers in these mixtures give rise to a very broad hydroxyl stretch IR band (~ 150 cm1). We have employed mixed quantumclassical 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 hydrogenstretch frequency and bond length thereby reducing the computational cost dramatically to simulate the complex nonequilibrium dynamics underlying pumpprobe spectra.
Quantum teleportation without classical channel
NASA Astrophysics Data System (ADS)
Al Amri, M.; Li, ZhengHong; Zubairy, M. Suhail
20161101
For the first time, we show how quantum teleportation can be achieved without the assistance of classical channels. Our protocol does not need any preestablished 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 nonlocal 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.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
20160701
Quantum localization of classical mechanics within the BRSTBFV and BV (or fieldantifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRSTBFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRSTBFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial nondegenerate 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.
Quantum to classical randomness extractors
NASA Astrophysics Data System (ADS)
Wehner, Stephanie; Berta, Mario; Fawzi, Omar
20130301
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 quantumtoclassical randomness extractors (QCextractors). We identify an entropic quantity that determines exactly how much randomness can be obtained. Furthermore, we provide constructions of QCextractors 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 QCextractor 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 noisystorage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.
NASA Astrophysics Data System (ADS)
Padilla, Antonio; Pérez, Justo
20151001
We have developed a mixed classicalquantum 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 theoreticalexperimental comparative analysis of the spectral profiles. We have considered different models for the HClAr binary anisotropic interaction, founding also different predictions for the absorption line shape, in one case with the presence of the central Qbranch observed in the experimental spectrum, and in another case with the absence of such spectral component. We have found that the theoretical Qbranch noticeably depends on the characteristic of the different anisotropic diatomicsolvent potentials proposed in the literature.
Quantum remnants in the classical limit
NASA Astrophysics Data System (ADS)
Kowalski, A. M.; Plastino, A.
20160901
We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semiclassic 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 quantumclassic transition. The socalled mutual information is the appropriate quantifier for this task. Additionally, we study the BandtPompe's symbolic patterns that characterize dynamical time series (representative of the semiclassical system under scrutiny) in their evolution towards the classical limit.
Strong Analog Classical Simulation of Coherent Quantum Dynamics
NASA Astrophysics Data System (ADS)
Wang, DongSheng
20170201
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
Classical analog of quantum phase
Ord, G.N.
19920701
A modified version of the Feynman relativistic chessboard model (FCM) is investigated in which the paths involved are spirals in the spacetime. Portions of the paths in which the particle`s proper time is reversed are interpreted in terms of antiparticles. With this intepretation the particleantiparticle field produced by such trajectories provides a classical analog of the phase associated with particle paths in the unmodified FCM. It is shwon that in the nonrelativistic limit the resulting kernel is the correct Dirac propagator and that particleantiparticle symmetry is in this case responsible for quantum interference. 7 refs., 3 figs.
BedardHearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.
20061121
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 onephoton excitation of the THFsolvated electron. We find that as photoexcited THFsolvated 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 THFsolvated 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 THFsolvated 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.
Larsen, Ross E; BedardHearn, Michael J; Schwartz, Benjamin J
20061012
Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensedphase 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 excitedstate relaxation dynamics of the prototypical condensedphase MQC system, the hydrated electron, calculated using different algorithms, including: fewestswitches surface hopping, stationaryphase surface hopping, and meanfield dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, meanfield dynamics with stochastic decoherence (MFSD), is to be implemented for condensedphase problems, and we apply MFSD to the excitedstate relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydratedelectron relaxation dynamics. We find that for three MQC methods that use Tully's fewestswitches criterion to determine surface hopping probabilities, the excitedstate 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 MFSD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an
Reexamining the QuantumClassical Relation
NASA Astrophysics Data System (ADS)
Bokulich, Alisa
20081001
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.
Secure quantum communication using classical correlated channel
NASA Astrophysics Data System (ADS)
Costa, D.; de Almeida, N. G.; VillasBoas, C. J.
20161001
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.
Yamada, Atsushi; Okazaki, Susumu
20080128
We present a quantum equation of motion for chemical reaction systems on an adiabatic doublewell potential surface in solution in the framework of mixed quantumclassical molecular dynamics, where the reactant and product states are explicitly defined by dividing the doublewell 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 zeropoint 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 highenergy 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.
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.
20110401
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.
Mixed quantumclassical dynamics of an amideI vibrational excitation in a protein α helix
NASA Astrophysics Data System (ADS)
Freedman, Holly; Martel, Paulo; Cruzeiro, Leonor
20101101
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 amideI vibrational energy are excited and utilized to bring about important structural changes in the protein. To study whether, and how, amideI vibrational excitations are capable of leading to protein structural changes, we have added components arising from quantummechanical amideI vibrational excitations to the total energy and force terms within a moleculardynamics simulation. This model is applied to helical decaalanine as a test case to investigate how its dynamics differs in the presence or absence of an amideI excitation. We find that the presence of an amideI excitation can bias the structure toward a more helical state.
Quantum Simulations of Classical Annealing Processes
NASA Astrophysics Data System (ADS)
Somma, R. D.; Boixo, S.; Barnum, H.; Knill, E.
20080901
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.
Jeon, Kiyoung; Yang, Mino
20170207
Three lowlying vibrational states of molecular systems are responsible for the signals of linear and thirdorder 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 01 and 12 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.
NASA Astrophysics Data System (ADS)
Jeon, Kiyoung; Yang, Mino
20170201
Three lowlying vibrational states of molecular systems are responsible for the signals of linear and thirdorder 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 01 and 12 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.
Quantum simulation of classical thermal states.
Dür, W; Van den Nest, M
20111021
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 5body 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 twobody 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.
