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

TL;DR

This paper rigorously derives the Chern-Simons-Schr"odinger equation as an effective description of the dynamics of an almost-bosonic-anyon gas in the large-particle limit, establishing a connection between microscopic and macroscopic behavior.

Contribution

It provides a rigorous derivation of the Chern-Simons-Schr"odinger equation from the microscopic dynamics of almost-bosonic-anyon gases, including a convergence rate.

Findings

Effective approximation of many-body dynamics by the Chern-Simons-Schr"odinger equation

Quantitative convergence rate depending on the extended anyons' radius

Establishment of a rigorous link between microscopic and macroscopic descriptions

Abstract

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.