Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Details Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

2005-10-13

arxiv.org/abs/cond-mat/0510359v2

Physics

Condensed Matter

Statistical Mechanics

NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari, Greece) Proceedings, submitted (this is essentially a shorter

Scientific paper

10.1140/epjb/e2006-00116-y

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function $f(\mathbf{x}, \mathbf{v}; t)$. Adopting an alternative approach, previously proposed for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

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