2000 Fiscal Year Final Research Report Summary
Study of Quantum Billiard System with Pointlike Obstacles
| Project/Area Number |
10640396
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | Kochi University of Technology |
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Principal Investigator |
CHEON Taksu Kochi Univ.of Technology, Lab.of Physics, Associate Professor, 工学部, 助教授 (60227353)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Low-dimensional quantum system / Contact interaction / Schroedinger Operator / Anholonomy / Duality / Quantum wire / Quantum chaos / Topological quantum theory |
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| Research Abstract |
We have investigated the mathematical and physical properties of one- and two-dimensional quantum billiard system with pointlike obstacles. We have found out that there are number of intriguing features in this seemingly innocent very simple system. On the two-dimensional system. which has been known to posses "chaotic" quantum level statistics, we have obtained the analytical expressions for the condition for the appearance of the chaotic spectra. On one-dimensional system with pointlike defect, it has been known that there exists a"second-class" of point interaction that causes the discontinuity of the wavefunction itself as opposed to the usual deltafunction interaction that causes the discontinuity in the derivative of the wavefunction. Very little has been known, however, on the physical realization and also on the phvsical properties of this second-class point interaction. which has been mostly thought as a mathematical curiosity. We have made a extensive study on this object clarifying
1) how to realize this second-class point interaction out of experimentally realizable local potential in its short-range limit,
2) the appearance of the "level anholonomy" in the system with the generalized point interaction that comprizes the delta-function and second-class point interactions,
3) the existence of duality (in the sense of equivalence with strong and weak coupling reversed) between the fermionic manybody system with second-class point interaction and the bosonic system with delta-function point interaction, and
4) the existence of the nontrivial topologyT^2xS^2 in the parameter space of generalized point interaction, which is behind the above mentioned exotic features.
Our results could be considered as a model case of the global analysis of a family of quantum systems, and thus should be useful for designing and tailoring quantum systems for particular properties for the "quantum engineering" purpose in the near future.
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