Environment-induced sudden transition in quantum discord dynamics

Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.     

Absence of thermalization in nonintegrable systems

We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.     

Thermodynamic aspects of Schrödinger's probability relations

Using Schrödinger's generalized probability relations of quantum mechanics, it is possible to generate a canonical ensemble, the ensemble normally associated with thermodynamic equilibrium, by at least two methods, statistical mixing and subensemble selection, that do not involve thermodynamic equilibration. Thus the question arises as to whether an observer making measurements upon systems from a canonical ensemble can determine whether the systems were prepared by mixing, equilibration, or selection. Investigation of this issue exposes antinomies in quantum statistical thermodynamics. It is conjectured that resolution of these paradoxes may involve a new law of motion in quantum dynamics.     

Quantum uncertainty relations of two generalized quantum relative entropies of coherence

In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.     

The Onsager relations for quantum systems weakly coupled to KMS reservoirs

We show that the Onsager relations for energy and matter flows through small quantum systems are generically direct consequences of the KMS (Kubo-Martin-Schwinger) property of the reservoir (Gibbs) equilibrium states in the (van Hove) weak coupling limit.     

Gibbs ensembles in relativistic classical and quantum mechanics

Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.     

Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].     

Quantum Gibbs Samplers: The Commuting Case

We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs state and the mixing time of the semigroup which drives the system to thermal equilibrium (the Gibbs sampler). We introduce a framework for analyzing the correlation and mixing properties of quantum Gibbs states and quantum Gibbs samplers, which is rooted in the theory of non-commutative \({\mathbb{L}_p}\) spaces. We consider two distinct classes of Gibbs samplers, one of them being the well-studied Davies generator modelling the dynamics of a system due to weak-coupling with a large Markovian environment. We show that their spectral gap is independent of system size if, and only if, a certain strong form of clustering of correlations holds in the Gibbs state. Therefore every Gibbs state of a commuting Hamiltonian that satisfies clustering of correlations in this strong sense can be prepared efficiently on a quantum computer. As concrete applications of our formalism, we show that for every one-dimensional lattice system, or for systems in lattices of any dimension at temperatures above a certain threshold, the Gibbs samplers of commuting Hamiltonians are always gapped, giving an efficient way of preparing the associated Gibbs states on a quantum computer.     

Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.     

Substantiating the Gibbs method in classical statistical mechanics

An approach for the substantiation of the Gibbs method in equilibrium statistical thermodynamics is described; this approach is based not on the quasiergodicity hypothesis, but on the weaker assumption of macroscopic determinacy of thermodynamic systems. A generalized microcanonical Gibbs distribution is obtained. An electron gas in a homogeneous magnetic field is taken as an example. It is shown that the classical diamagnetism of the given system is not zero in the sense of quasimean nor of generalized Gibbs ensemble distributions. The equation of state of an electron as in a magnetic field is obtained, and hence it is shown that classical diamagnetism only vanishes if isotropy of the pressure at the vessel wall is assumed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 65–68, June, 1978.     

A Real Ensemble Interpretation of Quantum Mechanics

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics.     

声子库的量子态对介观电路量子特性影响的研究

考虑电子与声子间相互作用,研究了两种声子库纯初始态(正则系综与粒子数态)下耗散介观电路的动力学特性.长时间极限下(t→∞)：当环境处于热平衡态时,电路系统中的电流和电荷的平均值只与电路所处初始量子态中的平均值有关,与环境无关;环境初态为粒子数态时,电荷与电流平均值随时间的演化特性与环境初始处于热平衡态下时完全一样,表明介观电路中的电荷与电流的平均值与环境量子态的某组占有数无关.电路中电流和电荷的量子涨落不仅与系统的初态有关,还与系统所处环境的量子态及温度有关.一般地说,电路系统与环境的纠缠会 关键词： 介观耗散电路 声子库 量子初态 量子态纯度     

Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics

The relation between chaotic dynamics of nonlinear Hamiltonian systems and equilibrium statistical mechanics in its canonical ensemble formulation has been investigated for two different nonlinear Hamiltonian systems. We have compared time averages obtained by means of numerical simulations of molecular dynamics type with analytically computed ensemble averages. The numerical simulation of the dynamic counterpart of the canonical ensemble is obtained by considering the behavior of a small part of a given system, described by a microcanonical ensemble, in order to have fluctuations of the energy of the subsystem. The results for the Fermi-Pasta-Ulam model (i.e., a one-dimensional anharmonic solid) show a substantial agreement between time and ensemble averages independent of the degree of stochasticity of the dynamics. On the other hand, a very different behavior is observed for a chain of weakly coupled rotators, where linear exchange effects are absent. In the high-temperature limit (weak coupling) we have a strong disagreement between time and ensemble averages for the specific heat even if the dynamics is chaotic. This behavior is related to the presence of spatially localized chaos, which prevents the complete filling of the accessible phase space of the system. Localized chaos is detected by the distribution of all the characteristic Liapunov exponents.     

Dissipative evolution of quantum statistical ensembles and nonlinear response to a time-periodic perturbation

We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation.Received: 26 November 2003, Published online: 30 January 2004PACS: 05.30.-d Quantum statistical mechanics - 33.35. + r Electron resonance and relaxation - 33.25. + k Nuclear resonance and relaxation     

Phase-Dependent Effects in Stern-Gerlach Experiments

In the frame of quantum mechanics, we consider an ensemble of spin-1/2 neutral particles passing through a Stern-Gerlach apparatus and explore how their motions depend on the initial phase difference between two internal spin states. Assuming the particles moving along y-axis, due to the initial phase difference between spin states, they not only split along the longitudinal direction （z-axis） but also separate along the lateral direction （x-axis）. The dependence of the lateral displacement on the initial phase difference reminds one of the picture of a quantum interference. This generalized interference provides an alternative approach to measuring the initial phase difference. The experimental realization with ultracold atoms or Bose-Einstein condensates is also discussed.     

Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.     

Estimation of concurrence for multipartite mixed states

We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.     

Entropy of isolated quantum systems after a quench

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.