Variational Formula for the Relaxation Time in the Boltzmann Equation

Author

L. Giuggioli
V. M. Kenkre
Paul Ernest Parris, Missouri University of Science and TechnologyFollow

Abstract

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the Boltzmann equation, which allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility for a one-dimensional (1D) tight-binding band indicate that our analysis typically provides a better approximation than the standard RTA.

Recommended Citation

L. Giuggioli et al., "Variational Formula for the Relaxation Time in the Boltzmann Equation," Journal of Physical Chemistry, American Chemical Society (ACS), Jan 2006.

The definitive version is available at https://doi.org/10.1021/jp0574955

Department(s)

Physics

Keywords and Phrases

Relaxation Time Approximation

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 American Chemical Society (ACS), All rights reserved.

Publication Date

01 Jan 2006