Scale invariance and viscosity of a two-dimensional Fermi gas

TL;DR

This study explores the collective excitations and viscosity of a two-dimensional Fermi gas, revealing a scaling symmetry and providing insights into its dynamical behavior across different regimes.

Contribution

It demonstrates the presence of a dynamical SO(2,1) scaling symmetry and measures the shear viscosity's temperature dependence in a 2D Fermi gas.

Findings

Breathing mode frequency is twice the dipole mode frequency across various conditions.

Breathing mode remains undamped, indicating a scaling symmetry.

Shear viscosity varies with temperature, affecting collective excitations.

Abstract

We investigate the collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed at a frequency two times the dipole mode frequency for a large range of interaction strengths and temperatures, and the amplitude of the breathing mode is undamped. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.