  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.
