Vortex structures inside spherical mesoscopic superconductor plus magnetic dipole
type: Item
instance of: scholarly article
title: Vortex structures inside spherical mesoscopic superconductor plus magnetic dipole
zbMATH Open document ID: 1440.82012
DOI: 10.1155/2018/8652151
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We investigate the existence of multivortex states in a superconducting mesoscopic sphere with a magnetic dipole placed at the center. We obtain analytic solutions for the order parameter \(\Psi(\overset{\rightarrow} {r})\) inside the sphere through the linearized Ginzburg-Landau (GL) model, coupled with mixed boundary conditions, and under regularity conditions and decoupling coordinates approximation. The solutions of the linear GL equation are obtained in terms of Heun double confluent functions, in dipole coordinates symmetry. The analyticity of the solutions and the associated eigenproblem are discussed thoroughly. We minimize the free energy for the fully nonlinear GL system by using linear combinations of linear analytic solutions, and we provide the conditions of occurring multivortex states. The results are not restricted to the particular spherical geometry, since the present formalism can be extended for large samples, up to infinite superconducting space plus magnetic dipole.
Mathematics Subject Classification ID: 82D55
zbMATH DE Number: 6992033
author: Andrei Ludu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8652151
OpenAlex ID: W2899243260
cites work: Q3756011
cites work: Quantum Magnetic Hamiltonians with Remarkable Spectral Properties
cites work: The generalized Coulomb problem: an exactly solvable model
cites work: Extending the class of solvable potentials. I. The infinite potential well with a sinusoidal bottom
cites work: Q3994494
cites work: Heun functions and the energy spectrum of a charged particle on a sphere under a magnetic field and Coulomb force
cites work: Behaviour of three charged particles on a plane under perpendicular magnetic field
cites work: Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes
cites work: The central two-point connection problem for the reduced confluent Heun equation
cites work: Susy, Gauss, Heun and physics: a magic square?
cites work: Vortex patterns beyond hypergeometric
cites work: Vortex states in axially symmetric superconductors in applied magnetic field
cites work: Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field
cites work: Q4112233
cites work: Factorization of some confluent Heun's differential equations
cites work: The double confluent Heun equation: Characteristic exponent and connection formulae
cites work: Asymptotic and numeric study of eigenvalues of the double confluent Heun equation
cites work: Q5540675
cites work: Heun’s Equation and the Hypergeometric Equation
cites work: Symmetry and the Chazy equation
cites work: Normalization integrals of orthogonal Heun functions
cites work: Q5427940
cites work: Ince’s limits for confluent and double-confluent Heun equations
cites work: On certain Heun functions, associated functions of discrete variables, and applications
cites work: Q5558293
cites work: Spheroidal and bipolar coordinates
description: scientific article; zbMATH DE number 6992033