Diffusive behavior from a quantum master equation

Abstract

We study a general class of translation invariant quantum Markov evolutions for a particle on ${\mathbb{Z}}^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and exponentially fast relaxation of the momentum distribution. It is shown that the particle position diffuses in the long time limit. This generalizes standard results about central limit theorems for classical (non-quantum) Markov processes.

21 pages. Minor corrections of previous version

References in corpus (11)

• Diamondoid Molecules
• Collisional decoherence reexamined
• Quantum linear Boltzmann equation
• The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
• Monitoring derivation of the quantum linear Boltzmann equation
• Damped Bloch oscillations of cold atoms in optical lattices
• Diffusion of wave packets in a Markov random potential
• Quantum Brownian Motion in a Simple Model System
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Cited by in corpus (5)

• Quantum linear Boltzmann equation
• Scattering induced current in a tight-binding band
• Diffusive propagation of wave packets in a fluctuating periodic potential
• Diffusive limit for a quantum linear Boltzmann dynamics
• Non-markovian limits of additive functionals of Markov processes