Semiclassical theory for transmission through open billiards: convergence towards quantum transport.
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--> infinity. Unitarity of the semiclassical theory is restored as K approaches infinity. Moreover, we find excellent agreement with the quantum path-length power spectrum up to very long path length.
Wirtz
Ludger
L
Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria.
Stampfer
Christoph
C
Rotter
Stefan
S
Burgdörfer
Joachim
J