J. Phys. I France 7 (1997) 1267-1296
DOI: 10.1051/jp1:1997123

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

Eduardo R. Mucciolo¹, Rodolfo A. Jalabert^{2, 3} and Jean-Louis Pichard<sup>2, 4

1</sup>  Departamento de Física, Pontifícia Universidade Católica, CP 38071, 22452-970 Rio de Janeiro, RJ, Brazil
²  Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA
³  Université Louis Pasteur, IPCMS-GEMME, 23 rue du Loess, 67037 Strasbourg Cedex, France
⁴  Service de Physique de l'État Condensé, CEA Saclay, 91191 Gif-sur-Yvette, France

(Received 21 March 1997, received in final form 27 May 1997, accepted 6 June 1997)

Abstract
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.

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