Non-perturbative effects in complex systems: A study through the theory of random matrices and orthogonal polynomials
复杂系统中的非微扰效应:随机矩阵和正交多项式理论的研究
基本信息
- 批准号:EP/F014074/1
- 负责人:
- 金额:$ 6.53万
- 依托单位:
- 依托单位国家:英国
- 项目类别:Research Grant
- 财政年份:2007
- 资助国家:英国
- 起止时间:2007 至 无数据
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The paradigm of complex systems is that an extermely simple model (for example, a collection of a large number of identical particles, called Fermions, which only communicate through an extremely simple rule: no two particles are allowed to occupy the same point in space) can exhibit highly organised behaviour as n, the number of constituents, becomes large.A random matrix is an array of numbers arranged in an n columns by n rows grid with the numbers determined from say, the throw of a die, which introducesthe element of unpredictability. It turns out that for a particular, but ubiqiutous familyof random matrices, certain real numbers (eigenvalues) that are fundamental to its description are in one-to-one correspondence with the n Fermions mentioned above.To understand the collective behaviour of this system, we apply a small external probeand observe the response of the system. It turns out that if the probe is asmall and in some sense smooth perturbation, thesystem will tend to remain in the original unperturbed state.However, even a weak but non-smooth external probe can produce responses qualitatively distinct from what can be normally expected. In such situations, the usual approach of expansion in terms of small parameters --- the perturbative treatment --- breaks down completely. New methods to deal with non-perturbative effects will be developed in the proposed research to explain such behaviour.
复杂系统的范例是,一个极其简单的模型(例如,大量相同的粒子的集合,称为费米子,它们只通过一个极其简单的规则进行通信:不允许两个粒子占据空间中的同一个点)可以表现出高度有组织的行为,因为n(成分)的数量变大。随机矩阵是以n列x n行网格排列的数字阵列,数字由掷骰子确定,这引入了不可预测性元素。结果表明,对于一个特殊但普遍存在的随机矩阵族,其描述基础的某些实数(本征值)与上面提到的n个费米子一一对应。为了了解这个系统的集体行为,我们使用一个小的外部探测器并观察系统的响应。结果表明,如果探头很小,并且在某种意义上是光滑的扰动,系统将倾向于保持原始的无扰状态。然而,即使是一个微弱但非光滑的外部探头也可以产生与正常情况下预期的定性不同的响应。在这种情况下,通常的小参数展开方法-微扰处理--完全崩溃。在拟议的研究中,将开发处理非微扰效应的新方法来解释这种行为。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Yang Chen其他文献
Identification and expression analysis of a TLR11 family gene in the sea urchin Strongylocentrotus intermedius
海胆Strongylocentrotus intermedius TLR11家族基因的鉴定及表达分析
- DOI:
10.1007/s00251-017-1035-1 - 发表时间:
2018-05 - 期刊:
- 影响因子:3.2
- 作者:
Yinan Wang;Shixiong Cheng;Yaqing Chang;Kaiquan Li;Yang Chen;Yi Wang - 通讯作者:
Yi Wang
Temperature induced modulation of near-infrared photoluminescence in BaTiO3:Er
BaTiO3:Er 中近红外光致发光的温度诱导调制
- DOI:
10.1016/j.jlumin.2020.117220 - 发表时间:
2020-07 - 期刊:
- 影响因子:3.6
- 作者:
Yang Lou;Yang Chen;Chengzhen Liu;Ping Chen;Ruoyu Jia;Xiaofen Liu;Luyun Yang;Jinyan Li;Nengli Dai - 通讯作者:
Nengli Dai
Efficient remote image-based situational queries through mobile devices
通过移动设备进行高效的远程基于图像的态势查询
- DOI:
10.1145/2999508.2999524 - 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
Xiaoming Leng;Ying Yan;Yang Chen;Börje F. Karlsson;T. Moscibroda - 通讯作者:
T. Moscibroda
Vibrationally mediated photodissociation of carbon dioxide cation
振动介导的二氧化碳阳离子光解
- DOI:
- 发表时间:
2013 - 期刊:
- 影响因子:0
- 作者:
Rui Mao;Qun Zhang;Min Chen;Chao He;Dan-na Zhou;Xi-lin Bai;Limin Zhang;Yang Chen - 通讯作者:
Yang Chen
High Resolution Laser Excitation Spectra and the Franck-Condon Factors of the A2Π−X2Σ+ Electronic Transition of MgF
高分辨率激光激发光谱和 MgF 的 A2π →X2π 电子跃迁的 Franck-Condon 因子
- DOI:
10.1063/1674-0068/cjcp2110210 - 发表时间:
- 期刊:
- 影响因子:1
- 作者:
Jingwang Gu;Zengjun Xiao;Chunting Yu;Qiang Zhang;Yang Chen;Dongfeng Zhao - 通讯作者:
Dongfeng Zhao
Yang Chen的其他文献
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{{ truncateString('Yang Chen', 18)}}的其他基金
DMS-EPSRC Collaborative Research: Advancing Statistical Foundations and Frontiers for and from Emerging Astronomical Data Challenges
DMS-EPSRC 合作研究:为新出现的天文数据挑战推进统计基础和前沿
- 批准号:
2113397 - 财政年份:2021
- 资助金额:
$ 6.53万 - 项目类别:
Standard Grant
Collaborative Research: Highly Principled Data Science for Multi-Domain Astronomical Measurements and Analysis
合作研究:用于多领域天文测量和分析的高度原理性数据科学
- 批准号:
1811083 - 财政年份:2018
- 资助金额:
$ 6.53万 - 项目类别:
Standard Grant
Topics in random matrix theory and spectral theory of operators on Riemannian manifolds.
随机矩阵理论和黎曼流形算子谱理论的主题。
- 批准号:
EP/H023127/1 - 财政年份:2009
- 资助金额:
$ 6.53万 - 项目类别:
Research Grant
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