Internally orthogonal and tracking solutions of the Ginzburg-Landau and Schrödinger equations

Stephen B. Haley, Herman J. Fink, G. Fáth

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The Ginzburg-Landau (GL) and Schrödinger equations with a nonuniform magnetic flux density B(r) admit a class of internally orthogonal solutions with ∇g = -∇ln|ψ|, the gradient of the logarithm of the order parameter |ψ| (wave function magnitude) orthogonal to Q, the gradient of the gauge invariant phase. Constrained cases with ∇g=-αn̂xQ are minimum energy solutions, referred to as tracking solutions. For the macroscopic GL model virtually all solutions are in the internally orthogonal class. In two dimensions, we find multifluxoid quantum vortex, dot and wall nucleation, and surface tracking solutions for κ=λ/ξ=1/√2, with B(r)=ẑBc2(1-|ψ|2). For the microscopic Schrödinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.

Original languageEnglish
Pages (from-to)4353-4360
Number of pages8
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume61
Issue number6
Publication statusPublished - Feb 1 2000

Fingerprint

gradients
Magnetic flux
Wave functions
logarithms
Gages
magnetic flux
Vortex flow
Nucleation
flux density
nucleation
wave functions
vortices
energy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Internally orthogonal and tracking solutions of the Ginzburg-Landau and Schrödinger equations. / Haley, Stephen B.; Fink, Herman J.; Fáth, G.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 61, No. 6, 01.02.2000, p. 4353-4360.

Research output: Contribution to journalArticle

@article{43335f9cc2b14fe5865ed13ebbba9298,
title = "Internally orthogonal and tracking solutions of the Ginzburg-Landau and Schr{\"o}dinger equations",
abstract = "The Ginzburg-Landau (GL) and Schr{\"o}dinger equations with a nonuniform magnetic flux density B(r) admit a class of internally orthogonal solutions with ∇g = -∇ln|ψ|, the gradient of the logarithm of the order parameter |ψ| (wave function magnitude) orthogonal to Q, the gradient of the gauge invariant phase. Constrained cases with ∇g=-αn̂xQ are minimum energy solutions, referred to as tracking solutions. For the macroscopic GL model virtually all solutions are in the internally orthogonal class. In two dimensions, we find multifluxoid quantum vortex, dot and wall nucleation, and surface tracking solutions for κ=λ/ξ=1/√2, with B(r)=ẑBc2(1-|ψ|2). For the microscopic Schr{\"o}dinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.",
author = "Haley, {Stephen B.} and Fink, {Herman J.} and G. F{\'a}th",
year = "2000",
month = "2",
day = "1",
language = "English",
volume = "61",
pages = "4353--4360",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Physical Society",
number = "6",

}

TY - JOUR

T1 - Internally orthogonal and tracking solutions of the Ginzburg-Landau and Schrödinger equations

AU - Haley, Stephen B.

AU - Fink, Herman J.

AU - Fáth, G.

PY - 2000/2/1

Y1 - 2000/2/1

N2 - The Ginzburg-Landau (GL) and Schrödinger equations with a nonuniform magnetic flux density B(r) admit a class of internally orthogonal solutions with ∇g = -∇ln|ψ|, the gradient of the logarithm of the order parameter |ψ| (wave function magnitude) orthogonal to Q, the gradient of the gauge invariant phase. Constrained cases with ∇g=-αn̂xQ are minimum energy solutions, referred to as tracking solutions. For the macroscopic GL model virtually all solutions are in the internally orthogonal class. In two dimensions, we find multifluxoid quantum vortex, dot and wall nucleation, and surface tracking solutions for κ=λ/ξ=1/√2, with B(r)=ẑBc2(1-|ψ|2). For the microscopic Schrödinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.

AB - The Ginzburg-Landau (GL) and Schrödinger equations with a nonuniform magnetic flux density B(r) admit a class of internally orthogonal solutions with ∇g = -∇ln|ψ|, the gradient of the logarithm of the order parameter |ψ| (wave function magnitude) orthogonal to Q, the gradient of the gauge invariant phase. Constrained cases with ∇g=-αn̂xQ are minimum energy solutions, referred to as tracking solutions. For the macroscopic GL model virtually all solutions are in the internally orthogonal class. In two dimensions, we find multifluxoid quantum vortex, dot and wall nucleation, and surface tracking solutions for κ=λ/ξ=1/√2, with B(r)=ẑBc2(1-|ψ|2). For the microscopic Schrödinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.

UR - http://www.scopus.com/inward/record.url?scp=0037689977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037689977&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0037689977

VL - 61

SP - 4353

EP - 4360

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 6

ER -