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

Abstract

We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.

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

“…In Ref. [61], we have shown that depending upon the value used for such parameters, one can obtain completely different physical results. In the present work, we want to study exclusively the influence of the length of the system and the baths' temperatures on the thermal transport properties.…”

“…In a recent paper [61], we have discussed the advantages of the GLE-2B approach over other more conventional thermostatting approaches such as Nose-Hoover or simple Langevin thermostats. Here, we use our GLE-2B approach as it does not rely on the use of adjustable parameter(s) to describe the relaxation processes in the 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 . We call it the GLE-2B scheme.…”

“…By solving Newton's equations of motion for all the DOFs, and integrating out the baths' DOFs, one obtains the following "embedded" dissipative dynamics for the DOF of the central system 56,61 :…”

“…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].…”