1D localisation and the symmetric group

Abstract

Earlier investigations making use of a density matrix formalism to study the average resistance of a disordered solid are extended in the 1D case to calculate moments of the resistance within a diagonal-disorder model. Application of the symmetric group greatly simplifies the problem, reducing matrices from of order 2^2N to of order 2N+1 for the Nth moment. The symmetry-reduced matrix enables a transparent discussion to be made of the analytic properties of the mean conductance which is shown to have a number of remarkable properties. Finally, some analytic results are presented in various limiting cases and compared with earlier work.