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

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

Research output: Contribution to journalArticle

3 Citations (Scopus)


The Ginzburg-Landau (GL) and Schrödinger equations with a nonuniform magnetic flux density (Formula presented) admit a class of internally orthogonal solutions with (Formula presented) the gradient of the logarithm of the order parameter (Formula presented) (wave function magnitude) orthogonal to (Formula presented) the gradient of the gauge invariant phase. Constrained cases with (Formula presented) 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 (Formula presented) with (Formula presented) 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
Issue number6
Publication statusPublished - Jan 1 2000

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Internally orthogonal and tracking solutions of the Ginzburg-Landau and Schrödinger equations'. Together they form a unique fingerprint.

  • Cite this