Validity of nth-Order Conductivity by the General Projection-Reduction Method(Condensed Matter Physics)

概要

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Utilizing the generalized state-dependent projectors and the KC reduction identities [For the first kind, see: Prog. Theor. Phys. 96 (1996), 307, Eq. (18)] introduced by the authors, the nth-order conductivity (n=1, 2, 3,…) of electron systems in solids, in which electrons are scattered by background, is derived. The result for n≥4 is derived by applying mathematical inference to the results obtained up to the third order by direct calculations. It is also known that the results up to the third order are applicable to general electron systems including those undergoing confinement potentials, which yield non-equispaced energy spectra, and satisfy the population criterion that the distributions of electrons and background members should be given in multiplicative forms [J. of Phys. A 43 (2010), 165203]. As the iteration-based mathematical inference taken here for deriving the result is acceptable, we may conclude that the nth-order conductivity for n≥4 is also applicable to general electron systems and satisfies the population criterion.
2011-05-25