Shakib, Farnaz A.; Hanna, Gabriel
20160114
In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model protoncoupled electron transfer (PCET) reaction via the mixed quantumclassical 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 timedependent populations of the three lowest adiabatic states in the ETPT (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 secondexcited state can be mediated by dynamics on the mean of the ground and secondexcited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the firstexcited 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 PTET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT
Shakib, Farnaz A; Hanna, Gabriel
20160114
In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model protoncoupled electron transfer (PCET) reaction via the mixed quantumclassical 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 timedependent populations of the three lowest adiabatic states in the ETPT (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 secondexcited state can be mediated by dynamics on the mean of the ground and secondexcited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the firstexcited 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 PTET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT
Dynamics in the quantum/classical limit based on selective use of the quantum potential
Garashchuk, Sophya Dell’Angelo, David; Rassolov, Vitaly A.
20141221
A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the timedependent Schrödinger equation. The quantum potential is a nonlocal quantity, defined in the trajectorybased form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantummechanical 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 meanfield, 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 doublewell potentials, using conventional gridbased and approximate quantumtrajectory 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.
Coherent quantum states from classical oscillator amplitudes
NASA Astrophysics Data System (ADS)
Briggs, John S.; Eisfeld, Alexander
20120501
In the first days of quantum mechanics Dirac pointed out an analogy between the timedependent 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 timedependent amplitudes which are identical to the complex quantum amplitudes of the coupled wave function of an Nlevel quantum system with real coupling matrix elements. Hence classical motion can reproduce quantum coherence.
Rekik, Najeh; Hsieh, ChangYu; Freedman, Holly; Hanna, Gabriel
20130414
We apply two approximate solutions of the quantumclassical Liouville equation (QCLE) in the mapping representation to the simulation of the laserinduced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the ForwardBackward (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 surfacehopping 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 QCLEbased solutions is tested on a nontrivial electron transfer model involving more than two quantum states, a timedependent Hamiltonian, strong subsystembath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystembath coupling. In particular, we calculate the timedependent population of the photoexcited donor state in response to an ultrafast, onresonance pump pulse in a threestate 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 threestate electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLEbased surfacehopping 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 subsystembath 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 QCLEbased surfacehopping results. These findings
Rekik, Najeh; Freedman, Holly; Hanna, Gabriel; Hsieh, ChangYu
20130414
We apply two approximate solutions of the quantumclassical Liouville equation (QCLE) in the mapping representation to the simulation of the laserinduced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the ForwardBackward (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 surfacehopping 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 QCLEbased solutions is tested on a nontrivial electron transfer model involving more than two quantum states, a timedependent Hamiltonian, strong subsystembath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystembath coupling. In particular, we calculate the timedependent population of the photoexcited donor state in response to an ultrafast, onresonance pump pulse in a threestate 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 threestate electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLEbased surfacehopping 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 subsystembath 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 QCLEbased surfacehopping results. These findings
Kwac, Kijeong; Geva, Eitan
20130627
We present a mixed quantumclassical molecular dynamics study of the nonequilibrium hydrogenbond dynamics following vibrational energy relaxation of the hydroxyl stretch in a 10 mol % methanol/carbon tetrachloride mixture and pure methanol. The ground and firstexcited 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 steadystate absorption spectra and excited state lifetime [Kwac, K.; Geva, E. J. Phys. Chem. B 2011, 115, 9184; 2012, 116, 2856]. The relaxation from the firstexcited state to the ground state is treated as a nonadiabatic transition. Within the mixed quantumclassical treatment, relaxation from the excited state to the ground state is accompanied by a momentumjump 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 blueshifting the transition frequency by more than the Stokes shift between the steadystate 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 pumpprobe spectrum is analyzed in detail. The calculated pumpprobe spectrum is found
Shkrob, Ilya A; Glover, William J; Larsen, Ross E; Schwartz, Benjamin J
20070621
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 BeckeLeeYangParr functional and singleexcitation 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 redshifted 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 190nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, manyelectron effects must be accounted for: oneelectron models that do not allow for mixing of the excess
Unraveling Quantum Annealers using Classical Hardness.
MartinMayor, Victor; Hen, Itay
20151020
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 'DWave' 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 spinglass 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 DWave Two chip on different temperaturechaotic 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.
Semenov, Alexander; Babikov, Dmitri
20140128
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 tenorders 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 fullquantum scattering theory.
Classical Trajectories and Quantum Spectra
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Reyes, Marco A.
19960101
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 nonperturbative 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.
Decoherence, chaos, the quantum and the classical
Zurek, W.H.; Paz, J.P.
19940401
The key ideas of the environmentinduced 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.``
Thermodynamic integration from classical to quantum mechanics.
Habershon, Scott; Manolopoulos, David E
20111214
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 wellestablished method with an analysis of a onedimensional 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.
Quantum and Classical Electrostatics Among Atoms
NASA Astrophysics Data System (ADS)
Doerr, T. P.; Obolensky, O. I.; Ogurtsov, A. Y.; Yu, YiKuo
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)/augccpV5Z and CCSD(T)/augccpV5Z 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.
Classical and Quantum Spreading of Position Probability
ERIC Educational Resources Information Center
Farina, J. E. G.
19770101
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)
Unraveling Quantum Annealers using Classical Hardness
NASA Astrophysics Data System (ADS)
MartinMayor, Victor; Hen, Itay
20151001
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 ‘DWave’ 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 spinglass 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 DWave Two chip on different temperaturechaotic 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.
Unraveling Quantum Annealers using Classical Hardness
MartinMayor, Victor; Hen, Itay
20150101
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 ‘DWave’ 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 spinglass 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 DWave Two chip on different temperaturechaotic 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
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
20140321
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.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
20070720
We present a new approach to study the thermodynamic properties of ddimensional classical systems by reducing the problem to the computation of ground state properties of a ddimensional quantum model. This classicaltoquantum 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.
Understanding singularities — Classical and quantum
NASA Astrophysics Data System (ADS)
Konkowski, Deborah A.; Helliwell, Thomas M.
20160101
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 HusainMartinezNuñez spacetime and the Fonarev spacetime. The importance of understanding spacetime singularity structure is discussed.
