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 conceming universal conductance fluctuations and 1/f noise are emphasized.