For almost-bosonic anyon gases with smeared charges, the average-field approximation is rigorously justified for radii R=N^-eta for any eta>0 and even R=e^{-N^kappa}, 0<kappa<1.
Derivation of the Chern-Simons-Schr\"odinger equation from the dynamics of an almost-bosonic-anyon gas
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We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern--Simons--Schr\"odinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius $R = (\log N)^{\frac{1}{2}+\varepsilon}$ of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern--Simons--Schr\"odinger equation.
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Average-field approximation for very dilute almost-bosonic anyon gases
For almost-bosonic anyon gases with smeared charges, the average-field approximation is rigorously justified for radii R=N^-eta for any eta>0 and even R=e^{-N^kappa}, 0<kappa<1.