ISSN:
1572-9613
Keywords:
Boltzmann equation
;
Variational principles
;
upper and lower bounds
;
transport coefficient
;
Fermi liquid
;
frequency dependent conductivity
;
magnetoresistivity
;
Fermi surface
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01012184
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