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

Journal Article · Sun Dec 15 04:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4842375· OSTI ID:22217743

Berkolaiko, G. ^[1]; Kuipers, J. ^[2]

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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)

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.

• OSTI ID: 22217743
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
ALGEBRA
ASYMPTOTIC SOLUTIONS
CHAOS THEORY
DIAGRAMS
GRAPH THEORY
MATRICES
QUANTUM DOTS
SCATTERING
SEMICLASSICAL APPROXIMATION
SYMMETRY