2012/11/30 by Marcel Novaes
Mathematics · Physics and Astronomy · #Chaotic #Combinatorial method #Conjecture #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Random matrix #Semiclassical physics #Series (stratigraphy) #Spectral Theory in Mathematical Physics #nlin.CD
paper · pdf · doi:10.1088/1751-8113/46/9/095101
published as J. Phys. A: Math. Theor. 46, 95101 (2013) · 13 pages, 2 figures. v2-minor changes, including title
openalex publication_date 2013/02/12 · arxiv created 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
A semiclassical approach to the calculation of transport moments M m = Tr[( t † t ) m ], where t is the transmission matrix, was developed by this author (2012 Europhys. Lett. 98 20006) for chaotic cavities with two leads and broken time-reversal symmetry. The result is an expression for M m as a perturbation series in 1/ N , where N is the total number of open channels, which is in agreement with random matrix theory predictions. The coefficients in this series were related to two open combinatorial problems. Here we expand on this work, including the solution to one of the combinatorial problems. As a by-product, we also present a conjecture relating two kinds of factorizations of permutations.