Hydrodynamics with spacetime-dependent scattering length

TL;DR

This paper develops hydrodynamic equations for nonrelativistic fluids with spacetime-dependent scattering length, revealing new dissipative effects and proposing a novel method to measure bulk viscosity in ultracold-atom experiments.

Contribution

It introduces a hydrodynamic framework incorporating spacetime-dependent scattering length and identifies its impact on dissipation and entropy production.

Findings

Leading dissipative correction to contact density proportional to bulk viscosity.

Entropy density produced by slow scattering length variation without fluid flow.

Potential experimental probe for bulk viscosity in ultracold-atom systems.

Abstract

Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a spacetime-dependent scattering length and show that it enters constitutive relations uniquely so as to represent the fluid expansion and contraction in both normal and superfluid phases. As a consequence, we find that a leading dissipative correction to the contact density due to the spacetime-dependent scattering length is proportional to the bulk viscosity ($\zeta_2$ in the superfluid phase). Also, when the scattering length is slowly varied over time in a uniform system, the entropy density is found to be produced even without fluid flows in proportion to the bulk viscosity, which may be useful as a novel probe to measure the bulk viscosity in ultracold-atom experiments.