Applications of the generalized Langevin equation: Towards a realistic description of the baths

Abstract

The generalized Langevin equation (GLE) method, as developed previously [L. Stella et al., Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalizes toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

“…The method and its implementation in the molecular dynamics package LAMMPS 58 have been well documented in recent papers 59,60 . The extension of the original GLE scheme to situations where the central system is interacting with several independent baths has been recently given in 61 .…”

“…In the energy representation, the polarization matrix Π bν ,b ν (ω) represents the vibrational density of states of the corresponding bath [56,[59][60][61]. Finally, the terms η (ν) iα contain all the information about the initial conditions of the bath ν DOFs.…”

“…where g iα,bν is the derivative of the coupling force g iα,bν = ∂f bν (r)/∂r iα and the polarization matrix Π bν ,b ν (t − t ) is related to the harmonic dynamical matrix of the bath ν [56,[59][60][61].…”

Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

“…II, we generalize the methodology of Refs. [42,52,53] to the cases of two independent baths ν = 1,2 each having its temperature T ν . The generalization, called GLE-2B, includes the use of two sets of auxiliary degrees of freedom (DOFs) corresponding to each bath and their stochastic dynamics.…”

“…[42,52,53] to the systems consisting of a central region connected to two spatially separated thermal baths. With such an approach, we can study the nonequilibrium processes in nanoscale systems by using molecular dynamics (MD) simulations.…”