Quantum Backreaction on Classical'' Variables
Anderson, A. Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2BZ )
19950130
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled HamiltonHeisenberg 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.
Classical and QuantumMechanical State Reconstruction
ERIC Educational Resources Information Center
Khanna, F. C.; Mello, P. A.; Revzen, M.
20120101
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…
Quantum phase uncertainties in the classical limit
NASA Technical Reports Server (NTRS)
Franson, James D.
19940101
Several sources of phase noise, including spontaneous emission noise and the loss of coherence due to whichpath information, are examined in the classical limit of high field intensities. Although the origin of these effects may appear to be quantummechanical in nature, it is found that classical analogies for these effects exist in the form of chaos.
Classical underpinnings of gravitationally induced quantum interference
Mannheim, P.D.
19980201
We show that the gravitational modification of the phase of a neutron beam [the ColellaOverhauserWerner (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}
Classical noise, quantum noise and secure communication
NASA Astrophysics Data System (ADS)
Tannous, C.; Langlois, J.
20160101
Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudonoise) as performed in spreadspectrum communication used presently in WiFi 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.
Kwac, Kijeong; Geva, Eitan
20110728
We present a mixed quantumclassical 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 quantummechanically, while the remaining degrees of freedom are treated classically. The adiabatic Hamiltonian of the quantummechanical hydroxyl is diagonalized onthefly 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 quantummechanical state of the tagged hydroxyl stretch via the corresponding HellmannFeynman forces. The ability of five different forcefield 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 groundstate hydrogenbonding 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), hydrogenbond acceptors (β), hydrogenbond donors (γ), simultaneous hydrogenbond donors and acceptors (δ), and simultaneous hydrogenbond donors and doubleacceptors (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
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, DaShin; Helou, Bassam; Chen, Yanbei
20130426
We apply the manyparticle SchrödingerNewton equation, which describes the coevolution of a manyparticle quantum wave function and a classical spacetime geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective SchrödingerNewton equation for their centers of mass, which can be monitored and manipulated at quantum levels by stateoftheart 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 eigenfrequencywith a difference that depends on the internal structure of the objectand can be observable using current technology. For several objects, the SchrödingerNewton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
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.
20160601
The control of quantum systems requires the ability to change and readout 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.
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.
20141001
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 DWave Vesuvius machine with revealing—though inconclusive—results.
Classical teleportation of a quantum Bit
Cerf; Gisin; Massar
20000313
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 positiveoperatorvalued measurements is also discussed.
Classical and Quantum Thermal Physics
NASA Astrophysics Data System (ADS)
Prasad, R.
20161101
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.
Quantumclassical crossover in electrodynamics
Polonyi, Janos
20060915
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 Diracsea 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 oneloop 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 quantumclassical crossover and the AbrahamLorentz 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 quantumclassical crossover in a systematical manner.
Entanglement in QuantumClassical Hybrid
NASA Technical Reports Server (NTRS)
Zak, Michail
20110101
It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, nonclassical systems such as quantumclassical 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 quantuminspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the HamiltonJacobi 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. Nonlocality 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 nonlocality in physics.
NUCLEAR MIXING METERS FOR CLASSICAL NOVAE
Kelly, Keegan J.; Iliadis, Christian; Downen, Lori; Champagne, Art; José, Jordi
20131110
Classical novae are caused by mass transfer episodes from a mainsequence 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 electrondegenerate 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 mainsequence 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 postprocessing network calculations with temperaturedensity 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.
Large classical universes emerging from quantum cosmology
PintoNeto, Nelson
20090415
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 WheelerDeWitt 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 abovementioned 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 transPlanckian problem.
Classical Ising model test for quantum circuits
NASA Astrophysics Data System (ADS)
Geraci, Joseph; Lidar, Daniel A.
20100701
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 RobertsonSeymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of nonnearestneighbor gates which admit an efficient classical simulation.
Quantum and classical opticsemerging links
NASA Astrophysics Data System (ADS)
Eberly, J. H.; Qian, XiaoFeng; Qasimi, Asma Al; Ali, Hazrat; Alonso, M. A.; GutiérrezCuevas, R.; Little, Bethany J.; Howell, John C.; Malhotra, Tanya; Vamivakas, A. N.
20160601
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 coexistence of separately identifiable and readily available vector spaces. Exploitation of these vectorspace relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantumclassical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.
Kwac, Kijeong; Geva, Eitan
20131227
The intramolecular hydrogenbond structure of stereoselectively synthesized syntetrol and antitetrol dissolved in deuterated chloroform is investigated via a mixed quantumclassical 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 AM1BCC). 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 hydrogenbond structure is elucidated.
Diamantis, Polydefkis; Gonthier, Jérôme Florian; Tavernelli, Ivano; Rothlisberger, Ursula
20140410
The oxidation of groundstate (singlet) and triplet [Ru(bpy)3](2+) were studied by full quantummechanical (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 singlepoint 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).
Communication: quantum dynamics in classical spin baths.
Sergi, Alessandro
20130721
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 openpath offdiagonal 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 nonMarkovian 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.
Classical enhancement of quantum vacuum fluctuations
NASA Astrophysics Data System (ADS)
De Lorenci, V. A.; Ford, L. H.
20170101
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 lightcone 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 thirdorder 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.
Uniform Additivity in Classical and Quantum Information
NASA Astrophysics Data System (ADS)
Cross, Andrew; Li, Ke; Smith, Graeme
20170101
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.
Gaugefields and integrated quantumclassical theory
Stapp, H.P.
19860101
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 quantumclassical 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 quantumclassical connection. 17 refs.
Quantumtoclassical transition in cavity quantum electrodynamics.
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
20101015
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 occupationor effective temperatureis raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantumtoclassical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and timeresolved vacuum Rabi measurements.
