Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach
- Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States)
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)
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.
- OSTI ID:
- 22251491
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
Semiclassical methods in chemical reaction dynamics