Relaxation regimes of the holographic electrons at charge neutrality after a local quench of chemical potential

Abstract

In this work we study the relaxation of the system of strongly correlated electrons, at charge neutrality, when the chemical potential undergoes a local change. This setup is a model for for the X-ray absorbtion edge study in the half-filled graphene. We use holographic duality to describe the system as a classical Schwarzschild black hole in curved 4-dimensional AdS spacetime. Assuming the amplitude of the quench is small, we neglect the backreaction on the geometry. We numerically study the two relaxation regimes: the adiabatic relaxation when the quench is slow and the relaxation governed by the quasinormal modes of the system, when the quench is fast. We confirm the expectation that the scale of separation between the slow and fast regimes is set by the characteristic frequency of the quasinormal modes.