Semiclassical theory for transmission through open billiards: Convergence towards quantum transport
Abstract
We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths and pseudopaths which consist of classical path segments joined by “kinks,” i.e., diffractive scattering at lead mouths. For a rectangular billiard we show numerically that the sum over all such paths with a given number of kinks K converges to the quantum transmission amplitude as K→∞. Unitarity of the semiclassical theory is restored as K approaches infinity. Moreover, we find excellent agreement with the quantum pathlength power spectrum up to very long path length.
 Publication:

Physical Review E
 Pub Date:
 January 2003
 DOI:
 10.1103/PhysRevE.67.016206
 Bibcode:
 2003PhRvE..67a6206W
 Keywords:

 05.45.Mt;
 73.23.Ad;
 73.50.Bk;
 Quantum chaos;
 semiclassical methods;
 Ballistic transport;
 General theory scattering mechanisms