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

Fumihiko Nakano

doi:10.1007/s10955-014-0987-x

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

Fumihiko Nakano

Research output: Contribution to journal › Article › peer-review

18 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 language	English
Pages (from-to)	66-93
Number of pages	28
Journal	Journal of Statistical Physics
Volume	156
Issue number	1
DOIs	https://doi.org/10.1007/s10955-014-0987-x
Publication status	Published - 2014 Jul
Externally published	Yes

Keywords

Beta ensemble
Level statistics
Random Schroedinger operators

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-014-0987-x

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abstract = "We study the level statistics for two classes of 1-dimensional random Schr{\"o}dinger 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.",

keywords = "Beta ensemble, Level statistics, Random Schroedinger operators",

author = "Fumihiko Nakano",

note = "Funding Information: This work is partially supported by JSPS Grant Kiban-C No. 22540140.",

year = "2014",

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language = "English",

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AU - Nakano, Fumihiko

N1 - Funding Information: This work is partially supported by JSPS Grant Kiban-C No. 22540140.

PY - 2014/7

Y1 - 2014/7

N2 - 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.

AB - 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.

KW - Beta ensemble

KW - Level statistics

KW - Random Schroedinger operators

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EP - 93

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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