Localization Transitions from Free Random Variables

Details Localization Transitions from Free Random Variables Localization Transitions from Free Random Variables

1997-05-11

arxiv.org/abs/cond-mat/9705098v1

Acta Physica Polonica B30 (1999) 45.

Physics

Condensed Matter

4 pages RevTeX with 5 EPS figures included

Scientific paper

We motivate and use the concept of free random variables for the studies of the de-pinning transition of flux lines in superconductors as recently discussed by Hatano and Nelson. We derive analytical conditions for the critical points of the eigenvalue distribution in the complex plane for all values of the transverse magnetic field in one-dimension, in agreement with numerical calculations. We suggest a relation between reduced nonhermitean quantum mechanics in D-dimensions and nonhermitean random matrix models with weak nonhermiticity.

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