Disorder Effects on Quantum Spectra and Dynamics
无序对量子光谱和动力学的影响
基本信息
- 批准号:0602360
- 负责人:
- 金额:$ 31.5万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-06-01 至 2011-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Disorder Effects on Quantum Spectra and Dynamics Abstract of Proposed ResearchMichael AizenmanThe research will address the effects of disorder on spectra and dynamics of operators which play a role in the dynamics of quantum systems. The incorporation of even weak but extensive disorder is known to result in delocalization of at least some of the normal modes, and in the creation of pure-point spectral regimes, characterized by a dense collection of eigenvalues corresponding to well separated eigenfunctions. The focus of the proposed research is on the less understood question of the existence of extended states in the presence of disorder, and the corresponding Lebesgue absolutely continuous spectra. Also to be investigated is a possible relation of the spectral gap statistics of local operators incorporating disorder with the known eigenvalue statistics of random matrix ensembles. As the effects of randomness are dimension dependent, the initial goal is to clarify some of the issues in high dimensions, where loop effects are in general more controllable. In the converse direction, a new -fluctuation based- method is envisioned for the derivation and analysis of localization in low dimensions, where the effect is most drastic.Disorder effects play a key role in the conduction properties of quantum systems modeled by random operators, and are of direct relevance for quantum networks. The work will capitalize on recent progress made by the PI with collaborators, and on his past work on the Anderson localization and on other effects of fluctuations, such as the rounding of fist-order phase transitions in low dimensions, in what is known as the Imry-Ma effect. The subject provides the meeting grounds for techniques involving mathematical analysis with ideas drawn from statistical mechanics, where science is made of disorder. The challenge of shedding light on issues of physics enriches also fields of mathematics.
无序对量子光谱和动力学的影响拟议研究摘要Michael Aizenman该研究将解决无序对量子系统动力学中起作用的算子的光谱和动力学的影响。 结合甚至弱,但广泛的障碍是已知的,导致在离域的至少一些正常模式,并在创建纯点光谱制度,其特征在于由一个密集的收集对应于良好分离的本征函数的本征值。 拟议的研究的重点是在不太了解的问题的存在下,在无序的扩展状态,以及相应的勒贝格绝对连续谱。还将调查的是一个可能的关系的频谱间隙统计的本地运营商纳入混乱与已知的随机矩阵合奏的特征值统计。由于随机性的影响是维度相关的,最初的目标是澄清高维中的一些问题,其中循环效应通常更可控。在匡威的方向上,我们设想了一种新的基于涨落的方法来推导和分析低维中的局域化,在低维中,无序效应对随机算符模型的量子系统的传导特性起着关键的作用,并且与量子网络直接相关。这项工作将利用PI与合作者最近取得的进展,以及他过去在安德森本地化和波动的其他影响方面的工作,例如低维中一阶相变的舍入,即所谓的Imry-Ma效应。 这门学科为涉及数学分析的技术提供了会议场地,这些技术来自统计力学,其中科学是由无序组成的。揭示物理问题的挑战也丰富了数学领域。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Michael Aizenman其他文献
Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit
- DOI:
10.1007/bf01202528 - 发表时间:
1978-10-01 - 期刊:
- 影响因子:2.600
- 作者:
Michael Aizenman;Sheldon Goldstein;Joel L. Lebowitz - 通讯作者:
Joel L. Lebowitz
Geometric analysis of φ4 fields and Ising models. Parts I and II
- DOI:
10.1007/bf01205659 - 发表时间:
1982-03-01 - 期刊:
- 影响因子:2.600
- 作者:
Michael Aizenman - 通讯作者:
Michael Aizenman
Local Ward identities and the decay of correlations in ferromagnets
- DOI:
10.1007/bf01982713 - 发表时间:
1980-10-01 - 期刊:
- 影响因子:2.600
- 作者:
Michael Aizenman;Barry Simon - 通讯作者:
Barry Simon
Finite-Volume Fractional-Moment Criteria¶for Anderson Localization
- DOI:
10.1007/s002200100441 - 发表时间:
2014-01-25 - 期刊:
- 影响因子:2.600
- 作者:
Michael Aizenman;Jeffrey H. Schenker;Roland M. Friedrich;Dirk Hundertmark - 通讯作者:
Dirk Hundertmark
Entanglement Entropy Bounds for Pure States of Rapid Decorrelation
- DOI:
10.1007/s00220-025-05324-3 - 发表时间:
2025-06-23 - 期刊:
- 影响因子:2.600
- 作者:
Michael Aizenman;Simone Warzel - 通讯作者:
Simone Warzel
Michael Aizenman的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Michael Aizenman', 18)}}的其他基金
Critical Phenomena and Disorder Effects
关键现象和紊乱效应
- 批准号:
1613296 - 财政年份:2016
