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

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