Quantitative Hydrodynamic Limit of the Chern--Simons--Higgs System

TL;DR

This paper rigorously analyzes the combined non-relativistic and semi-classical limit of the Chern--Simons--Higgs system, establishing convergence rates to the Euler--Chern--Simons system using a modulated energy approach.

Contribution

It introduces a unified scaling parameter to study both limits simultaneously and provides quantitative convergence rates for the hydrodynamic limit.

Findings

Established convergence rates toward the Euler--Chern--Simons system.

Unified the non-relativistic and semi-classical limits under a single scaling.

Retained the influence of the Chern--Simons gauge structure in the limit.

Abstract

We study the hydrodynamic limit of the Chern--Simons--Higgs system, a relativistic gauge field model involving the Chern--Simons interaction. We introduce a single scaling parameter capturing both the non-relativistic (infinite speed of light) and semi-classical (vanishing Planck constant) regimes. This unified scaling allows us to justify the simultaneous non-relativistic and semi-classical limit, while retaining the nontrivial influence of the Chern--Simons gauge structure. Using a modulated energy method, we establish quantitative convergence rates toward the corresponding compressible Euler--Chern--Simons system as the scaling parameter tends to zero.