Vortex dynamics for the two dimensional non homogeneous Gross-Pitaevskii equation

TL;DR

This paper derives the asymptotic vortex dynamics for the 2D inhomogeneous Gross-Pitaevskii equation under Schrödinger evolution, introducing new estimates and approximations for vortex core behavior.

Contribution

It provides the first derivation of vortex dynamics in an inhomogeneous background for the 2D Gross-Pitaevskii equation, with novel core estimates and approximation techniques.

Findings

Vortex dynamics governed by a new asymptotic law

Lower bound estimates for vortex cores established

Effective approximations for vortex behavior in inhomogeneous media

Abstract

We derive the asymptotical dynamical law for Ginzburg-Landau vortices in an inhomogeneous background density under the Schr\"odinger dynamics, when the Ginzburg-Landau parameter goes to zero. New ingredients involve across the cores lower bound estimates and approximations.