Project/Area Number  10640396 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
物理学一般

Research Institution  Kochi University of Technology 
Principal Investigator 
CHEON Taksu Kochi Univ.of Technology, Lab.of Physics, Associate Professor, 工学部, 助教授 (60227353)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 2000 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1999 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  Lowdimensional quantum system / Contact interaction / Schroedinger Operator / Anholonomy / Duality / Quantum wire / Quantum chaos / Topological quantum theory / 低次元量子系 / 接触相互作用 / シュレディンガー演算子 / 非ホロノミー / 双対性 / 量子細線 / 量子カオス / 位相幾何的量子論 / 多様体構造 / 対称性 / 局所相互作用 / 時間反転非対称 / 量子フィルター / Luttinger液体 / 接触力 / 非連続波動函数 / 二重螺旋 
Research Abstract 
We have investigated the mathematical and physical properties of one and twodimensional 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 twodimensional 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 onedimensional system with pointlike defect, it has been known that there exists a"secondclass" 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 secondclass 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 secondclass point interaction out of experimentally realizable local potential in its shortrange limit, 2) the appearance of the "level anholonomy" in the system with the generalized point interaction that comprizes the deltafunction and secondclass point interactions, 3) the existence of duality (in the sense of equivalence with strong and weak coupling reversed) between the fermionic manybody system with secondclass point interaction and the bosonic system with deltafunction 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.
