Derivation of the Chern-Simons-Schrödinger equation from the dynamics of an almost-bosonic-anyon gas

2024/12/17 by Théotime Girardot, Jinyeop Lee, Girardot, Théotime +1 · 2 citations
#math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.2412.13080

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--Schrödinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius R = (log N)^(1)/(2)+ε 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.

Cited by

• Dimensional reduction for anyons in the average-field approximation
• The 2D Chern-Simons-Schrödinger system reduced to 1D

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