1D localisation and the symmetric group
- 20 August 1982
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 15 (23) , 4821-4834
- https://doi.org/10.1088/0022-3719/15/23/019
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 22N 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.Keywords
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