Schrodinger Operators with Spectral Transitions
Schrodinger Operators with Spectral Transitions
批准号:
1901462
负责人:
Svetlana Jitomirskaya
金额:
$30.0万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2019
资助国家:
美国
项目状态:
已结题
起止时间:
2019-08-01 至 2022-07-31
中文摘要
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英文摘要
The project concerns the anomalous spectral and diffusive properties of quasiperiodic and other deterministic and random structures. This is research on the fundamental properties of disordered systems that serve as models of systems with impurities. Quasiperiodic operators provide central or important models for integer quantum Hall effect, experimental quasicrystals and the quantum chaos theory. The development of the rigorous theory is expected to contribute to the understanding of all the above phenomena, and in particular, may lead to finding new materials with desired physical properties. Disordered systems are also used in modeling many other micro and macro effects: from quantum localization to earthquakes. The proposed topics include studying properties of both highly and weakly disordered systems of Quantum Mechanics that demonstrate certain anomalous behavior. An integral part of the project concerns educating graduate students and other young researchers. The project consists of several parts. One is to prove the extended states for multidimensional quasiperiodic operators. Another is to study the effects of interaction in tight-binding quasi-periodic models. One more is to develop a new, determinantal, approach to multidimensional Anderson localization. Other important objectives are the study of issues related to certain models of quantum chaos. The project involves the continuing development of non-perturbative methods for the proofs of localization type effects both in Schrodinger operators and in quantum spin systems, percolation and contact processes in disordered environments, as well as for the study of absolutely continuous spectrum.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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On point spectrum of critical almost Mathieu operators
关键的几乎 Mathieu 算子的点谱
DOI:
10.1016/j.aim.2021.107997
发表时间:
2021
期刊:
Advances in Mathematics
影响因子:
1.7
作者:
[Jitomirskaya, S.]
通讯作者:
Jitomirskaya, S.
DOI:
10.1063/5.0054834
发表时间:
2021-04
期刊:
Journal of Mathematical Physics
影响因子:
1.3
作者:
[S. Jitomirskaya;Wencai Liu]
通讯作者:
S. Jitomirskaya;Wencai Liu
DOI:
10.4310/mrl.2020.v27.n3.a8
发表时间:
2018-12
期刊:
Mathematical Research Letters
影响因子:
1
作者:
[S. Jitomirskaya;Helge Kruger;Wencai Liu]
通讯作者:
S. Jitomirskaya;Helge Kruger;Wencai Liu
DOI:
10.1016/j.aim.2019.106773
发表时间:
2019
期刊:
Advances in Mathematics
影响因子:
1.7
作者:
[Jitomirskaya, Svetlana, Liu, Wencai]
通讯作者:
Liu, Wencai
Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
具有嵌入到拉普拉斯基本谱中的奇异连续谱的非紧完备黎曼流形,I. 双曲情况
DOI:
10.1090/tran/8112
发表时间:
2020
期刊:
Transactions of the American Mathematical Society
影响因子:
1.3
作者:
[Jitomirskaya, Svetlana, Liu, Wencai]
通讯作者:
Liu, Wencai
共 7 条
Spectral Transitions and Critical Phenomena
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批准号:2155211
-
项目类别:Continuing Grant
-
资助金额:$72.5万
-
财政年份:2022
-
负责人:Svetlana Jitomirskaya
-
依托单位:
FRG: Collaborative Research: Non-Perturbative Analysis for Multi-Dimensional Quasiperiodic Systems
-
批准号:2052899
-
项目类别:Standard Grant
-
资助金额:$56.64万
-
财政年份:2021
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral theory of ergodic Schrodinger operators and related models
-
批准号:1401204
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项目类别:Continuing Grant
-
资助金额:$50.0万
-
财政年份:2014
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral theory of ergodic Schrodinger operators and related models
-
批准号:1101578
-
项目类别:Continuing Grant
-
资助金额:$41.99万
-
财政年份:2011
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral Properties of Ergodic Schroedinger Operators
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批准号:0601081
-
项目类别:Continuing Grant
-
资助金额:$26.0万
-
财政年份:2006
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral and Transport Theory of Schrodinger Operators
-
批准号:0300974
-
项目类别:Continuing Grant
-
资助金额:$27.3万
-
财政年份:2003
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral and Transport Theory of Schrodinger Operators
-
批准号:0070755
-
项目类别:Continuing Grant
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资助金额:$18.6万
-
财政年份:2000
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Spectral Theory of Schrodinger Operators and Localization Type Effects in Disordered Environments
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批准号:9706443
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项目类别:Standard Grant
-
资助金额:$8.01万
-
财政年份:1997
-
负责人:Svetlana Jitomirskaya
-
依托单位:
Mathematical Sciences: Singular Continuous Spectum and Localization Type Effects if Disordered Systems
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批准号:9501265
-
项目类别:Standard Grant
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资助金额:$4.0万
-
财政年份:1995
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负责人:Svetlana Jitomirskaya
-
依托单位:
海外基金