Random matrix theory and universal statistics for disordered quantum conductors with spin-dependent hopping

Abstract

Transfer matrix spectra, which are directly related to the conductance g of a many channel elastic scatterer, are studied in presence of random spin-orbit interactions. A first method, inspired by Imry's theory of universal conductance fluctuations, leads us to describe these spectra by a distribution of maximum information entropy. Using a second method, we write the transfer matrices in terms of a microscopic Hamiltonian, for which a statistical law is assumed. One shows that the level spacing distribution and the spectral rigidity, yielded by these two different procedures, are identical and agree with the statistics of the symplectic ensemble for sample size smaller than the localization length and larger than the elastic mean free path. Scaling theory of localization is discussed in the light of this new random matrix theory approach. Important consequences of spin-orbit coupling concerning universal conductance fluctuations and 1/f noise are emphasized Etude des spectres des matrices de transfert de diffuseurs elastiques avec couplages spin-orbite aleatoires dans la limite d'un grand nombre de canaux de diffusion et deduction de la conductance g des diffuseurs a partir de ces spectres: 1) par une methode de type Imry des fluctuations universelles de conductance en decrivant les spectres par une distribution d'entropie d'information maximale; et 2) par une methode de matrices de transfert d'hamiltoniens microscopiques dont on donne la statistique