Universal many-body diffusion from momentum dephasing

TL;DR

This paper demonstrates that momentum dephasing in quantum many-body systems universally induces diffusive behavior in local densities, affecting dynamics and sound-wave propagation, with implications for understanding decoherence and transport.

Contribution

It introduces a general framework showing momentum dephasing causes diffusive dynamics in quantum many-body systems, with universal effects on diffusion constants and sound-wave damping.

Findings

Momentum dephasing induces diffusive behavior in local densities.

Dephasing introduces a universal additive term to the diffusion constant.

Sound-wave dispersion is damped similarly to Navier-Stokes predictions.

Abstract

The open dynamics of quantum many-body systems involve not only the exchange of energy, but also of other conserved quantities, such as momentum. This leads to additional decoherence, which may have a profound impact in the dynamics. Motivated by this, we consider a many-body system subject to total momentum dephasing and show that under very general conditions this leads to a diffusive component in the dynamics of any local density, even far from equilibrium. Such component will usually have an intricate interplay with the unitary dynamics. To illustrate this, we consider the case of a superfluid and show that momentum dephasing introduces a damping in the sound-wave dispersion relation, similar to that predicted by the Navier-Stokes equation for ordinary fluids. Finally, we also study the effects of dephasing in linear response, and show that it leads to a universal additive contribution to the diffusion constant, which can be obtained from a Kubo formula.