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Local density approximation for the almost-bosonic anyon gas. (English) Zbl 1371.35231

Summary: We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas-Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., “less-bosonic” anyons).

MSC:

35Q40 PDEs in connection with quantum mechanics
81V70 Many-body theory; quantum Hall effect
81S05 Commutation relations and statistics as related to quantum mechanics (general)
46N50 Applications of functional analysis in quantum physics
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