Statistical Mechanics of Anyons
Project/Area Number  02640222 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  Shizuoka University 
Principal Investigator 
NAKAHARA Mikio Shizuoka Univ. Faculty of Liberal Arts, Assistant Professor, 教養部, 助教授 (90189019)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

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)

Keywords  Anyon / Virial Expansion / Superconductivity / Vortex Line / Free Energy / Heat Kernel / Ginzburg Landau Expansion / ChernSimons Gauge Theory / エニオン / ヴィリアル展開 / 超伝導 / 渦糸 / 自由エネルギ / 熱核 / ギンズブルクランダウ展開 / チャン・サイモンズ理論 / 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 
Research Abstract 
1. First, threebody problem of anyons is studied. It has been known for sometime that semiclassical twobody partition function reproduces exact second virial coefficient. We tried to generalize this for threeanyon 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 manyanyon 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 multianyon 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 ChernSimons 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 vortexbearing 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 ChernSimons vortex is under progress.

Report
(4results)
Research Output
(16results)