2007/08/06 by D. Boosé, D. Boose, J. M. Luck · 1 citation
Physics and Astronomy · #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #cond-mat.mes-hall #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/40/47/002
published as J. Phys. A 40 (2007) 14045-14067 · 26 pages, 4 figures, 1 table
arxiv created 2007/08/06 · openalex publication_date 2007/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the logarithm of the transmission probability through this unit. Unit actions and lengths are independent random variables, with a common distribution that is either narrow or broad. This investigation is motivated by results on disordered systems with nonstationary random potentials whose fluctuations grow with distance. In the statistical ensemble at fixed total sample length four phases can be distinguished, according to the values of the indices characterizing the distribution of the unit actions and lengths. The sample action, which is proportional to the logarithm of the conductance across the sample, is found to obey a fluctuating scaling law, and therefore to be non-self-averaging, in three of the four phases. According to the values of the two above mentioned indices, the sample action may typically grow less rapidly than linearly with the sample length (underlocalization), more rapidly than linearly (superlocalization), or linearly but with non-trivial sample-to-sample fluctuations (fluctuating localization).