Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization

TL;DR

This paper investigates how non-equilibrium density profiles evolve in quantum systems, revealing that pure states with certain randomness exhibit linear response behavior, while coherences lead to different dynamics.

Contribution

It demonstrates that specific pure states with randomized off-diagonal elements can reproduce linear response broadening, highlighting the importance of initial-state structure.

Findings

Pure states with randomized off-diagonal elements follow linear response broadening.

Coherences in initial states cause deviations from expected diffusion behavior.

The results clarify the role of initial-state realization in quantum transport dynamics.

Abstract

The real-time broadening of density profiles starting from non-equilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum amplitude yield a broadening in perfect agreement with linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior.