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Integral Representation of the Incoherent Field in Disordered Matarials. I. Current Balance, Density‐of‐States Test, and New Mobility Formula
Author(s) -
Lenk R.
Publication year - 1982
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221090220
Subject(s) - autocorrelation , representation (politics) , current (fluid) , limit (mathematics) , path integral formulation , field (mathematics) , mathematics , balance (ability) , function (biology) , statistical physics , current density , physics , mathematical analysis , quantum mechanics , statistics , pure mathematics , medicine , physical medicine and rehabilitation , evolutionary biology , politics , biology , political science , law , quantum , thermodynamics
For a disordered material composed of many point‐like single scatterers a representation considered first by Foldy for the autocorrelation function of the incoherent field guarantees in a general way a loss‐free total current which consists of a coherent and an incoherent part. This demand fixes uniquely the representation mentioned. An exact connection with the density of states allows for an additional test independent from the current balance. By the generalizing inclusion of a driving force into the coherent wave equation a non‐classical prescription for the calculation of the mobility is derived. In three as well as in one dimensions the new formula reproduces exactly the classical limit for a large mean free path. For a filled band it yields no current. In the case d = 1 for short mean free paths the conductivity departs significantly from its classical value, but not for d = 3.