The holographic spectral function in non-equilibrium states

TL;DR

This paper develops a holographic method to compute spectral functions in non-equilibrium states, enabling analysis of energy and spin shifts of quasi-particles and revealing relaxation dynamics in strongly coupled systems.

Contribution

It introduces a universal holographic prescription for spectral functions in non-equilibrium states, overcoming limitations of previous boundary conditions, and relates spectral features to relaxation modes.

Findings

Horizon regularity condition enables perturbative expansion in non-equilibrium holography.

Spectral functions encode information about system relaxation modes.

A temperature and chemical potential window exists where non-equilibrium states are characterized by few operators.

Abstract

We develop holographic prescriptions for obtaining spectral functions in non-equilibrium states and space-time dependent non-equilibrium shifts in the energy and spin of quasi-particle like excitations. We reproduce strongly coupled versions of aspects of non-equilibrium dynamics of Fermi surfaces in Landau's Fermi-liquid theory. We find that the incoming wave boundary condition at the horizon does not suffice to obtain a well-defined perturbative expansion for non-equilibrium observables. Our prescription, based on analysis of regularity at the horizon, allows such a perturbative expansion to be achieved nevertheless and can be precisely formulated in a universal manner independent of the non-equilibrium state, provided the state thermalizes. We also find that the non-equilibrium spectral function furnishes information about the relaxation modes of the system. Along the way, we argue that in a typical non-supersymmetric theory with a gravity dual, there may exist a window of temperature and chemical potential at large N, in which a generic non-equilibrium state can be characterized by just a finitely few operators with low scaling dimensions, even far away from the hydrodynamic limit.