Level statistics of one-dimensional schrödinger operators with random decaying potential

Shinichi Kotani, Fumihiko Nakano

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)

Abstract

We study the level statistics of one-dimensional Schrödinger operator with random potential decaying like x-a at infinity. We consider the point process L consisting of the rescaled eigenvalues and show that: (i) (ac spectrum case) for formula, L converges to a clock process, and the fluctuation of the eigenvalue spacing converges to Gaussian. (ii) (critical case) for formula, L converges to the limit of the circular ß-ensemble.

Original languageEnglish
Title of host publicationFestschrift Masatoshi Fukushima
Subtitle of host publicationIn Honor Of Masatoshi Fukushima’s Sanju
PublisherWorld Scientific Publishing Co.
Pages343-373
Number of pages31
ISBN (Electronic)9789814596534
DOIs
Publication statusPublished - 2014 Nov 27
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Fingerprint

Dive into the research topics of 'Level statistics of one-dimensional schrödinger operators with random decaying potential'. Together they form a unique fingerprint.

Cite this