Notes on frequencies and timescales in nonequilibrium Green's functions

TL;DR

This paper investigates how the nonequilibrium Green's function relaxes in a strongly coupled holographic theory, revealing that quasinormal modes govern the relaxation timescale during rapid temperature changes.

Contribution

It provides detailed numerical analysis of spectral function relaxation in holographic models, highlighting the role of quasinormal modes in nonequilibrium dynamics.

Findings

Relaxation timescale matches the lowest quasinormal mode frequency.

Spectral function evolution is governed by quasinormal modes.

Background temperature change timescale influences frequency analysis.

Abstract

We discuss the ringdown behavior of the nonequilibrium Green's function in a strongly coupled theory with the holographic dual with a focus on quasinormal-mode equilibration. We study the time resolved spectral function for a probe scalar in Vaidya-AdS spacetime in detail as a complement to the preceding work arXiv:1603.06935 using further numerical results in very nonadiabatic temperature changes. It is shown that the relaxation of the nonequilibrium spectral function obtained through the Wigner transform is governed by the lowest quasinormal mode frequency. The timescale of the background temperature change is also observed in the frequency analysis. We then consider a toy model motivated by the quasinormal mode behavior and discuss these main features in numerical results are simply realized.