Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. I : Elliptic Billiard

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概要

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• We derive an analytical trace formula for the level density of two-dimensional elliptic billiards using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula, which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We show that the circular disk limit of the diameter-orbit contribution is also reached through contributions from closed (periodic and non-periodic) orbits of the hyperbolic type with an even number of reflections from the boundary. We obtain the Maslov indices depending on deformation and energy in terms of the phases of the complex error and Airy functions. We find enhancement of the amplitudes near the common bifurcation points of short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones.

• 理論物理学刊行会の論文
• 1999-09-25

著者

• 松柳 研一

  Theoretical Nuclear Physics Laboratory Riken Nishina Center:yukawa Institute For Theoretical Physics

• Arita Ken-ichiro

  Department Of Physics Kyoto University

• Matsuyanagi Kenichi

  Department Of Physics Graduate School Of Science Kyoto University

• Brack Matthias

  Institute For Theoretical Physics University Of Regensburg

• FEDOTKIN Sergey

  Institute for Nuclear Research

• Fedotkin Sergey

  Institute For Nuclear Research : Institute For Theoretical Physics University Of Regensburg

• MAGNER Alexander

  Institute for Nuclear Research

• ARITA Kenichiro

  Department of Physics, Nagoya Institute of Technology

• MISU Toshiyuki

  Cyclotron Radio-isotope Center, Tohoku University

• SCHACHNER Thomas

  Institute for Theoretical Physics, University of Regensburg

• Misu Toshiyuki

  Cyclotron Radio-isotope Center Tohoku University

• Arita Kenichiro

  Department Of Physics Nagoya Institute Of Technology

• Magner Alexander

  Institute For Nuclear Research : Institute For Theoretical Physics University Of Regensburg : Depart

• Schachner Thomas

  Institute For Theoretical Physics University Of Regensburg

• BRACK Matthias

  Institute for Theoretical Physics, University of Regensburg

• MAGNER Alexander

  Institute for Nuclear Research : Institute for Theoretical Physics, University of Regensburg : Department of Physics, Graduate School of Science, Kyoto University

• ARITA Ken-ichiro

  Department of Physics, Nagoya Institute of Technology

• ARITA Ken-ichiro

  Department of Physics, Kyoto University

• Fedotkin Sergey

  Institute for Nuclear Research:Institute for Theoretical Physics, University of Regensburg

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