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Topics in the Spectral Theory of Random Operators and in Statistical Mechanics
随机算子谱理论和统计力学主题
- 批准号:
1305472 - 财政年份:2013
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Fluctuations, Resonances, and Critical Phenomena
波动、共振和关键现象
- 批准号:
1104596 - 财政年份:2011
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Critical Phenomena and Stochastic Geometry
临界现象和随机几何
- 批准号:
9971149 - 财政年份:1999
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Disorder Effects and Critical Behavior in Statistical Mechanics and in Quantum Systems
统计力学和量子系统中的无序效应和关键行为
- 批准号:
9512729 - 财政年份:1996
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Disorder Effects and Critical Behavior in Statistical Mechanics and in Quantum Systems
统计力学和量子系统中的无序效应和关键行为
- 批准号:
9214654 - 财政年份:1992
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Critical Behavior and Disorder Effects in Statistical Mechanics and in Quantum Systems (Physics)
统计力学和量子系统中的临界行为和无序效应(物理学)
- 批准号:
9196114 - 财政年份:1991
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Critical Behavior and Disorder Effects in Statistical Mechanics and in Quantum Systems (Physics)
统计力学和量子系统中的临界行为和无序效应(物理学)
- 批准号:
8912067 - 财政年份:1989
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Critical Behavior in Statistical Mechanics and Quantum FieldTheory (Physics)
统计力学和量子场论(物理学)中的关键行为
- 批准号:
8896163 - 财政年份:1988
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Mathematical Sciences: Block Travel Support to 1988 IAMP Congress
数学科学:为 1988 年 IAMP 大会提供全程旅行支持
- 批准号:
8806456 - 财政年份:1988
- 资助金额:
$ 31.5万 - 项目类别:
Standard Grant
相似国自然基金
Dynamic Credit Rating with Feedback Effects
- 批准号:
- 批准年份:2024
- 资助金额:万元
- 项目类别:外国学者研究基金项目
水环境中新兴污染物类抗生素效应(Like-Antibiotic Effects,L-AE)作用机制研究
- 批准号:21477024
- 批准年份:2014
- 资助金额:86.0 万元
- 项目类别:面上项目
相似海外基金
Interaction, Disorder and Dynamical Effects in Strongly Correlated Bosonic and Fermionic Ultracold Quantum Gases
强相关玻色子和费米子超冷量子气体中的相互作用、无序和动力学效应
- 批准号:
46321956 - 财政年份:2007
- 资助金额:
$ 31.5万 - 项目类别:
Research Units
CAREER: Non-Equilibrium Transport and Disorder Effects in Quantum Wires and Related Systems
职业:量子线及相关系统中的非平衡输运和无序效应
- 批准号:
0544116 - 财政年份:2006
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Phase transitions in quantum fluids and solids: Effects of confinement and disorder
量子流体和固体中的相变:限制和无序的影响
- 批准号:
105459-2002 - 财政年份:2006
- 资助金额:
$ 31.5万 - 项目类别:
Discovery Grants Program - Individual
Phase transitions in quantum fluids and solids: Effects of confinement and disorder
量子流体和固体中的相变:限制和无序的影响
- 批准号:
105459-2002 - 财政年份:2005
- 资助金额:
$ 31.5万 - 项目类别:
Discovery Grants Program - Individual
Phase transitions in quantum fluids and solids: Effects of confinement and disorder
量子流体和固体中的相变:限制和无序的影响
- 批准号:
105459-2002 - 财政年份:2004
- 资助金额:
$ 31.5万 - 项目类别:
Discovery Grants Program - Individual
Phase transitions in quantum fluids and solids: Effects of confinement and disorder
量子流体和固体中的相变:限制和无序的影响
- 批准号:
105459-2002 - 财政年份:2003
- 资助金额:
$ 31.5万 - 项目类别:
Discovery Grants Program - Individual
Phase transitions in quantum fluids and solids: Effects of confinement and disorder
量子流体和固体中的相变:限制和无序的影响
- 批准号:
105459-2002 - 财政年份:2002
- 资助金额:
$ 31.5万 - 项目类别:
Discovery Grants Program - Individual
Collaborative Research: Quasiparticle Transport in Organic Materials: Vibrational Dressing, Static Disorder, Nanoscale Confinement, and Quantum Effects
合作研究:有机材料中的准粒子输运:振动修整、静电无序、纳米级约束和量子效应
- 批准号:
0097204 - 财政年份:2001
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
CAREER: Interplay of Disorder and Quantum Effects in Low Dimensional Magnets and Superconductors
职业:低维磁体和超导体中无序与量子效应的相互作用
- 批准号:
0296119 - 财政年份:2001
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant
Collaborative Research: Quasiparticle Transport in Organic Materials: Vibrational Dressing, Static Disorder, Nanoscale Confinement, and Quantum Effects
合作研究:有机材料中的准粒子输运:振动修整、静电无序、纳米级约束和量子效应
- 批准号:
0097210 - 财政年份:2001
- 资助金额:
$ 31.5万 - 项目类别:
Continuing Grant