We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for “less-bosonic” anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model. The results presented here mainly summarize [Anal. PDE 10 (2017), 1169-1200] with additional remarks and strengthening of some statements.

Local density approximation for almost-bosonic anyons

Correggi M.;
2018-01-01

Abstract

We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for “less-bosonic” anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model. The results presented here mainly summarize [Anal. PDE 10 (2017), 1169-1200] with additional remarks and strengthening of some statements.
MATHEMATICAL PROBLEMS IN QUANTUM PHYSICS
978-1-4704-3681-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1134367
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