Abstract
We consider the spectral problem resulting from the Schrödinger equation for a quantum system ofn≧2 indistinguishable, spinless, hard-core particles on a domain in two dimensional Euclidian space. For particles obeying fractional statistics, and interacting via a repulsive hard core potential, we provide a rigorous framework for analysing the spectral problem with its multi-valued wave functions.
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References
Adams, R.: Sobolev Spaces, New York: Academic Press 1975
Chen, Yi-H., Wilczek, F., Witten, E., Halperin, B.I.: On anyon superconductivity. Int. J. Mod. Phys. B3, 1001–1067 (1989)
Deuschel, J., Strook, D.: Hypercontractivity and spectral gap of symmetric diffusion with applications to stochastic Ising model. J. Funct. Anal.92, 30–48 (1990)
Dowker, J.S.: Quantum mechanics and field theory on multiply connected and on homogeneous spaces. J. Phys. A5 936–943 (1972)
Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second Order. Berlin, Heidelberg, New York: Springer 1983
Goldin, R., Menikoff, R., Sharp, D.H.: Particle statistics from induced representations of a local current group. J. Math. Phys.21, 650 (1980)
Goldin, G.A., Menikoff, R., Sharp, D.H.: Representations of a local current algebra in non-simply connected space and the Aharonov-Bohm effect. J. Math. Phys.22, 1664 (1981)
Goldin, G.A., Menikoff, R., Sharp, D.H.: Diffeomorphism groups, gauge groups and Quantum Theory. Phys. Rev. Lett.51, 2246 (1983)
Goldin, G.A., Sharp, D.H.: Rotation generators in two-dimensional space and particles obeying unusual statistics. Phys. Rev. D28, 830 (1983)
Imbo, C.S., Imbo, T.D., Sudarshan, E.C.G.: Identical particles, exotic statistics and Braid Groups. Phys. Lett. B234, 103–109 (1990)
Kato, T.: Perturbation Theory for Linear Operators. New York: Springer 1966
Laidlaw, M.G., DeWitt, C.M.: Feynman functional integrals for systems of indistinguishable particles. Phys. Rev. D3, 6, 1375–1378 (1971)
Laughlin, R.B.: Fractional statistics in the Quantum Hall Effect. In: Wilczek, F. (ed.) Fractional Statistics and Anyon Superconductivity. pp. 262–303. Singapore. World Scientific 1990
Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Nuovo Cimento37B, 1–23 (1977)
Loss, D., Fu, Y.: Second virial coefficient of an interacting anyon gas (to appear). Phys. Rev. Lett.
Necas, J.: Sur une méthode pour resoudre les equations aux derivees partielles du type elliptique voisine de la variationnelle. Ann. Scoula Normale Superiore di Pisa, Serie III16, 4, 305–326 (1962)
Schulman, L.S.: Approximate topologies. J. Math. Phys.12, 2, 304–308 (1971)
Thouless, D.J., Wu, Yong-Shi: Remarks on fractional statistics. Phys. Rev. B31, 2, 1191–1193 (1985)
Wilczek, F.: Magnetic flux, angular momentum and statistics. Phys. Rev. Lett.48, 1144–1146 (1982)
Wilczek, F.: Quantum Mechanics of fractional spin particles. Phys. Rev. Lett.49, 957–959 (1982)
Wilczek, F.: Fractional Statistics and Anyon Superconductivity. Singapore: World Scientific 1990
Wu, Yong-Shi: General theory for Quantum statistics in two dimensions. Phys. Rev. Lett.52, 24, 2103–2106 (1984)
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Communicated by B. Simon
Partially supported by the Mathematical Sciences Research Institute, Berkeley California, under NSF Grant # DMS 8505550
Partially supported under NSF Grant no. DMR-9101542
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Baker, G.A., Canright, G.S., Mulay, S.B. et al. On the spectral problem for anyons. Commun.Math. Phys. 153, 277–295 (1993). https://doi.org/10.1007/BF02096644
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DOI: https://doi.org/10.1007/BF02096644