Diffusion for Holographic Lattices

TL;DR

This paper develops a systematic method to analyze diffusion modes in holographic models with broken translational symmetry, relating their dispersion relations to thermoelectric conductivities and susceptibilities, and linking thermodynamic and dynamical instabilities.

Contribution

It introduces a perturbative approach to construct diffusion quasinormal modes in holographic lattices and derives a generalized Einstein relation connecting transport and thermodynamic properties.

Findings

Dispersion relations expressed via thermoelectric conductivities.

Generalized Einstein relation from Einstein's equations.

Thermodynamic instabilities lead to specific dynamical instabilities.

Abstract

We consider black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. We discuss how the quasinormal modes associated with diffusion of heat and charge can be systematically constructed in a long wavelength perturbative expansion. We show that the dispersion relation for these modes is given in terms of the thermoelectric DC conductivity and static susceptibilities of the dual field theory and thus we derive a generalised Einstein relation from Einstein's equations. A corollary of our results is that thermodynamic instabilities imply specific types of dynamical instabilities of the associated black hole solutions.