Classical Simulated Annealing Using Quantum Analogues
NASA Astrophysics Data System (ADS)
La Cour, Brian R.; Troupe, James E.; Mark, Hans M.
20160801
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.
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20151221
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative 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 temperaturedepending 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 quantumtoclassical crossover.« less
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20150101
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative 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 temperaturedepending 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 quantumtoclassical crossover. PMID:26688102
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20151221
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative 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 temperaturedepending 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 quantumtoclassical crossover.
Quantumtoclassical crossover near quantum critical point.
Vasin, M; Ryzhov, V; Vinokur, V M
20151221
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative 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 temperaturedepending 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 quantumtoclassical crossover.
Noisy quantum cellular automata for quantum versus classical excitation transfer.
Avalle, Michele; Serafini, Alessio
20140502
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.
Noisy Quantum Cellular Automata for Quantum versus Classical Excitation Transfer
NASA Astrophysics Data System (ADS)
Avalle, Michele; Serafini, Alessio
20140501
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.
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.
20161001
Using a watt balance and a frequency comb, a massenergy 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.
Comparing classical and quantum PageRanks
NASA Astrophysics Data System (ADS)
Loke, T.; Tang, J. W.; Rodriguez, J.; Small, M.; Wang, J. B.
20170101
Following recent developments in quantum PageRanking, we present a comparative analysis of discretetime and continuoustime quantumwalkbased 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 discretetime 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.
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
19790101
Comparisons are made for the particleinabox, the harmonic oscillator, and the oneelectron atom. A classical uncertainty principle is derived and compared with its quantummechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Categorical quantum mechanics II: Classicalquantum interaction
NASA Astrophysics Data System (ADS)
Coecke, Bob; Kissinger, Aleks
20160801
This is the second part of a threepart overview, in which we derive the categorytheoretic 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 classicalquantum 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 GHZstate and the Wstate come from spiderlike 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.
NASA Astrophysics Data System (ADS)
Kojima, H.; Yamada, A.; Okazaki, S.
20150501
The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantumclassical 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 doublewell shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zeropoint 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 solutesolvent interactions.
Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems
NASA Astrophysics Data System (ADS)
CárdenasLópez, F. A.; Allende, S.; Retamal, J. C.
20170301
Classical to quantum decoherence transition, an issue existing for incoherent superposition of Belldiagonal 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.
Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems.
CárdenasLópez, F A; Allende, S; Retamal, J C
20170320
Classical to quantum decoherence transition, an issue existing for incoherent superposition of Belldiagonal 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.
Isoperiodic classical systems and their quantum counterparts
NASA Astrophysics Data System (ADS)
Asorey, M.; Cariñena, J. F.; Marmo, G.; Perelomov, A.
20070601
Onedimensional 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.
Classical simulation of quantum fields I
NASA Astrophysics Data System (ADS)
Hirayama, T.; Holdom, B.
20061001
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zeropoint energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by WheelerFeynman 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 npoint 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 onshell simultaneously.
Geometric uncertainty relation for mixed quantum states
Andersson, Ole Heydari, Hoshang
20140415
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 RobertsonSchrödinger 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.
Monogamy properties of quantum and classical correlations
Giorgi, Gian Luca
20111115
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 threequbit 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 twoqubit states, discord and classical correlations are bounded from above by singlequbit von Neumann entropies.
Classical and quantummechanical state reconstruction
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Mello, P. A.; Revzen, M.
20120701
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 computeraided 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 graduatelevel readers.
The classicalquantum boundary for correlations: Discord and related measures
NASA Astrophysics Data System (ADS)
Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko
20121001
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 quantuminformation 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 classicalquantum 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 quantuminformationprocessing tasks, quantum thermodynamics, opensystem dynamics, and manybody physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
Nonadiabatic dynamics in open quantumclassical systems: forwardbackward trajectory solution.
Hsieh, ChangYu; Kapral, Raymond
20121214
A new approximate solution to the quantumclassical Liouville equation is derived starting from the formal solution of this equation in forwardbackward form. The time evolution of a mixed quantumclassical 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 2Ndimensional 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 quantumclassical Liouville equation exactly. Relations to other mixed quantumclassical and semiclassical schemes are discussed.
Mapping quantumclassical Liouville equation: projectors and trajectories.
Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond
20120228
The evolution of a mixed quantumclassical 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 quantumclassical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectorybased 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.
Mesoscopic systems: classical irreversibility and quantum coherence.
Barbara, Bernard
20120928
Mesoscopic physics is a subdiscipline of condensedmatter 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 largespin magnetic molecules called singlemolecule magnets (SMMs) with archetype Mn(12)ac. In general, the mesoscopic scale can be relatively large (e.g. micrometresized 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 LandauZener 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 nonMarkovian channel in which shortliving entanglements with distributions of twolevel systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)like
New variables for classical and quantum gravity
NASA Technical Reports Server (NTRS)
Ashtekar, Abhay
19860101
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 YangMills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.
Time in classical and in quantum mechanics
NASA Astrophysics Data System (ADS)
Elçi, A.
20100701
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 DiracHeisenbergvon Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the DiracHeisenbergvon Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.
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 quantummechanical explanation of the "emergence" of classicality.
Quantumclassical path integral. I. Classical memory and weak quantum nonlocality.
Lambert, Roberto; Makri, Nancy
20121214
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 largescale 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.
Statistical mechanics of quantumclassical systems with holonomic constraints.
Sergi, Alessandro
20060114
The statistical mechanics of quantumclassical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantumclassical bracket in matrix form. The resulting Dirac quantumclassical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentumjump 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 linearresponse function of constrained quantumclassical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
Sharing the Quantum State and the Classical Information Simultaneously
NASA Astrophysics Data System (ADS)
Qin, Huawang; Dai, Yuewei
20160801
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 quantumcontrollednot and Hadamard gate to encode the secret quantum state and classical information, and the participants use the singleparticle 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.
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
20010901
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.
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 inhomogeneityinduced 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 singlecrystalline 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.
