T. Shigehara

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

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}

WAVE CHAOS IN QUANTUM BILLIARDS WITH A SMALL BUT FINITE-SIZE SCATTERER

We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is formulated in terms of self-adjoint extension theory of functional analysis. The condition for the appearance of so-called wave chaos is clarified. We then relate the pointlike scatterer to a finite-size scatterer through the appropriate truncation of basis. We show that the signature of wave chaos in low energy states is most prominent when the scatterer is weakly attractive. As an illustration, numerical results of a rectangular billiard with a small rectangular scatterer inside are exhibited.

Level-spacing distribution of a singular billiard.

In this paper, we examine the level spacing distribution

Chaos and symmetry in the interacting boson model

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Flux string in quantum billiards with two particles

of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed

Resonance tunneling in double-well billiards with a point-like scatterer

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Nuclear mass dependence of chaotic dynamics in the Ginocchio model

is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for

Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths

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Band Spectra of Kronig-Penney Model with Generalized Contact Interaction

, although the level repulsion still remains in the small

Wave Chaos in Quantum Pseudointegrable Billiards

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