Semiclassical treatment of quantum chaotic transport with a tunnel barrier
Abstract
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as power series in the reflection probability of the barrier, whose coefficients are rational functions of the number of open channels M. Our results are therefore valid in the quantum regime and not only when M ≫ 1. The expressions we arrive at are not identical with the corresponding predictions from random matrix theory, but are in fact much simpler. Both theories agree as far as we can test.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2021
 DOI:
 10.1088/17518121/abcf58
 arXiv:
 arXiv:2008.07419
 Bibcode:
 2021JPhA...54l5201B
 Keywords:

 semiclassical approximation;
 quantum chaotic transport;
 matrix models;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics
 EPrint:
 17 pages, 5 figures