### 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)=ẑB_{c2}(1-|ψ|^{2}). For the microscopic Schrödinger model there exists a broad class of internally orthogonal, and closed form tracking solutions.

Original language | English |
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Pages (from-to) | 4353-4360 |

Number of pages | 8 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 61 |

Issue number | 6 |

Publication status | Published - Feb 1 2000 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*61*(6), 4353-4360.

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

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 61, no. 6, pp. 4353-4360.

}

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 -