Local density approximation for the almost-bosonic anyon gas

Abstract

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).

Minor typo corrected, version accepted in Analysis and PDEs

References in corpus (4)

• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
• Fractional angular momentum in cold atom systems

Cited by in corpus (16)

• Exclusion bounds for extended anyons
• Vortex patterns in the almost-bosonic anyon gas
• A Quantum Impurity Model for Anyons
• Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field
• Magnetic Perturbations of Anyonic and Aharonov-Bohm Schrödinger Operators
• Kohn-Sham Density Functional Theory of Abelian Anyons
• Fermionic behavior of ideal anyons
• Composite anyons on a torus
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Semiclassical limit for almost fermionic anyons
• Properties of 2D anyon gas
• Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
• Quadratic forms for Aharonov-Bohm Hamiltonians
• Effects of Corners in Surface Superconductivity
• 2D magnetic stability
• Differential Equations of Quantum Mechanics