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

H Ness and L Stella and CD Lorenz and L Kantorovich, PHYSICAL REVIEW B, 91, 014301 (2015).

DOI: 10.1103/PhysRevB.91.014301

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.

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