Statistical Mechanics of Anyons
| Project/Area Number |
02640222
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | Shizuoka University |
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Principal Investigator |
NAKAHARA Mikio Shizuoka Univ. Faculty of Liberal Arts, Assistant Professor, 教養部, 助教授 (90189019)
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| Project Period (FY) |
1990 – 1991
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| Project Status |
Completed (Fiscal Year 1991)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1991: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1990: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Anyon / Virial Expansion / Superconductivity / Vortex Line / Free Energy / Heat Kernel / Ginzburg Landau Expansion / Chern-Simons Gauge Theory / ヴイリアル展開 / ヴィリアル係数 / 組み紐群 / ギンズブルグランダウ展開 |
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| Research Abstract |
1. First, three-body problem of anyons is studied. It has been known for sometime that semiclassical two-body partition function reproduces exact second virial coefficient. We tried to generalize this for three-anyon problem. By introducing a projective operator written in terms of hyperspherical coordinate, we could separate the trace into a subtrace over the space of irreducible representation of the symmetric group. This will be reported shortly.
2. We also looked at many-anyon problem on topologically nontrivial surface. According to the braid group analysis, the statistical parameter is quantized on a cylinder. We studied this problem by requiring the uniqueness of the anyon wave function and found that the wave function is well defined for any value of the statistical parameter. We also studied an exact multi-anyon wave function. We are seeking for a possibility that with a certain interaction the exact wave function may be obtained.
3, In the quantum field theory, an anyon is realized as a vortex in Chern-Simons gauge theory and it is quite important to investigate the structure of the vortices in general system. For this purpose, we have developed a technique to compute the free energy of a vortex-bearing system at an arbitrary temperature. We have applied this technique to a solution in polyacetylene and a vortex line in a type II superconductor as a preliminary. Application to Chern-Simons vortex is under progress.
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Report
(3 results)
Research Products
(16 results)