Li Zhenni; Jin Jiasen; Yu Changshui
20110115
We present schemes for a type of oneparameter 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.
NASA Astrophysics Data System (ADS)
Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.
20150801
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and backactions 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.
Kwac, Kijeong; Geva, Eitan
20131121
The effect of vibrational excitation and relaxation of the hydroxyl stretch on the hydrogenbond structure and dynamics of stereoselectively synthesized syntetrol and antitetrol dissolved in deuterated chloroform are investigated via a mixed quantumclassical molecular dynamics simulation. Emphasis is placed on the changes in hydrogenbond structure upon photoexcitation and the nonequilibrium hydrogenbond 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 redshift 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 harmonicSchofield quantum correction factor, and found to be sensitive reporters of the underlying hydrogenbond 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.
Classical and nonclassical randomness in quantum measurements
NASA Astrophysics Data System (ADS)
Farenick, Douglas; Plosker, Sarah; Smith, Jerrod
20111201
The space POVM_H(X) of positive operatorvalued 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 ddimensional Hilbert space H, is studied from the perspectives of classical and nonclassical convexity through a transform Γ that associates any positive operatorvalued 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 operatorvalued integral in which nonclassical random variables (that is, operatorvalued functions) are integrated with respect to positive operatorvalued 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.
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 noncanonical scalar field showing that signals can escape black holes in the kessence 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 nexttoleading eikonal order is performed. We find that this correction to the scattering amplitude exponentiates, and that these power corrections probe smaller impact parameters
Quantum evaporation of flavormixed particles
NASA Astrophysics Data System (ADS)
Medvedev, Mikhail V.
20140301
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 masseigenstates can result in their interconversions. Most intriguing and counterintuitive 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 ``flavormixed 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 DEFG0207ER54940 and NSF grant AST1209665.
Classical simulation of quantum energy flow in biomolecules.
Stock, Gerhard
20090320
Based on a comparison of classical and quantummechanical 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.
Coarsening Measurement References and the QuantumtoClassical Transition
NASA Astrophysics Data System (ADS)
Jeong, Hyunseok; Lim, Youngrong; Kim, M. S.
20140101
We investigate the role of inefficiency in quantum measurements in the quantumtoclassical transition, and consistently observe the quantumtoclassical 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.
Emergence of a classical Universe from quantum gravity and cosmology.
Kiefer, Claus
20120928
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.
Classical Physics and the Bounds of Quantum Correlations.
Frustaglia, Diego; Baltanás, José P; VelázquezAhumada, María C; FernándezPrieto, Armando; Lujambio, Aintzane; Losada, Vicente; Freire, Manuel J; Cabello, Adán
20160624
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 metersize transmissionline 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.
QuantumClassical Hybrid for Information Processing
NASA Technical Reports Server (NTRS)
Zak, Michail
20110101
Based upon quantuminspired entanglement in quantumclassical hybrids, a simple algorithm for instantaneous transmissions of nonintentional messages (chosen at random) to remote distances is proposed. The idea is to implement instantaneous transmission of conditional information on remote distances via a quantumclassical 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 xcoordinate 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
Excited State QuantumClassical Molecular Dynamics
NASA Astrophysics Data System (ADS)
Krstic, Predrag
20050501
The development of a new theoretical, algorithmic, and computational framework is reported describing the corresponding excited state manybody dynamics by applying multiphysics described by classical equations of motion for nuclei and HartreeFock/MultiConfiguration HartreeFock 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 electrontransition dynamics which involves molecular clusters, containing hundreds of atoms, perturbed by a slow ionic/atomic/molecular projectile, with possible applications in plasmasurface interactions, cluster physics, chemistry and biotechnology. The validation of the developed technique is performed at threebody systems. Application to the transition dynamics in small carbon clusters and hydrocarbons perturbed by slow carbon ions resolves some longstanding issues in the ionsurface interactions in fusion tokamaks.
Trotterbased simulation of quantumclassical dynamics.
Kernan, Dónal Mac; Ciccotti, Giovanni; Kapral, Raymond
20080117
Quantum rate processes in condensed phase systems are often computed by combining quantum and classical descriptions of the dynamics. An algorithm for simulating the quantumclassical 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 quantumclassical propagator, in conjunction with Monte Carlo sampling of quantum transitions, to yield a surfacehopping 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 quantumclassical Liouville dynamics for the time evolution. The algorithm is tested by calculations on the spinboson 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 quantumclassical Liouville dynamics.
Extended hydrodynamic approach to quantumclassical nonequilibrium evolution. I. Theory.
Bousquet, David; Hughes, Keith H; Micha, David A; Burghardt, Irene
20110214
A mixed quantumclassical formulation is developed for a quantum subsystem in strong interaction with an Nparticle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the Nparticle distribution and the corresponding reduced singleparticle distribution, exact quantum hydrodynamic equations are obtained for the momentum moments of the singleparticle distribution coupled to a discretized quantum subsystem. The quantumclassical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a GradHermitetype closure, (ii) a Gaussian closure at the level of a quantumclassical 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 quantumclassical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys. 134, 343 (2006).
Clean Quantum and Classical Communication Protocols
NASA Astrophysics Data System (ADS)
Buhrman, Harry; Christandl, Matthias; Perry, Christopher; Zuiddam, Jeroen
20161201
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.
Beyond quantumclassical analogies: high time for agreement?
NASA Astrophysics Data System (ADS)
Marrocco, Michele
Lately, many quantumclassical 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 quantumclassical 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 quantummechanical 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.
NASA Astrophysics Data System (ADS)
Henner, Victor K.; Klots, Andrey; Belozerova, Tatyana
20161201
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.
Complementarity of quantum discord and classically accessible information
Zwolak, Michael P.; Zurek, Wojciech H.
20130520
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 observableindependent 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 quasiclassical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an antisymmetry 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.
