Langevin dynamics with spatial correlations as a model for electron-phonon coupling

TL;DR

This paper introduces a generalized Langevin dynamics model with spatial correlations to better simulate electron-phonon interactions, capturing mode-specific relaxation and improving non-equilibrium and equilibrium modeling of dense systems.

Contribution

It proposes a novel spatially correlated Langevin dynamics framework that models mode-dependent electron-phonon coupling, enhancing the two-temperature model for dense materials.

Findings

Model captures wavevector- and polarization-dependent relaxation.

Effectively describes ion-electron equilibration dynamics.

Can be used as a thermostat for equilibrium sampling.

Abstract

Stochastic Langevin dynamics has been traditionally used as a tool to describe non-equilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their wavelength. We propose a generalization of Langevin dynamics that can capture a differential coupling between collective modes and the bath, by introducing spatial correlations in the random forces. This allows modeling the electronic subsystem in a metal as a generalized Langevin bath endowed with a concept of locality, greatly improving the capabilities of the two-temperature model. The specific form proposed here for the spatial correlations produces physical wavevector- and polarization-dependency of the relaxation produced by the electron-phonon coupling in a solid. We show that the resulting model can be used for describing the path to equilibration of ions and electrons, and also as a thermostat to sample the equilibrium canonical ensemble. By extension, the family of models presented here can be applied in general to any dense system, solids, alloys and dense plasmas. As an example, we apply the model to study the non-equilibrium dynamics of an electron-ion two-temperature Ni crystal.