Quantum Brownian Motion in a Simple Model System

Abstract

We consider a quantum particle coupled (with strength $\la$) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the long-time behavior of the particle is diffusive for small, but finite $\la$. Our proof relies on an expansion around the kinetic scaling limit ($\la \searrow 0$, while time and space scale as $\la^{-2}$) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of $O(\la^2)$.

v1--> v2, mistake corrected in Lemma 6.2, to appear in CMP

References in corpus (4)

• Another Return of 'Return to Equilibrium'
• Introduction to representations of the canonical commutation and anticommutation relations
• Diffusion of wave packets in a Markov random potential
• Adiabatic-Nonadiabatic Transition in the Diffusive Hamiltonian Dynamics of a Classical Holstein Polaron

Cited by in corpus (10)

• The Open Quantum Brownian Motion
• Scattering induced current in a tight-binding band
• Diffusive behavior from a quantum master equation
• Diffusive propagation of wave packets in a fluctuating periodic potential
• On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• The weak coupling limit for the random Schrödinger equation: The average wave function
• Quantum Diffusion with Drift and the Einstein Relation I
• Quantum Diffusion with Drift and the Einstein Relation II
• Diffusive limit for a quantum linear Boltzmann dynamics
• Differential Equations of Quantum Mechanics