Complementarity of quantum discord and classically accessible information
Zwolak, Michael P.; Zurek, Wojciech H.
20130520
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 observableindependent 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 quasiclassical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an antisymmetry 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
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.
20150501
Categorytheoretic 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.
Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems
CárdenasLópez, F. A.; Allende, S.; Retamal, J. C.
20170101
Classical to quantum decoherence transition, an issue existing for incoherent superposition of Belldiagonal 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
Quantum and classical behavior in interacting bosonic systems
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
20161101
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 microstate 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 microstate are approximated by a corresponding classical ensemble average over many classical microstates. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single microstate. So the correlation functions of the quantum and classical field theories of a single microstate 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.
Quantum and classical behavior in interacting bosonic systems
Hertzberg, Mark P.
20161121
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 microstate 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 microstate are approximated by a corresponding classical ensemble average over many classical microstates. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single microstate. So the correlation functions of the quantum and classical field theories of a single microstate 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.
On the correspondence between quantum and classical variational principles
Ruiz, D. E.; Dodin, I. Y.
20150610
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 pointparticle and coldfluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and KleinGordon particles.
INCLINATION MIXING IN THE CLASSICAL KUIPER BELT
Volk, Kathryn; Malhotra, Renu
20110720
We investigate the longterm 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 highinclination populations. We find that some classical KBOs undergo large changes in inclination over gigayear timescales, which means that a current member of the lowinclination population may have been in the highinclination 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 sizeinclination and colorinclination 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 nonbinary objects. Our study of resonant objects in the classical Kuiper Belt region includes objects in the 3:2, 7:4, 2:1, and eight higherorder mean motion resonances. We find that these objects (some of which were previously classified as nonresonant) undergo larger changes in inclination compared to the nonresonant population, indicating that their current inclinations are not generally representative of their original inclinations. They are also less stable on gigayear timescales.
Noiseenhanced classical and quantum capacities in communication networks.
Caruso, Filippo; Huelga, Susana F; Plenio, Martin B
20101105
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.
Quasisuperactivation for the classical capacity of quantum channels
Gyongyosi, Laszlo; Imre, Sandor
20141204
The superactivation effect has its roots in the extreme violation of additivity of the channel capacity and enables to reliably transmit quantum information over zerocapacity 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.
Classical and quantum stability in putative landscapes
NASA Astrophysics Data System (ADS)
Dine, Michael
20170101
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 wouldbe 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.
FokkerPlanck quantum master equation for mixed quantumsemiclassical dynamics.
Ding, JinJin; Wang, Yao; Zhang, HouDao; Xu, RuiXue; Zheng, Xiao; Yan, YiJing
20170114
We revisit CaldeiraLeggett's quantum master equation representing mixed quantumclassical theory, but with limited applications. Proposed is a FokkerPlanck quantum master equation theory, with a generic biexponential 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 quasiclassical description on environments. Various parametrization schemes, both analytical and numerical, for the generic biexponential environment bath correlation functions are proposed and scrutinized. The FokkerPlanck quantum master equation theory is of the same numerical cost as the original CaldeiraLeggett'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.
Functional methods underlying classical mechanics, relativity and quantum theory
NASA Astrophysics Data System (ADS)
Kryukov, A.
20130401
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 nontrivial 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.
Generic emergence of classical features in quantum Darwinism
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Piani, Marco; Horodecki, Paweł
20150801
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 systemofinterest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.
Generic emergence of classical features in quantum Darwinism.
Brandão, Fernando G S L; Piani, Marco; Horodecki, Paweł
20150812
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 systemofinterest 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.
Models on the boundary between classical and quantum mechanics.
Hooft, Gerard 't
20150806
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.
Quantum physics of classical waves in plasma
NASA Astrophysics Data System (ADS)
Dodin, I. Y.
20121001
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 MaxwellVlasov system is abandoned. Oscillations are rather treated as physical entities, namely, abstract vectors ψ> in a specific Hilbert space. The invariant product <ψψ> 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 WignerMoyal 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 ManleyRowe relations, then becomes manifest and in partial equilibrium can modify statistical properties of plasma fluctuations. In the quasimonochromatic 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 energymomentum 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 singleparticle oscillationcenter 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.
Twoslit experiment: quantum and classical probabilities
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
20150601
Interrelation 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 quantumclassical interrelation 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 twoslit 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 twoslit experiment have the nonKolmogorovian 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 nonclassicality of quantum probability. We compare this embedding of nonKolmogorovian quantum probabilities into the Kolmogorov model with wellknown embeddings of nonEuclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).
Line mixing effects in isotropic Raman spectra of pure N2: a classical trajectory study.
Ivanov, Sergey V; Boulet, Christian; Buzykin, Oleg G; Thibault, Franck
20141114
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 uptodate intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve offdiagonal crosssections 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 semiclassical RobertBonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semiclassical) 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.
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
20141101
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 uptodate intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve offdiagonal crosssections 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 semiclassical RobertBonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semiclassical) 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.
Quantumclassical correspondence in steady states of nonadiabatic systems
Fujii, Mikiya; Yamashita, Koichi
20151231
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., quantumclassical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantumclassical 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.
Manikandan, Paranjothy; Hase, William L
20120514
Previous studies have shown that classical trajectory simulations often give accurate results for shorttime intramolecular and unimolecular dynamics, particularly for initial nonrandom 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 nonRRKM 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.
Classical and quantum distinctions between weak and strong coupling
NASA Astrophysics Data System (ADS)
RahimzadehKalaleh Rodriguez, Said
20160301
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 quantumclassical 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 nonHermitian 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 nonHermitian 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.
Classical to quantum correspondence in dissipative directed transport
NASA Astrophysics Data System (ADS)
Carlo, Gabriel G.; Rivas, Alejandro M. F.; Spina, María E.
20151101
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 PerronFrobenius 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 WeylWigner 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.
Is classical flat Kasner spacetime flat in quantum gravity?
