Rate of decoherence for an electron weakly coupled to a phonon gas

TL;DR

This paper analyzes how an electron's quantum coherence diminishes over time due to weak interactions with a phonon gas, revealing an exponential decay of interference effects linked to scattering cross sections.

Contribution

It provides a detailed analysis of decoherence dynamics in the kinetic regime for an electron coupled to phonons, highlighting the decay rate's dependence on scattering properties.

Findings

Non-diagonal density matrix terms decay exponentially.

Decoherence rate proportional to total scattering cross section.

Interference between localized electron states is destroyed over time.

Abstract

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.