Localization transitions from free random variables

Romuald A. Janik, Maciej A. Nowak, Gabor Papp, Ismail Zahed

Research output: Contribution to journalArticle

9 Citations (Scopus)


We motivate and use the concept of free random variables for the study of the de-pinning transition of flux lines in superconductors as recently discussed by Hatano and Nelson in one dimension. Our analysis yields naturally to a generalization of the concept of Coherent Phase Appproximation (CPA) for nonhermitean Hamiltonians, and is exact for Cauchy randomness. We derive analytical conditions for the critical points of the complex eigenvalue distribution, in very good agreement with numerical calculations. We suggest a relation between dimensionally reduced nonhermitean quantum mechanics and weak nonhermiticity.

Original languageEnglish
Pages (from-to)45-58
Number of pages14
JournalActa Physica Polonica B
Issue number1
Publication statusPublished - Dec 1 1999

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    Janik, R. A., Nowak, M. A., Papp, G., & Zahed, I. (1999). Localization transitions from free random variables. Acta Physica Polonica B, 30(1), 45-58.