Derivation of the Chern-Simons-Schr\"odinger equation from the dynamics of an almost-bosonic-anyon gas

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--Schrödinger 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--Schrödinger equation.