Wang Wen-Ge, Li Baowen
Department of Physics and Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Singapore), National University of Singapore, 117542, Republic of Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066203. doi: 10.1103/PhysRevE.71.066203. Epub 2005 Jun 3.
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.
我们通过统一的半经典方法研究保真度衰减，涵盖三种微扰 regime：即微扰 regime、费米黄金规则（FGR） regime 和李雅普诺夫 regime。针对宽度为有效普朗克常数 h 的平方根量级的初始高斯波包的保真度，推导出了一个半经典表达式。还针对半经典方法中引入的两个时间尺度，研究了初始高斯波包保真度的短时衰减。在微扰 regime 中，通过数值确认在高斯衰减开始之前保真度具有 FGR 型衰减。对于经典极限下具有弱混沌的系统在 FGR regime 中的非 FGR 衰减，通过使用列维分布作为作用差分布的近似给出了一种解释。在李雅普诺夫 regime 中，表明在经典极限下有限时间李雅普诺夫指数存在大波动的系统中，保真度对数的平均值在某个时间间隔内可能大致具有李雅普诺夫衰减。
