Wen-ge Wang

Crossover of quantum Loschmidt echo from golden-rule decay to perturbation-independent decay

We study the crossover of the quantum Loschmidt echo (or fidelity) from the golden-rule regime to the perturbation-independent exponential decay regime by using the kicked top model. It is shown that the deviation of the perturbation-independent decay of the averaged fidelity from the Lyapunov decay results from quantum fluctuations in individual fidelity, which are caused by the coherence in the initial coherent states. With an averaging procedure suppressing the quantum fluctuations effectively, the perturbation-independent decay is found to be close to the Lyapunov decay. We also show that the Fourier transform of the fidelity is determined directly by the initial state and the eigenstates of the Floquet operators of the two classically chaotic systems concerned. The absolute value part and the phase part of the Fourier transform of the fidelity are found to be divided into several correlated parts, which is a manifestation of the coherence of the initial coherent state. In the whole crossover region, some important properties of the fidelity, such as the exponent of its exponential decay and the short initial time within which the fidelity almost does not change, are found to be closely related to the properties of the central part of its Fourier transform.

Fidelity for the quantum evolution of a Bose-Einstein condensate

Jie Liu, Wenge Wang, Chuanwei Zhang, Qian Niu and Baowen Li Department of Physics, National University of Singapore, 117542, Republic of Singapore Institute of Applied Physics and Computational Mathematics, P.O.Box 100088, Beijing, P. R. China Department of Physics, Southeast University, Nanjing 210096, P. R. China 4 Department of Physics, The University of Texas, Austin, Texas 78712-1081 USA 5 Center for Nonlinear Dynamics, The University of Texas, Austin, Texas 78712-1081 USA (Dated: today)

Stability of quantum motion: Beyond Fermi-golden-rule and Lyapunov decay

We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay. In particular, when the underlying classical dynamics is weakly chaotic, deviations from Fermi-golden-rule and Lyapounov regimes are observed and discussed.

Entanglement-induced decoherence and energy eigenstates

Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help with understanding the dynamics of quantum entanglement generation in chaotic quantum systems.

Uniform semiclassical approach to fidelity decay in the deep Lyapunov regime.

We use the uniform semiclassical approximation in order to derive the fidelity decay in the regime of large perturbations. Numerical computations are presented which agree with our theoretical predictions. Moreover, our theory allows us to explain previous findings, such as the deviation from the Lyapunov decay rate in cases where the classical finite-time instability is nonuniform in phase space.

Uniform semiclassical approach to fidelity decay : From weak to strong perturbation

We study fidelity decay by a uniform semiclassical approach, in the three perturbation regimes: namely, the perturbative regime, the Fermi golden rule (FGR) regime, and the Lyapunov regime. A semiclassical expression is derived for the fidelity of initial Gaussian wave packets with width of the order sqare root h (h being the effective Planck constant). The short-time decay of the fidelity of initial Gaussian wave packets is also studied with respect to two time scales introduced in the semiclassical approach. In the perturbative regime, it is confirmed numerically that fidelity has FGR-type decay before Gaussian decay sets in. An explanation is suggested for a non-FGR decay in the FGR regime of a system with weak chaos in the classical limit by using the Levy distribution as an approximation for the distribution of the action difference. In the Lyapunov regime, it is shown that the average of the logarithm of fidelity may have roughly Lyapunov decay within some time interval in systems possessing large fluctuations in the finite-time Lyapunov exponent in the classical limit.

Preferred States of Decoherence under Intermediate System-Environment Coupling

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understanding of decoherence and quantum thermalization processes.

Stability of quantum motion in regular systems: a uniform semiclassical approach.

We study the stability of quantum motion of classically regular systems in the presence of small perturbations. On the basis of a uniform semiclassical theory we derive the fidelity decay which displays a quite complex behavior, from Gaussian to power law decay t(-alpha), with 1 <or= alpha <or= 2. Semiclassical estimates are given for the time scales separating the different decaying regions, and numerical results are presented which confirm our theoretical predictions.

Statistically preferred basis of an open quantum system: its relation to the eigenbasis of a renormalized self-Hamiltonian.

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.

Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart.

We study the stability of a two-component Bose-Einstein condensate (BEC) in the parameter regime in which its classical counterpart has regular motion. The stability is characterized by the fidelity for both the same and different initial states. We study as initial states the Fock states with definite numbers of atoms in each component of the BEC. It is found that for some initial times the two Fock states with all the atoms in the same component of the BEC are more stable than Fock states with atoms distributed in the two components. An experimental scheme is discussed, in which the fidelity can be measured in a direct way.