Universal Transport Properties of Continuous quantum gases

TL;DR

This paper uses advanced theoretical methods to exactly compute and relate the ballistic transport properties of one-dimensional quantum gases, providing universal laws and experimental protocols for measurement.

Contribution

It introduces an exact, universal relationship between Drude weight components and thermodynamic quantities in continuous integrable quantum gases.

Findings

Derived analytical expressions for Drude weights in different regimes.

Identified universal scaling laws near quantum phase transitions.

Proposed experimental protocols for measuring Drude weights.

Abstract

The Drude weight characterizes ballistic transport in quantum many-body systems, yet a comprehensive understanding and exact analytical results for it remain elusive, especially in multi-component quantum gases. In this work, we leverage Generalized Hydrodynamics and the Thermodynamic Bethe Ansatz method to precisely compute the Drude weights of one-dimensional continuous integrable systems, such as the Lieb-Liniger model and the Bose-Fermi mixture model. We establish an exact, universal relationship between components of the Drude weight matrix and fundamental thermodynamic quantities (e.g., particle, enthalpy, and entropy densities) for the constituent particles with distinct statistics undergo dynamic coupling. For both models, we further derive analytical approximations of the Drude weight in distinct physical regimes and identify universal scaling laws for the Drude weight near quantum phase transitions.Finally, to connect theory with experiment, we propose and simulate two feasible measurement protocols--a linear potential quench and a bipartitioning setup-verifying that they can reliably extract the Drude weights. Our results establish a direct link between macroscopic transport phenomena and microscopic quasiparticle structure, furnishing critical theoretical benchmarks for future ultracold atomic gas experiments.