Level Statistics for One-Dimensional Schrödinger Operators and Gaussian Beta Ensemble

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15 Citations (Scopus)

Abstract

We study the level statistics for two classes of 1-dimensional random Schrödinger operators: (1) for operators whose coupling constants decay as the system size becomes large, and (2) for operators with critically decaying random potential. As a byproduct of (2) with our previous result (Kotani and Nakano in Festschrift Masatoshi Fukushima, 2013) imply the coincidence of the limits of circular and Gaussian beta ensembles.

Original languageEnglish
Pages (from-to)66-93
Number of pages28
JournalJournal of Statistical Physics
Volume156
Issue number1
DOIs
Publication statusPublished - 2014 Jul
Externally publishedYes

Keywords

  • Beta ensemble
  • Level statistics
  • Random Schroedinger operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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