1993/10/28 by C. W. J. Beenakker, B. Rejaei, B. Rajaei
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevb.49.7499
published as Phys.Rev.B 49 (1994) 7499 · 20 pages, REVTeX-3.0, INLO-PUB-931028a
arxiv created 1993/10/28 · openalex publication_date 1994/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the complete probability distribution P(Tn) of the transmission eigenvalues T1,T2,...,TN of a disordered quasi-one-dimensional conductor (length L much greater than width W and mean free path l). The Fokker-Planck equation which describes the evolution of P with increasing L is mapped onto a Schr"odinger equation by a Sutherland-type transformation. In the absence of time-reversal symmetry (e.g., because of a magnetic field), the mapping is onto a free-fermion problem, which we solve exactly. The resulting distribution is compared with the predictions of random-matrix theory (RMT) in the metallic regime (L\ensuremath≪Nl) and in the insulating regime (L\ensuremath≫Nl). We find that the logarithmic eigenvalue repulsion of RMT is exact for Tn's close to unity, but overestimates the repulsion for weakly transmitting channels. The nonlogarithmic repulsion resolves several long-standing discrepancies between RMT and microscopic theory, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the log-normal conductance distribution in the insulating regime.