Parametric Statistics of the Scattering Matrix: From Metallic to Insulating Quasi-Unidimensional Disordered SystemsEduardo R. Mucciolo1, Rodolfo A. Jalabert2, 3 and Jean-Louis Pichard2, 4
1 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)
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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