APPLICATIONS OF CLASSICAL PERIODIC ORBIT THEORY TO CIRCULAR BILLIARDS WITH SMALL SCATTERING CENTERS

S.M. Reimann, M. Brack, A.G. Magner and M.V.N. Murthy
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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

Surface Review and Letters (SRL), 1996, vol. 03, issue 01, 19-23

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.

Date: 1996
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DOI: 10.1142/S0218625X96000061

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