Parametric Statistics of the Scattering Matrix: From Metallic to Insulating Quasi-Unidimensional Disordered Systems

Eduardo Mucciolo , Rodolfo A. Jalabert , Jean-Louis Pichard

We investigate the statistical properties of the scattering matrix S describing the electron transport through quasi-one-dimensional disordered systems. For weak disorder (metallic regime), the energy dependence of the phase shifts of S is found to yield the same universal parametric correlations as those characterizing chaotic Hamiltonian eigenvalues driven by an external parameter. This is analyzed within a Brownian motion model for S, which is directly related to the distribution of the Wigner-Smith time delay matrix. For large disorder (localized regime), transport is dominated by resonant tunneling and the universal behavior disappears. A model based on a simplified description of the localized wave functions qualitatively explains our numerical results. In the insulator, the parametric correlation of the phase shift velocities follows the energy-dependent autocorrelator of the Wigner time. The Wigner time and the conductance are correlated in the metal and in the insulator.

Domaines: Articles anciens

Eduardo Mucciolo, Rodolfo A. Jalabert, Jean-Louis Pichard. Parametric Statistics of the Scattering Matrix: From Metallic to Insulating Quasi-Unidimensional Disordered Systems. Journal de Physique I, 1997, 7 (10), pp.1267-1296. ⟨10.1051/jp1:1997123⟩. ⟨jpa-00247454⟩