Level Statistics for Random Schroedinger Operators
| Project/Area Number |
22540140
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Gakushuin University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
MINAMI Nariyuki 慶応大学, 医学部, 教授 (10183964)
UEKI Naomasa 京都大学, 人間環境学研究科, 教授 (80211069)
SADAHIRO Taizo 津田塾大学, 学芸学部, 准教授 (00280454)
|
|---|
| Project Period (FY) |
2010-04-01 – 2014-03-31
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | ランダムシュレーディンガー作用素 / 準位統計 / ランダム行列 / 点過程 / ベータアンサンブル / ランダムポテンシャル / 確率微分方程式 / ランダムシュレディンガー作用素 / βアンサンブル / シュレーディンガー作用素 / 確率論 |
|---|
| Research Abstract |
We study the level statistics problem for 1-dimensional Schroedinger operators with random decaying potential. That is, we restrict our Hamiltonian on a bounded interval, consider a point process composed of the rescaled eigenvalues of this truncated Hamiltonian, and then study its infinite volume limit. The result is : (i) rapid decay case : the point process converges to the clock process, and second order asymptotics converges to Gaussian, (ii) critical decay case : the point process converges to that of the circular beta ensemble, as well as that of the Gaussian beta ensemble, thus yielding the coincidence of these two processes as a corollary.
|
Report
(5 results)
Research Products
(99 results)
