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Applications Of Classical Periodic Orbit Theory To Circular Billiards With Small Scattering Centers

Author

Listed:
  • S.M. REIMANN

    (Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany)

  • M. BRACK

    (Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany)

  • A.G. MAGNER

    (Institute for Nuclear Research, 252028 Prospekt Nauki 47, Kiev-28, Ukraine)

  • M.V.N. MURTHY

    (Institute of Mathematical Sciences, Madras 600 113, India)

Abstract

Mesoscopic systems like metallic clusters in three dimensions as well as quantum dots in two dimensions have raised a particular interest in the semiclassical interpretation of shell effects. We use periodic orbit theory to calculate the density of states for two-dimensional circular billiards. When a singular magnetic flux line is added at the center of the disk, we show that the Aharonov-Bohm (AB) effect manifests itself through the cancellation of periodic orbits and the appearance of a new signal in the Fourier transform of the quantum density of states. The same effects are also found analytically for a two-dimensional harmonic oscillator potential with flux line. Finally, we show that a homogeneous magnetic field B perpendicular to the disk plane leads to B-periodic oscillations of the level density, which recently have also been observed experimentally in two-dimensional circular quantum dots.

Suggested Citation

  • S.M. Reimann & M. Brack & A.G. Magner & M.V.N. Murthy, 1996. "Applications Of Classical Periodic Orbit Theory To Circular Billiards With Small Scattering Centers," Surface Review and Letters (SRL), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 19-23.
    • Handle: RePEc:wsi:srlxxx:v:03:y:1996:i:01:n:s0218625x96000061
    DOI: 10.1142/S0218625X96000061
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