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Parametric statistics of the scattering matrix: From metallic to insulating quasi-unidimensional disordered systems

E. R. Mucciolo·R. A. Jalabert·J. -L. Pichard
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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 delay time 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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E. R. Mucciolo, R. A. Jalabert, J. -L. Pichard. 1997-03-19. Parametric statistics of the scattering matrix: From metallic to insulating quasi-unidimensional disordered systems. https://doi.org/10.1051/jp1%3A1997123

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