Propagation and attenuation of sound in one-dimensional quantum liquids

TL;DR

This paper investigates how sound propagates and attenuates in one-dimensional quantum liquids, revealing the nature of two sound modes and their transformation under dissipation, with distinctions based on particle spin properties.

Contribution

It provides a detailed analysis of sound modes in 1D quantum liquids, including the effects of dissipation and the role of particle spin, extending understanding of two-fluid hydrodynamics in these systems.

Findings

Identification of two sound modes analogous to superfluid helium.

Description of how dissipation transforms second sound into heat diffusion.

Elucidation of the crossover from two-fluid to single-fluid regimes at low frequencies.

Abstract

At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid $^4$He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid the entropy and density oscillations are strongly coupled, and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.