Random walk and the heat equation on superspace and anyspace. (English) Zbl 0808.60090
Summary: Random walks are used to study diffusion on anyspace. Anyspace is characterized by coordinate \(\xi\) with \(\xi^ N = 0\) and statistics \(\xi \xi' = e^{2 \pi i/N} \xi' \xi\) between independent copies. Anyonic integration and anyonic Dirac \(\delta\) functions are introduced, and reduced to familiar results for supersymmetry when \(N = 2\). These ingredients are then used to formulate and solve the resulting anyonic diffusion equation.
MSC:
| 60K40 | Other physical applications of random processes |
| 60G50 | Sums of independent random variables; random walks |
| 81R99 | Groups and algebras in quantum theory |
References:
| [1] | DOI: 10.1007/BF00403542 · Zbl 0745.16019 · doi:10.1007/BF00403542 |
| [2] | DOI: 10.1063/1.530154 · Zbl 0786.17013 · doi:10.1063/1.530154 |
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