Emergent Viscous Hydrodynamics From a Single Quantum Particle

TL;DR

This paper demonstrates how a single quantum particle coupled to a thermal bath can exhibit emergent hydrodynamic behavior at late times, bridging quantum decoherence and classical fluid dynamics.

Contribution

It introduces a method to derive hydrodynamic equations from a quantum particle system interacting with an environment, revealing the quantum-to-classical transition in open systems.

Findings

Hydrodynamic equations resemble those used in quark-gluon plasma simulations.

Transport coefficients are linked to the environment's damping constant.

Asymptotic behavior reduces to Navier-Stokes equations with drag.

Abstract

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the non-relativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant $\gamma$, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.