Variational Formula for the Relaxation Time in the Boltzmann Equation

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 emplo...

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Bibliographic Details
Published in:The journal of physical chemistry. B 2006-09, Vol.110 (38), p.18921-18924
Main Authors: Giuggioli, L, Parris, P. E, Kenkre, V. M
Format: Article
Language:English
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Summary: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.
ISSN:1520-6106
1520-5207
DOI:10.1021/jp0574955