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

8 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)

Access to Document

10.1142/9789814596534_0018

Cite this

@inbook{6e1b295540144eb6ac2893cfaf3228a8,

title = "Level statistics of one-dimensional schr{\"o}dinger operators with random decaying potential",

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.",

author = "Shinichi Kotani and Fumihiko Nakano",

note = "Publisher Copyright: {\textcopyright} 2015 by World Scientific Publishing Co. Pte. Ltd.",

year = "2014",

month = nov,

day = "27",

doi = "10.1142/9789814596534_0018",

language = "English",

pages = "343--373",

booktitle = "Festschrift Masatoshi Fukushima",

publisher = "World Scientific Publishing Co.",

}

TY - CHAP

T1 - Level statistics of one-dimensional schrödinger operators with random decaying potential

AU - Kotani, Shinichi

AU - Nakano, Fumihiko

PY - 2014/11/27

Y1 - 2014/11/27

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.

UR - http://www.scopus.com/inward/record.url?scp=84957628026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957628026&partnerID=8YFLogxK

U2 - 10.1142/9789814596534_0018

DO - 10.1142/9789814596534_0018

M3 - Chapter

AN - SCOPUS:84957628026

SP - 343

EP - 373

BT - Festschrift Masatoshi Fukushima

PB - World Scientific Publishing Co.

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this