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On the use of variational methods for solving Boltzmann equations involving non-Hermitian operators
Authors:L E G Ah-Sam  H HØjgaard Jensen  H Smith
Institution:(1) Physics Laboratory I, H. C. Ørsted Institute, University of Copenhagen, Denmark
Abstract:Variational principles yielding upper and lower bounds on transport coefficients can readily be applied to the Boltzmann equation, provided it has the form of a linear, inhomogeneous integrodifferential equation with a Hermitian operator acting on the deviation from equilibrium of the distribution function. In transport problems involving a magnetic field or an alternating electric field, this operator is non-Hermitian. By suitably transforming the transport equation, we show how Variational principles may still give upper and lower bounds. The bounds are used for considering the frequency-dependent conductivity associated with a general scattering operator, and the longitudinal magnetoresistivity in the relaxation time approximation for the scattering operator. Explicit results are presented for (1) the frequency-dependent conductivity of a charged Fermi liquid and (2) the longitudinal magnetoresistivity for a weakly anisotropic Fermi surface.
Keywords:Boltzmann equation  Variational principles  upper and lower bounds  transport coefficient  Fermi liquid  frequency dependent conductivity  magnetoresistivity  Fermi surface
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