Quantum Diffusion

TL;DR

This paper investigates how a quantum system influenced by classical noise evolves, deriving a stochastic Liouville equation that reveals unique quantum diffusion effects absent in classical systems.

Contribution

It introduces a generalized framework for quantum diffusion under classical noise, including new quantum-specific diffusion terms and special cases with non-Fokker-Planck dynamics.

Findings

Derivation of a stochastic Liouville equation for quantum systems with classical noise

Identification of quantum diffusion terms absent in classical diffusion

Analysis of special cases with localized and spatially modulated noise sources

Abstract

We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ``quantum diffusion'' terms arise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source.