2004/08/29 by Vadym Apalkov, V. M. Apalkov, M. E. Raikh +3
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum chaos and dynamical systems #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0408642
14 pages, 8 figures
arxiv created 2004/08/29 · openalex publication_date 2004/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We demonstrate that the tail of transmission distribution through 1D disordered Anderson chain is a strong function of the correlation radius of the random potential, a, even when this radius is much shorter than the de Broglie wavelength, kF-1. The reason is that the correlation radius defines the phase volume of the trapping configurations of the random potential, which are responsible for the low-T tail. To see this, we perform the averaging over the low-T disorder configurations by first introducing a finite lattice spacing ∼ a, and then demonstrating that the prefactor in the corresponding functional integral is exponentially small and depends on a even as a → 0. Moreover, we demonstrate that this restriction of the phase volume leads to the dramatic change in the shape of the tail of \cal P(ln T) from universal Gaussian in ln T to a simple exponential (in ln T ) with exponent depending on a. Severity of the phase-volume restriction affects the shape of the low-T disorder configurations transforming them from almost periodic (Bragg mirrors) to periodically-sign-alternating (loose mirrors).