Comparison of different thermostats in the Holstein model

TL;DR

This paper compares Langevin thermostats and Hamiltonian systems in modeling charge dynamics in the Holstein model, revealing that polaron disruption depends on thermal energy and that results converge at high temperatures, supporting ergodicity.

Contribution

It provides a comparative analysis of thermostat methods in the Holstein model, highlighting how thermal energy influences polaron stability and demonstrating the equivalence of results at high temperatures.

Findings

Polaron disruption occurs at similar thermal energy levels in both methods.

Results from Langevin and Hamiltonian systems converge at high temperatures.

Thermal energy T is derived from kinetic energy after simulation.

Abstract

When modeling charge dynamics in a chain of N sites at a temperature T, a Langevin thermostat and a Hamiltonian system, i.e., a chain heated to a given temperature before charge is injected, are compared. It is shown that the polaron disruption occurs in the same range of values of the thermal energy NT, however, T is not given by the initial data, but obtained after simulation from the average kinetic energy. For large T, the results averaged over a set of trajectories in a system with a Langevin thermostat and the results averaged over time for a Hamiltonian system are close, which does not contradict the Ergodic hypothesis.