Non-Hydrodynamic Initial Conditions are Not Soon Forgotten

TL;DR

This paper demonstrates that non-hydrodynamic initial conditions can have long-lasting effects in systems described by hydrodynamics, challenging the common assumption that only hydrodynamic variables matter over time.

Contribution

It reveals the importance of non-hydrodynamic initial conditions and their long-term influence, using diffusion in disordered electron systems as an example.

Findings

Non-hydrodynamic initial conditions affect long-term dynamics.

Long-time-tail effects are prevalent in hydrodynamic systems.

Hydrodynamic descriptions may be incomplete without considering initial non-hydrodynamic variables.

Abstract

Solutions to hydrodynamic equations, which are used for a vast variety of physical problems, are assumed to be specified by boundary conditions and initial conditions on the hydrodynamic variables only. Initial values of other variables are assumed to be irrelevant for a hydrodynamic description. This assumption is not correct because of the existence of long-time-tail effects that are ubiquitous in systems governed by hydrodynamic equations. We illustrate this breakdown of a hydrodynamic description by means of the simple example of diffusion in a disordered electron system.