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).
Keywords
mean-field energy, anyons, fractional statistics,
Thomas–Fermi theory, magnetic
Schrödinger operator