By a News Reporter-Staff News Editor at Journal of Mathematics -- Data detailed on Combinatorics have been presented. According to news reporting originating from Regensburg, Germany, by VerticalNews correspondents, research stated, "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."
Our news editors obtained a quote from the research from the University of Regensburg, "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."
According to the news editors, the research concluded: "The equivalence is proved for systems with and without time reversal symmetry."
For more information on this research see: Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach. Journal of Mathematical Physics, 2013;54(11):168-193. Journal of Mathematical Physics can be contacted at: Amer Inst Physics, Circulation & Fulfillment Div, 2 Huntington Quadrangle, Ste 1 N O 1, Melville, NY 11747-4501, USA. (American Institute of Physics - www.aip.org/; Journal of Mathematical Physics - jmp.aip.org/)
The news editors report that additional information may be obtained by contacting G. Berkolaiko, University of Regensburg, Inst Theoret Phys, D-93040 Regensburg, Germany.
Keywords for this news article include: Europe, Germany, Regensburg, Combinatorial
Our reports deliver fact-based news of research and discoveries from around the world. Copyright 2014, NewsRx LLC