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 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.
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
Keywords and Phrases
Relaxation Time Approximation
Article - Journal
© 2006 American Chemical Society (ACS), All rights reserved.