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Title: Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, calculation of transport moments reduces to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders further than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.
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:
22217743
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; 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; 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; ASYMPTOTIC SOLUTIONS; CHAOS THEORY; DIAGRAMS; GRAPH THEORY; MATRICES; QUANTUM DOTS; SCATTERING; SEMICLASSICAL APPROXIMATION; SYMMETRY