| Project/Area Number |
10640244
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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 |
素粒子・核・宇宙線
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
EZAWA Zyun f. Graduate School of Science, TOHOKU UNIVERSITY Professor, 大学院・理学研究科, 教授 (90133925)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Conformal Field Theory / Quantum Hall (QH) Effect / Bilayer QH System / Composite Boson / Fractional Statistics / Quantum Coherence / Skyrmion / Noncommutative Geometry / 巨視的量子コヒーレンス |
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| Research Abstract |
In low-dimensional spaces there exist intriguing phenomena solely due to the peculiarity of their topological property. Choosing explicitly the Quantum Hall (QH) system I analyzed rich physics intrinsic to the two-dimensional space field-theoretically. In so doing I proposed a theory of composite bosons and used a technique of conformal field theory.
The keys are the following two properties : (i) Because there exists no intrinsic spin-statistics relation in the planar system, it is possible that electrons condense without making Cooper pairs and that quasi-particles possesses fractional statistics. A concrete example is the QH state, which is a condensate of composite bosons each of which is a flux-electron composite. (ii) The QH effect is a physics played by electrons confined within the lowest Landau level (LLL). Due to this confinement, the χ and γcoordinates turn out to be noncommutative. This gives a simplest and concrete example of the noncommutative geometry. It follows from the
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se two items that quantum coherece develops spontaneously in QH systems. Topological solitons (called skyrmions) arise as coherent excitations. They have already been observed experimentally as quasiparticles.
I analyzed the bilayer QH system in detail, where the system possesses the SU (4) isospin symmetry due to the layer and spin degrees of freedom. I showed that the Coulomb exchange interaction operates in the QH system though it is made of a liquid and not a lattice. The physical origin is the LLL constraint mentioned above. The interaction develops the SU (4) isospin coherence together with 3 independent isospin waves and 3 different skyrmions. I also studied how to measure them experimentally.
I have also worked with experimental physicists on bilayer QH systems. We have measured the activation energy in the bilayer quantum Hall state at filling factor ν=2, 1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells, and by tilting samples in the magnetic field. Their behaviors are remarkably different from one to another, which I explained in terms of skyrmion excitations successfully. Less
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