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Title: Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach

To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States)
  2. Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)
Publication Date:
OSTI Identifier:
22251491
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DIAGRAMS; EVALUATION; GRAPH THEORY; MATRICES; NONLINEAR PROBLEMS; QUANTUM DOTS; RANDOMNESS; SCATTERING; SEMICLASSICAL APPROXIMATION; SYMMETRY; TRAJECTORIES