Bulk viscosity of dual Bose and Fermi gases in one dimension

TL;DR

This paper demonstrates that the weak-strong duality in one-dimensional Bose and Fermi gases extends to their frequency-dependent bulk viscosities, providing new insights into their dynamic response properties across different coupling regimes.

Contribution

The study extends the known thermodynamic duality to dynamic bulk viscosity, including high-temperature agreement and perturbative calculations at weak coupling.

Findings

Bulk viscosities of Bose and Fermi gases agree at high temperature.

Perturbative calculations of bulk viscosities at weak coupling are performed.

Duality relates weak-coupling results of one system to strong-coupling of the other.

Abstract

One-dimensional Bose and Fermi gases with contact interactions are known to exhibit the weak-strong duality, where the equilibrium thermodynamic properties of one system at weak coupling are identical to those of the other system at strong coupling. Here, we show that such duality extends beyond the thermodynamics to the frequency-dependent complex bulk viscosity, which is provided by the contact-contact response function. In particular, we confirm that the bulk viscosities of the Bose and Fermi gases agree in the high-temperature limit, where the systematic expansion in terms of fugacity is available at arbitrary coupling. We also compute their bulk viscosities perturbatively in the weak-coupling limit at arbitrary temperature, which via the duality serve as those of the Fermi and Bose gases in the strong-coupling limit.