Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law

TL;DR

This paper analyzes the stability and interaction patterns of quantized vortices in superconductivity using reduced dynamical laws, providing insights into vortex behavior, stability, and collision phenomena through analytical and numerical methods.

Contribution

It introduces a reduced dynamical law framework for vortex interactions, deriving first integrals and analyzing stability and collision patterns, including analytical solutions for specific cases.

Findings

Orbital stability for vortices with same winding number.

Different collision patterns for vortices with different winding numbers.

Analytical solutions for special initial configurations.

Abstract

We study analytically and numerically stability and interaction patterns of quantized vortex lattices governed by the reduced dynamical law -- a system of ordinary differential equations (ODEs) -- in superconductivity. By deriving several non-autonomous first integrals of the ODEs, we obtain qualitatively dynamical properties of a cluster of quantized vortices, including global existence, finite time collision, equilibrium solution and invariant solution manifolds. For a vortex lattice with 3 vortices, we establish orbital stability when they have the same winding number and find different collision patterns when they have different winding numbers. In addition, under several special initial setups, we can obtain analytical solutions for the nonlinear ODEs.