NASA Astrophysics Data System (ADS)
Singh, Parampreet
20160501
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 BianchiI 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 BianchiI 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.
Surface hopping from the perspective of quantumclassical Liouville dynamics
NASA Astrophysics Data System (ADS)
Kapral, Raymond
20161201
Fewestswitches surface hopping is studied in the context of quantumclassical Liouville dynamics. Both approaches are mixed quantumclassical theories that provide a way to describe and simulate the nonadiabatic quantum dynamics of manybody systems. Starting from a surfacehopping solution of the quantumclassical Liouville equation, it is shown how fewestswitches 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.
Glover, William J; Larsen, Ross E; Schwartz, Benjamin J
20081028
The chargetransfertosolvent (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 singleelectron description of the atomic aniononly 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 oneelectron model and address the role of electronic exchange and correlation in both CTTS electronic structure and dynamics. To do this, we perform manyelectron mixed quantum/classical molecular dynamics simulations of the ground and excitedstate 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 oneelectron 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 twoelectron aqueous sodide. For example, the oneelectron model substantially underpredicts the size of sodide, which in turn results in a dramatically
Experimental deviceindependent tests of classical and quantum dimensions
NASA Astrophysics Data System (ADS)
Ahrens, Johan; Badziag, Piotr; Cabello, Adán; Bourennane, Mohamed
20120801
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 deviceindependent 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.
Quantum and classical operational complementarity for single systems
Luis, Alfredo
20050715
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.
Quantum nonlocality and the end of classical spacetime
NASA Astrophysics Data System (ADS)
Banerjee, Shreya; Bera, Sayantani; Singh, Tejinder P.
20160701
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.
Efficient classical simulation of optical quantum information circuits.
Bartlett, Stephen D; Sanders, Barry C
20021111
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, photodetectionbased measurement, and classical feedforward of measurement results, optimal cloning, and a wide range of other processes.
The Classical Scattering of Waves: Some Analogies with Quantum Scattering
19920101
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Genuine quantum and classical correlations in multipartite systems.
Giorgi, Gian Luca; Bellomo, Bruno; Galve, Fernando; Zambrini, Roberta
20111104
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 twobody mutual informations, or, equivalently, by onequbit entropies.
Entropies and correlations in classical and quantum systems
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe
20160901
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.
Playing with functions of positive type, classical and quantum
NASA Astrophysics Data System (ADS)
Aniello, Paolo
20150601
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 phasespace 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 quasiprobability distribution; hence, it can be regarded as a phasespace 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 classicalquantum 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 classicalnoise semigroups.
Isochronous classical systems and quantum systems with equally spaced spectra
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Perelomov, A. M.; Rañada, M. F.
20071101
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 creationlike differential operators. The harmonic oscillator and the isotonic oscillator are the two main essentially unique examples of such situation.
Reversing quantum dynamics with nearoptimal quantum and classical fidelity
NASA Astrophysics Data System (ADS)
Barnum, H.; Knill, E.
20020501
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.
NASA Astrophysics Data System (ADS)
Boche, Holger; Cai, Minglai; Deppe, Christian; Nötzel, Janis
20170101
We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classicalquantum 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 classicalquantum wiretap channels.
QuantumClassical Correspondence of Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
20170401
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Kortewegde Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of timedependent parameters. We use the HamiltonJacobi 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.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
20140315
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 BoseEinstein statistics with the related problem of the condensation and the FermiDirac statistics.
Efficient classical simulation of continuous variable quantum information processes.
Bartlett, Stephen D; Sanders, Barry C; Braunstein, Samuel L; Nemoto, Kae
20020304
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 GottesmanKnill 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.
Faithful actions of locally compact quantum groups on classical spaces
NASA Astrophysics Data System (ADS)
Goswami, Debashish; Roy, Sutanu
20170301
We construct examples of locally compact quantum groups coming from bicrossed product construction, including nonKac 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):141160, 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.
The ambiguity of simplicity in quantum and classical simulation
NASA Astrophysics Data System (ADS)
Aghamohammadi, Cina; Mahoney, John R.; Crutchfield, James P.
20170401
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 modelmemory. 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.
Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations.
Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor
20160617
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.
Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations
NASA Astrophysics Data System (ADS)
Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor
20160601
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.
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.
20151001
We derive a ‘master’ wave equation for a family of complexvalued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the HamiltonJacobi 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 manybody theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in nonrelativistic and relativistic quantum field theory.
Information security: from classical to quantum
NASA Astrophysics Data System (ADS)
Barnett, Stephen M.; Brougham, Thomas
20120901
Quantum cryptography was designed to provide a new approach to the problem of distributing keys for privatekey 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.
NASA Astrophysics Data System (ADS)
Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius
20170201
We address the dynamics of quantum correlations, including entanglement and quantum discord of a threequbit 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 GreenbergerHorneZeilinger (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 systemenvironment 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 Wtype state has strong dynamics under this noise than the GHZtype ones.
Planck's radiation law: is a quantumclassical perspective possible?
NASA Astrophysics Data System (ADS)
Marrocco, Michele
20160501
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 quantumclassical correspondence between classical Mie theory and quantummechanical 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.
Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates.
Bravyi, Sergey; Gosset, David
20160624
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 mediumsized quantum circuits dominated by Clifford gates. The first demonstrations of faulttolerant 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 nearterm 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.
Quantum correction to classical gravitational interaction between two polarizable objects
NASA Astrophysics Data System (ADS)
Wu, Puxun; Hu, Jiawei; Yu, Hongwei
20161201
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 leadingorder perturbation theory, we study, from a quantum fieldtheoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as twolevel harmonic oscillators. We find that the interaction potential behaves like r11 in the retarded regime and r10 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.
Classical and quantum dynamics of the sphere
NASA Astrophysics Data System (ADS)
Lasukov, Vladimir; Moldovanova, Evgeniia; Abdrashitova, Maria; Malik, Hitendra; Gorbacheva, Ekaterina
20160701
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 LemaitreFriedmann primordial atom in superspacetime, 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.
