J. Phys. I France
Volume 7, Numéro 5, May 1997
Page(s) 729 - 736
DOI: 10.1051/jp1:1997187
J. Phys. I France 7 (1997) 729-736

Landauer and Thouless Conductance: a Band Random Matrix Approach

Giulio Casati1, 2, 3, Italo Guarneri1, 2, 4 and Giulio Maspero1

1  International Center for the Study of Dynamical Systems, University of Milan at Como, via Lucini 3, 22100 Como, Italy
2  Istituto Nazionale di Fisica della Materia, Unitá di Milano, via Celoria 16, 20133, Milan, Italy
3  INFN, Sezione di Milano, via Celoria 16, 20133, Milan, Italy
4  INFN, Sezione di Pavia, via Bassi 6, 27100, Pavia, Italy

(Received 2 December 1996, received in final form 21 December 1996, accepted 21 January 1997)

We numerically analyze the transmission through a thin disordered wire of finite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances, and find that they are proportional to each other in the diffusive regime, while in the localized regime the Landauer conductance is approximately proportional to the square of the Thouless one. Fluctuations of the Landauer conductance were also numerically computed; they are shown to slowly approach the theoretically predicted value.

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