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Pseudopath semiclassical approximation to transport through open quantum billiards: Dyson equation for diffractive

Christoph Stampfer1, Stefan Rotter, Joachim Burgdörfer

  • 1Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria, European Union.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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We developed a new semiclassical theory for transport in open billiards, incorporating diffractive scattering paths. This theory accurately predicts quantum scattering in various billiards, matching experimental results.

Area of Science:

  • Quantum chaos
  • Mesoscopic physics
  • Transport theory

Background:

  • Understanding quantum transport in open systems is crucial.
  • Classical and semiclassical methods often struggle with diffractive scattering at openings.

Purpose of the Study:

  • To develop a semiclassical theory for transport through open billiards of arbitrary convex shape.
  • To include the effects of diffractive scattering at lead openings.

Main Methods:

  • Formulated a Dyson equation for the semiclassical Green's function.
  • Developed a diagrammatic expansion for systematic summation of classical and pseudopaths.
  • Pseudopaths are classical paths joined by diffractive scatterings ('kinks').

Main Results:

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  • The method is numerically tractable for regular and chaotic billiards.
  • Achieved good agreement with the quantum path length power spectrum for circular and Bunimovich stadium billiards.
  • Found excellent numerical agreement with experimental studies in microwave billiards.

Conclusions:

  • The presented semiclassical theory effectively incorporates diffractive scattering.
  • Pseudopaths play a significant role in quantum scattering phenomena.
  • The theory provides a robust framework for studying transport in open quantum systems.