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Random Transfer Matrix Theory and Conductance Fluctuations

  • Jean-Louis Pichard
  • Jean-Louis Pichard
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

Very often, in Physics and in particular in Quantum Mechanics, we are dealing with matrices. This can be the matrix H representing the Hamiltonian of the system, or its scattering matrix S, or, as studied in this work, its transfer matrix M at a given energy. In general, the matrix is huge and complex, especially if it is associated to a disordered system. An exact knowledge of this matrix, which corresponds to a particular system, on which measurements are made, is practically impossible and theoretically inadequate. On the one hand, the measurements are done on a real complex system, on the other hand the theory can only be based on a statistical ensemble of appropriate matrices. The definition of the matrix ensemble is an essential starting point. Very often, we consider microscopic models, e.g. an Anderson model [1] for disordered tight-binding Hamiltonians of non-interacting electrons
$$H = \sum\limits_i {{V_i}\left| i \right\rangle \left\langle i \right| + \sum\limits_{i\;n \cdot n\;j} {{T_{ij}}\left| i \right\rangle \left\langle j \right|} } $$
(1)

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Jean-Louis Pichard
    • 1
  • Jean-Louis Pichard
    • 1
  1. 1.Service de Physique du Solide et de Résonance MagnétiqueC.E.A. SaclayGif sur Yvette CedexFrance

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