Hydrodynamics from quantum fields: a regularized expansion from the Wigner distribution

TL;DR

This paper develops a quantum hydrodynamic expansion using the Wigner distribution, providing a systematic and regularized approach that converges even far from equilibrium, bridging quantum kinetic theory and hydrodynamics.

Contribution

It introduces a modified method of moments applied to the Wigner distribution to derive a regularized, systematically improvable quantum hydrodynamic expansion.

Findings

The regularized expansion converges numerically far from equilibrium.

Avoids divergences typical in quantum kinetic theory.

Demonstrates applicability beyond the kinetic limit.

Abstract

Second-order relativistic hydrodynamics is surprisingly predictive, even in the presence of large gradients. The hydrodynamic expansion from the method of moments does not require a gradient expansion, but it is intrinsically bound to the classic nature of relativistic kinetic theory. In this work a modified version of the method of moments is applied the Wigner distribution (the quantum precursor of the distribution function) to recover a systematically improvable hydrodynamic expansion, avoiding the divergences that would otherwise appear in the quantum case. The convergence of the regularized expansion is checked numerically in a far from equilibrium, distant from the kinetic limit case.