2013/05/31 by G. Berkolaiko, J. Kuipers · 25 citations
Mathematics · Physics and Astronomy · #Combinatorial method #Equivalence (formal languages) #Interpretation (philosophy) #Matrix (chemical analysis) #Quantum #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum many-body systems #Random matrix #S-matrix #Semiclassical physics #math-ph #math.CO #math.MP #msc:15B52 #msc:81Q20 #msc:81Q50 #msc:81V65 #nlin.CD
paper · pdf · doi:10.1063/1.4826442
published in Journal of Mathematical Physics 54(11) (American Institute of Physics) · 30 pages, 13 figures; added some examples
arxiv created 2013/09/20 · openalex publication_date 2013/11/01 · arxiv updated 2013/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.