# The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases

## TL;DR

This paper uncovers a hierarchy of exceptionally long-lived excitation modes in two-dimensional Fermi gases, revealing unique angular structures and long-time dynamics that bridge ballistic and hydrodynamic transport regimes.

## Contribution

It introduces a detailed analysis of long-lived excitation modes with specific angular dependencies and their impact on the transport properties of 2D Fermi gases, highlighting a new regime of angular (super)diffusion.

## Key findings

- Long-lived modes exceed conventional Fermi-liquid lifetimes by a factor of (T_F/T)^2.
- Odd m modes have lifetimes with m^4 log m dependence, while even m modes follow conventional lifetimes.
- Long-time dynamics exhibit angular (super)diffusion, leading to unusual memory effects.

## Abstract

Momentum-conserving quasiparticle collisions in two-dimensional Fermi gases give rise to a large family of exceptionally long-lived excitation modes. The lifetimes of these modes exceed by a factor $(T_F/T)^2\gg 1$ the conventional Landau Fermi-liquid lifetimes $\tau\sim T_F/T^2$. The long-lived modes have a distinct angular structure, taking the form of $\cos m\theta$ and $\sin m\theta$ with odd $m$ values for a circular Fermi surface, with relaxation rate dependence on $m$ of the form $m^4\log m$, valid at not-too-large $m$. In contrast, the even-$m$ harmonics feature conventional lifetimes with a weak $m$ dependence. The long-time dynamics, governed by the long-lived modes, takes the form of angular (super)diffusion over the Fermi surface. Altogether, this leads to unusual long-time memory effects, defining an intriguing transport regime that lies between the conventional ballistic and hydrodynamic regimes.