Quantum Generalized Hydrodynamics

TL;DR

This paper extends the classical Generalized Hydrodynamics framework to include quantum fluctuations in one-dimensional quantum gases, providing a more accurate description of non-equilibrium quantum systems.

Contribution

It introduces a quantized version of GHD, connecting it to Luttinger liquid theory with parameters derived from Thermodynamic Bethe Ansatz, capturing quantum effects.

Findings

Quantum GHD describes quantum fluctuations in non-equilibrium systems.

The theory is equivalent to a multi-component Luttinger liquid.

It improves predictions over traditional Luttinger liquid theory for zero-entropy states.

Abstract

Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed Generalized Hydrodynamics (GHD), was found for quantum integrable models in one spatial dimension. Despite its great predictive power, GHD, like any Euler hydrodynamic equation, misses important quantum effects, such as quantum fluctuations leading to non-zero equal-time correlations between fluid cells at different positions. Focusing on the one-dimensional gas of bosons with delta repulsion, and on states of zero entropy, for which quantum fluctuations are larger, we reconstruct such quantum effects by quantizing GHD. The resulting theory of quantum GHD can be viewed as a multi-component Luttinger liquid theory, with a small set of effective parameters that are fixed by the Thermodynamic Bethe Ansatz. It describes quantum fluctuations of truly nonequilibrium systems where conventional Luttinger liquid theory fails.