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Wen-ge Wang

Publications and source records attributed to Wen-ge Wang.

48 records · Page 3Linked to original sources
arXiv2008

Sensitivity of Quantum Motion to Perturbation in Triangle Map

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength $ε$. In the regime of weak perturbation, the fidelity decays as $\exp (-cε^2 t^γ)$ with $γ\simeq 1.7$. In the regime of strong perturbation, the fidelity is approximately a function of $εt^{2.5}$, which is predicted for the classical fidelity [G. Casati, {\it et al}, Phys.Rev.Lett.{\bf 94}, 114101 (2005)], and decays slower than power-law decay for long times. In an intermediate regime, the fidelity has approximately an exponential decay $\exp (-c' εt)$.

nlin.CD↗
arXiv2008

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 understanding the dynamics of quantum entanglement generation in chaotic quantum systems.

quant-ph↗
arXiv2007

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

We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to power law decay $t^{-α}$ with $1 \le α\le 2$. Semiclassical estimates are given for the time scales separating the different decaying regions and numerical results are presented which confirm our theoretical predictions.

quant-ph↗
arXiv2006

Entanglement and Disentanglement, Probabilistic Interpretation of Statevectors, and Transformation between Intrinsic Frames of Reference

We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors of systems outside the system satisfy Schrödinger equation. A process of collision-type interaction between a microscopic system and a macroscopic system is studied in an auxiliary frame of reference. In transforming the statevector of the two systems obtained in the auxiliary frame of reference to the intrinsic frame of reference of the macroscopic system, the above first assumption requires a discontinuous change of the statevector. A probabilistic interpretation is given to the statevector for the discontinuous change. For the microscopic system, the density matrix given in the theory here is equal to the reduced density matrix given in the usual quantum mechanics.

quant-ph↗
arXiv2005

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 to explain previous findings, such as the deviation from the Lyapunov decay rate in cases where the classical finite-time instability is non-uniform in phase space.

quant-ph↗
arXiv2004

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 fidelity of initial Gaussian wave packets with width of the order $\sqrt{\hbar}$ ($\hbar$ being the effective Planck constant). Short time decay of 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 the FGR decay before the Gaussian decay sets in. An explanation is suggested to a non-FGR decay in the FGR regime, which has been observed in a system with weak chaos in the classical limit, by using the Levy distribution as an approximation for the distribution of action difference. In the Lyapunov regime, it is shown that the average of the logarithm of fidelity may have roughly the Lyapunov decay within some time interval, in systems possessing large fluctuation of the finite-time Lyapunov exponent in the classical limit.

quant-ph↗
arXiv2003

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 properties of the central part of its Fourier transform.

nlin.CD↗
arXiv1998

Perturbative and non-perturbative parts of eigenstates and local spectral density of states: the Wigner band random matrix model

A generalization of Brillouin-Wigner perturbation theory is applied numerically to the Wigner Band Random Matrix model. The perturbation theory tells that a perturbed energy eigenstate can be divided into a perturbative part and a non-perturbative part with the perturbative part expressed as a perturbation expansion. Numerically it is found that such a division is important in understanding many properties of both eigenstates and the so-called local spectral density of states (LDOS). For the average shape of eigenstates, its central part is found to be composed of its non-perturbative part and a region of its perturbative part, which is close to the non-perturbative part. A relationship between the average shape of eigenstates and that of LDOS can be explained. Numerical results also show that the transition for the average shape of LDOS from the Breit-Wigner form to the semicircle form is related to a qualitative change in some properties of the perturbation expansion of the perturbative parts of eigenstates. The transition for the half-width of the LDOS from quadratic dependence to linear dependence on the perturbation strength is accompanied by a transition of a similar form for the average size of the non-perturbative parts of eigenstates. For both transitions, the same critical perturbation strength $λ_b$ has been found to play important roles. When perturbation strength is larger than $λ_b$, the average shape of LDOS obeys an approximate scaling law.

cond-mat↗
arXiv1998

Statistical Study for Eigenfunctions of 1-dimensional Tight Binding Model

For energy eigenfunctions of 1-dimensional tight binding model, the distribution of ratio of their nearest components, denoted by f(p), gives information for their fluctuation properties. The shape of f(p) is studied numerically for three versions of the 1D tight binding model. It is found that when perturbation is strong the shape of f(p) is usually quite close to that of the Lorentzian distribution. In the case of weak perturbation the shape of the central part of f(p) is model-dependent while tails of f(p) are still close to the Lorentzian form.

cond-mat.dis-nn↗
arXiv1997

Structure of Eigenstates and Local Spectral Density of States: A Three-Orbital Schematic Shell Model

The average shape of the Spectral Local Density of States (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) which can exhibit strong chaos in the classical limit. The attention is paid to the comparison of the shape of LDOS with that known for random matrix models, as well as to the shape of the EFs, for different values of the perturbation strength. The classical counterparts of the LDOS has also been studied and found in a remarkable agreement with the quantum calculations. Finally, by making use of a generalization of Brillouin- Wigner perturbation expansion, the form of long tails of LDOS and EFs is given analytically and confirmed numerically.

chao-dyn↗