Quantum trajectories for Brownian motion

Unraveling Quantum Brownian Motion: Pointer States and their Classical Trajectories

We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their phase space trajectories turn into those of classical diffusion, yielding a clear picture of the induced quantum- classical transition.

薛定谔波函数物理学能解释布朗运动吗？III：一个展现类布朗运动轨迹和扩散的一维重轻粒子模型

Can Schroedingerist Wavefunction Physics Explain Brownian Motion? III: A One-Dimensional Heavy and Light Particles Model Exhibiting Brownian-Motion-Like Trajectories and Diffusion

本文提出一个一维重轻粒子波函数模型，在有限微扰级数条件下证实重粒子展现类布朗运动轨迹与扩散，并发现普朗克常数和轻粒子分子质量影响扩散系数，从而区别于经典理论。

Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited

Stochastic Schr{ö}dinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schr{ö}dinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most-employed exactly soluble models of open system dynamics. We show explic…

Brownian Motion: The Quantum Perspective

We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.

Brownian Motion and Quantum Mechanics

A theoretical parallel between the classical Brownian motion and quantum mechanics is explored. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the two stochastic sources, the quantum Brownian motion takes place, which is theoretically described as well.

Overview: Brownian Motion and Dephasing due to Dynamical Disorder

The motion of a particle under the influence of a dynamical disorder is described by the DLD model. One motivation is to understand the motion of an electron inside a metal; Another is to understand quantal Brownian motion. The overview is based on a research report for 1996-1998.