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.
|Title of host publication||Festschrift Masatoshi Fukushima|
|Subtitle of host publication||In Honor Of Masatoshi Fukushima’s Sanju|
|Publisher||World Scientific Publishing Co.|
|Number of pages||31|
|Publication status||Published - 2014 Nov 27|
ASJC Scopus subject areas
- Physics and Astronomy(all)