标题： 面向非线性量子福克-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等人的平衡半经典方法，以更准确地描述演化过程。 结果推导出一个新的半经典Klein-Kramers方程，用于Wigner函数，该方程对于自由量子布朗粒子仍保持量子性。 它被转化为一个半经典Smoluchowski方程，从而得出我们之前推导的经典的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方程的可能性。 显示英文摘要

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