Time-dependence of the holographic spectral function: Diverse routes to thermalisation

TL;DR

This paper introduces a new method to compute the holographic spectral function in non-equilibrium states, revealing diverse thermalisation behaviors and non-adiabatic features during quenches in holographic models.

Contribution

The authors develop a novel approach for calculating the holographic retarded propagator in non-equilibrium states and analyze the spectral function's time-dependence during quenches.

Findings

Spectral function follows thermal form at long quench durations.

Shorter quenches exhibit non-adiabatic features like advanced time-dependence and spectral weight transfer.

Thermalisation patterns vary with momentum, showing complex top-down behavior.

Abstract

We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.