Umklapp collisions and center of mass oscillation of a trapped Fermi gas

TL;DR

This paper investigates how umklapp collisions affect the damping of center of mass oscillations in a trapped Fermi gas within a periodic potential, highlighting differences from superfluid behavior.

Contribution

It provides a theoretical analysis of damping mechanisms in a normal Fermi gas using the Boltzmann equation, emphasizing the role of umklapp processes.

Findings

Center of mass oscillations are strongly damped above the first Bloch band due to umklapp collisions.

Damping is prominent in the collisional regime, contrasting with superfluid oscillations.

The study offers insights into transport phenomena in trapped Fermi gases with periodic potentials.

Abstract

Starting from the the Boltzmann equation, we study the center of mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the the Fermi energy above the first Bloch band the center of mass motion is strongly damped in the collisional regime due to umklapp processes. This should be contrasted with the behaviour of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.