Takeoka, Masahiro; Fujiwara, Mikio; Mizuno, Jun; Sasaki, Masahide
20040501
Quantuminformation theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantumchannel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantumcoding 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 quantumcollective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantumclassical hybrid coding scheme. We show how the superadditive quantumcoding gain, even in a small code length, can boost the communication performance of conventional coding techniques.
Quantum Plasma Effects in the Classical Regime
Brodin, G.; Marklund, M.; Manfredi, G.
20080502
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 spinup and spindown are regarded as different fluids. By studying the propagation of Alfven wave solitons we demonstrate that quantum effects can survive in a relatively hightemperature plasma. The consequences of our results are discussed.
New mixed quantum/semiclassical propagation method
NASA Astrophysics Data System (ADS)
Antoniou, Dimitri; Gelman, David; Schwartz, Steven D.
20070501
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 lowdimensional systems, in which comparison to exact quantum dynamics is feasible.
Observation of Quantum Fingerprinting Beating the Classical Limit.
Guan, JianYu; Xu, Feihu; Yin, HuaLei; Li, Yuan; Zhang, WeiJun; Chen, SiJing; Yang, XiaoYan; Li, Li; You, LiXing; Chen, TengYun; Wang, Zhen; Zhang, Qiang; Pan, JianWei
20160617
Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantummechanical 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 proofofprinciple experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting singlephoton detectors and a stable fiberbased 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.
Observation of Quantum Fingerprinting Beating the Classical Limit
NASA Astrophysics Data System (ADS)
Guan, JianYu; Xu, Feihu; Yin, HuaLei; Li, Yuan; Zhang, WeiJun; Chen, SiJing; Yang, XiaoYan; Li, Li; You, LiXing; Chen, TengYun; Wang, Zhen; Zhang, Qiang; Pan, JianWei
20160601
Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantummechanical 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 proofofprinciple experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting singlephoton detectors and a stable fiberbased 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.
Quantumclassical transition and quantum activation of ratchet currents in the parameter space.
Beims, M W; Schlesinger, M; Manchein, C; Celestino, A; Pernice, A; Strunz, W T
20150501
The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zerotemperature 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.
Quantum mechanics can reduce the complexity of classical models.
Gu, Mile; Wiesner, Karoline; Rieper, Elisabeth; Vedral, Vlatko
20120327
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.
Classicaldrivingassisted quantum speedup
NASA Astrophysics Data System (ADS)
Zhang, YingJie; Han, Wei; Xia, YunJie; Cao, JunPeng; Fan, Heng
20150301
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 zerotemperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speedup evolution of an open system can be achieved in both the weak systemenvironment couplings and the strong systemenvironment couplings. By considering the relationship between nonMakovianity of environment and the classical field, we can drive the open system from the Markovian to the nonMarkovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speedup process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.
Electromagnetically induced classical and quantum Lau effect
NASA Astrophysics Data System (ADS)
Qiu, Tianhui; Yang, Guojian; Xiong, Jun; Xu, Deqin
20160701
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 twophoton coincidence measurement with a pair of entangled photons being the imaging light.
PREFACE: Particles and Fields: Classical and Quantum
NASA Astrophysics Data System (ADS)
Asorey, M.; ClementeGallardo, J.; Marmo, G.
20070701
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 lifelong 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 ClementeGallardo and G Marmo The Local Organizing Committee George Sudarshan
A. Ashtekhar (Pennsylvania State University, USA) 
L. J. Boya (Universidad de Zaragoza, Spain) 
I. Cirac (Max Planck Institute, Garching
Quantum and classical dynamics of Langmuir wave packets. Haas, F; Shukla, P K 20090601 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 Gaussianshaped localized solutions, via the RayleighRitz 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 lasersolid plasma compression experiment is discussed. Experimental deviceindependent tests of classical and quantum entropy NASA Astrophysics Data System (ADS) Zhu, Feng; Zhang, Wei; Chen, Sijing; You, Lixing; Wang, Zhen; Huang, Yidong 20161201 In quantum information processing, it is important to witness the entropy of the message in the deviceindependent 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 deviceindependent 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. Revivals and classicalmotion 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 issuesthe revivals of the shape and classical motion of these wave packets that occur long after their initial decay, and the classicalmotion bases that describe the quantum wavefunction in terms of constitutive objects that move classically. We study the infinite squarewell potential, a simple model of complete confinement in a onedimensional 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 wavemotion 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 squarewell potential and we show how the wavemotion 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 phasedifference 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 Classical and quantum cosmology of minimal massive bigravity NASA Astrophysics Data System (ADS) Darabi, F.; Mousavi, M. 20161001 In a FriedmannRobertsonWalker (FRW) spacetime 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 SchrodingerWheelerDeWitt 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 HartleHawking noboundary 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. NASA Astrophysics Data System (ADS) Malpetti, Daniele; Roscilde, Tommaso 20170201 The meanfield 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 manybody systems at finite temperature, twopoint 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, temperaturedependent quantum coherence length. The existence of these two different forms of correlation in quantum manybody 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 pathintegral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum meanfield (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster meanfield theory at T =0 , while at any finite temperature it produces a family of systematically improved, semiclassical 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 twodimensional quantum Ising model and of twodimensional 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 boundarytobulk 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 Generating shortcuts to adiabaticity in quantum and classical dynamics NASA Astrophysics Data System (ADS) Jarzynski, Christopher 20131001 Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counterdiabatic Hamiltonian to stifle nonadiabatic transitions. Here this shortcut to adiabaticity is cast in terms of a generator of adiabatic transport. This yields a classical analog of transitionless driving, and provides a strategy for constructing quantal counterdiabatic Hamiltonians. As an application of this framework, exact classical and quantal counterdiabatic terms are obtained for a particle in a box and for evenpowerlaw potentials in one degree of freedom.
