标题： 经典动力学对于线性系统：量子布朗运动的情况 显示英文标题

标题： Classical Dynamics for Linear Systems: The Case of Quantum Brownian Motion

摘要： 长期以来，人们一直认识到线性量子系统的动力学在Wigner表示中是经典的。 然而，许多概念上重要的线性问题通常使用诸如影响泛函和Bogoliubov变换等通用技术进行分析。 在本文中，我们指出经典运动方程为线性量子系统提供了一个更简单且更直观的形式化方法。 我们研究了独立振子模型中的布朗运动这一重要问题，并表明量子动力学可以直接且完整地由一个c数朗之万方程描述。 我们还能够应用关于量子布朗运动的最新见解，以表明无论环境的谱密度如何，经典Fokker-Planck方程在时间上总是局部的。 显示英文摘要

摘要： It has long been recognized that the dynamics of linear quantum systems is classical in the Wigner representation. Yet many conceptually important linear problems are typically analyzed using such generally applicable techniques as influence functionals and Bogoliubov transformations. In this Letter we point out that the classical equations of motion provide a simpler and more intuitive formalism for linear quantum systems. We examine the important problem of Brownian motion in the independent oscillator model, and show that the quantum dynamics is described directly and completely by a c-number Langevin equation. We are also able to apply recent insights into quantum Brownian motion to show that the classical Fokker-Planck equation is always local in time, regardless of the spectral density of the environment.