Quantum fluctuations in hydrodynamics and quantum long-time tails

TL;DR

This paper develops a quantum effective field theory for hydrodynamics that incorporates quantum fluctuations and non-Gaussian noise, leading to a quantum extension of hydrodynamic long-time tails and providing explicit one-loop correlation functions.

Contribution

It introduces a quantum Schwinger-Keldysh framework for diffusive hydrodynamics, revealing how quantum corrections generate non-Gaussian noise and long-time tail effects at all orders in 5.

Findings

Derived quantum corrections to density-density correlation functions.

Established a quantum generalization of hydrodynamic long-time tails.

Provided explicit polynomial and closed-form expressions for one-loop results.

Abstract

We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in $\hbar$. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.