Spectral properties of three-dimensional quantum billiards with a pointlike scatterer

Journal Article · Sun Jun 01 04:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.55.6832· OSTI ID:548814

Shigehara, T ^[1]; Cheon, T ^[2]

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1. Computer Centre, University of Tokyo, Yayoi, Bunkyo-ku, Tokyo 113 (Japan)
2. Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782 (Japan)

We examine the spectral properties of three-dimensional quantum billiards with a single pointlike scatterer inside. It is found that the spectrum shows chaotic (random-matrix-like) characteristics when the inverse of the formal strength {bar v}{sup {minus}1} is within a band whose width increases parabolically as a function of the energy. This implies that the spectrum becomes random-matrix-like at very high energy irrespective to the value of the formal strength. The predictions are confirmed by numerical experiments with a rectangular box. The findings for a pointlike scatterer are applied to the case for a small but finite-size impurity. We clarify the proper procedure for its zero-size limit which involves nontrivial divergence. The previously known results in one- and two-dimensional quantum billiards with small impurities inside are also reviewed from the present perspective. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 548814
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 6 Vol. 55; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ELASTIC SCATTERING
ENERGY SPECTRA
IMPURITIES
MULTIPLE SCATTERING
QUANTUM MECHANICS
STATISTICS
THREE-DIMENSIONAL CALCULATIONS