Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

C.W.J. Beenakker , B. Rejaei (Instituut-Lorentz , Leiden , the Netherlands)

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classification ❄️ cond-mat

keywords eigenvaluestransmissiondisordereddistributionexactrandom-matrixsolutiontheory

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An exact solution is presented of the Fokker-Planck equation which governs the evolution of an ensemble of disordered metal wires of increasing length, in a magnetic field. By a mapping onto a free-fermion problem, the complete probability distribution function of the transmission eigenvalues is obtained. The logarithmic eigenvalue repulsion of random-matrix theory is shown to break down for transmission eigenvalues which are not close to unity. ***Submitted to Physical Review B.****

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Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

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