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

Shinichi Kotani; Fumihiko Nakano

doi:10.1142/9789814596534_0018

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

Shinichi Kotani, Fumihiko Nakano

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English
Title of host publication	Festschrift Masatoshi Fukushima
Subtitle of host publication	In Honor Of Masatoshi Fukushima’s Sanju
Publisher	World Scientific Publishing Co.
Pages	343-373
Number of pages	31
ISBN (Electronic)	9789814596534
DOIs	https://doi.org/10.1142/9789814596534_0018
Publication status	Published - 2014 Nov 27
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)

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10.1142/9789814596534_0018

Cite this

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abstract = "We study the level statistics of one-dimensional Schr{\"o}dinger 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.",

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N2 - 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.

AB - 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.

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ER -

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

Abstract

ASJC Scopus subject areas

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