Local Density Approximation for Almost-Bosonic Anyons

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.

Contribution to the proceedings of QMath13: Mathematical Results in Quantum Physics, 8-11 October 2016, Atlanta, US

References in corpus (8)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Adiabatic Theorem for Quantum Spin Systems
• The adiabatic theorem and linear response theory for extended quantum systems
• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory

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