Second sound in systems of one-dimensional fermions

TL;DR

This paper investigates second sound phenomena in one-dimensional fermion systems, revealing conditions under which heat propagates ballistically or diffusively, depending on frequency and temperature.

Contribution

It introduces the existence of second sound in 1D fermions and characterizes its damping behavior across different frequency regimes.

Findings

Second sound exists in 1D fermions at certain frequencies.

Weak damping of second sound at high frequencies.

Heat propagation transitions from ballistic to diffusive at lower frequencies.

Abstract

We study sound in Galilean invariant systems of one-dimensional fermions. At low temperatures, we find a broad range of frequencies in which in addition to the waves of density there is a second sound corresponding to ballistic propagation of heat in the system. The damping of the second sound mode is weak, provided the frequency is large compared to a relaxation rate that is exponentially small at low temperatures. At lower frequencies the second sound mode is damped, and the propagation of heat is diffusive.