标题： 向非线性量子福克-普朗克方程 显示英文标题

标题： Towards Nonlinear Quantum Fokker-Planck Equations

摘要： 展示了如何改进Coffey等人最初的半经典方法，以正确描述时间演化。 结果推导出一个新的半经典Klein-Kramers方程，用于Wigner函数，即使对于自由量子布朗粒子也保持量子性。 它被转换为一个半经典Smoluchowski方程，从而得到我们对经典爱因斯坦布朗运动定律的半经典推广。 讨论了如何基于Fisher信息将这些半经典方程扩展为非线性量子Fokker-Planck方程。 显示英文摘要

摘要： It is demonstrated how the original semiclassical approach of Coffey et al can be improved to describe correctly the time evolution as well. As a result a new semiclassical Klein-Kramers equation for the Wigner function is derived, which remains quantum also for a free quantum Brownian particle. It is transformed to a semiclassical Smoluchowski equation, which leads to our semiclassical generalization of the classical Einstein law of Brownian motion. A possibility is discussed how to extend these semiclassical equations to nonlinear quantum Fokker-Planck equations based on the Fisher information.