Open AccessHydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields
Author(s) -
Jeongho Kim,
Bora Moon
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021202
Subject(s) - compressibility , limit (mathematics) , physics , nonlinear system , planck constant , chern–simons theory , mathematical analysis , mathematical physics , gauge theory , euler system , euler equations , classical limit , mathematics , quantum , quantum mechanics , thermodynamics
We present two types of the hydrodynamic limit of the nonlinear Schrödinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible and incompressible Euler system, coupled with the Chern-Simons equations and Poisson equation respectively, as the scaled Planck constant converges to 0. Our method is based on the modulated energy estimate. In the case of compressible limit, we observe that the classical theory of relative entropy method can be applied to show the hydrodynamic limit, with the additional quantum correction term. On the other hand, for the incompressible limit, we directly estimate the modulated energy to derive the desired asymptotic convergence.