Calogero-Sutherland techniques in the physics of disordered wires

1995/09/01 by M. Caselle · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1016/0920-5632(95)00621-4

published as Nucl.Phys.Proc.Suppl. 45A (1996)120-129 · 16 pages, Latex

arxiv created 1995/09/01 · openalex publication_date 1996/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We discuss the connection between the random matrix approach to disordered wires and the Calogero-Sutherland models. We show that different choices of random matrix ensembles correspond to different classes of CS models. In particular, the standard transfer matrix ensembles correspond to CS model with sinh-type interaction, constructed according to the C_n root lattice pattern. By exploiting this relation, and by using some known properties of the zonal spherical functions on symmetric spaces we can obtain several properties of the Dorokhov-Mello-Pereyra-Kumar equation, which describes the evolution of an ensemble of quasi one-dimensional disordered wires of increasing length L. These results are in complete agreement with all known properties of disordered wires. (To appear in the Proceedings of the Conference: Recent Developments in Statistical Mechanics and Quantum Field Theory (Trieste, 1995))

Citations

• Exact solution for the distribution of transmission eigenvalues in a disordered wire and comparison with random-matrix theory
• Electrical resistance of disordered one-dimensional lattices

Cited by

• Random matrix theory and symmetric spaces
• A new class of solutions of the Dorokhov–Mello–Pereyra–Kumar equation