2025/04/24 by Ataei, Alireza, Lundholm, Douglas, Girardot, Théotime · 3 citations
#35Q55 #47J30 #81V27 #81V70 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2504.17488
In this work we consider the N-body Hamiltonian describing the microscopic structure of a quantum gas of almost-bosonic anyons. This description includes both extended magnetic flux and spin-orbit/soft-disk interaction between the particles which are confined in a scalar trapping potential. We study a physically well-motivated ansatz for a sequence of trial states, consisting of Jastrow repulsive short-range correlations and a condensate, with sufficient variational freedom to approximate the ground state (and possibly also low-energy excited states) of the gas. In the limit N → ∞, while taking the relative size of the anyons to zero and the total magnetic flux 2πβ to remain finite, we rigorously derive the stationary Chern-Simons-Schrödinger/average-field-Pauli effective energy density functional for the condensate wave function. This includes a scalar self-interaction parameter γ which depends both on β, the diluteness of the gas, and the spin-orbit coupling strength g, but becomes independent of these microscopic details for a particular value of the coupling g=2 in which supersymmetry is exhibited (on all scales, both microscopic and mesoscopic) with γ=2π|β|. Our findings confirm and clarify the predictions we have found in the physics literature.