Complex Wishart matrices and conductance in mesoscopic systems: Exact results
- 1 December 1994
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (12) , 6736-6747
- https://doi.org/10.1063/1.530639
Abstract
It is noted that the hypothesis of independent random complex elements for the off diagonal blocks (say, M2 and M3) of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product M3°M3 (or M2°M2) to be computed exactly. Exact expressions, in terms of double Wronskian and Toeplitz determinants, are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products.This publication has 19 references indexed in Scilit:
- Asymptotic level spacing of the Laguerre ensemble: a Coulomb fluid approachJournal of Physics A: General Physics, 1994
- Level spacing distributions and the Bessel kernelCommunications in Mathematical Physics, 1994
- Nonlogarithmic repulsion of transmission eigenvalues in a disordered wirePhysical Review Letters, 1993
- Variance calculations and the Bessel kernelJournal of Statistical Physics, 1993
- Recurrence equations for the computation of correlations in the 1/r2 quantum many-body systemJournal of Statistical Physics, 1993
- Random-matrix theory of mesoscopic fluctuations in conductors and superconductorsPhysical Review B, 1993
- Universality in the random-matrix theory of quantum transportPhysical Review Letters, 1993
- New random matrix theory of scattering in mesoscopic systemsPhysical Review Letters, 1993
- Jacobi Polynomials Associated with Selberg IntegralsSIAM Journal on Mathematical Analysis, 1987
- Active Transmission Channels and Universal Conductance FluctuationsEurophysics Letters, 1986