权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Semiclassical foundations of single particle and collective phenomena in quantum chaos

量子混沌中单粒子和集体现象的半经典基础

基本信息

批准号：
178157760
负责人：
Dr. Boris Gutkin
金额：
--
依托单位：
Department of Applied Mathematics
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/178157760?language=en
关键词：
Semiclassical foundations single particle collective

项目摘要

In recent years the semiclassical theory has experienced considerable progress due to the development of the techniques for quantitative estimations of periodic orbit correlations in classically chaotic systems. The first part of the project focuses on the application of the semiclassical theory to a class of single particle chaotic systems with two types of motion separated from each other by a dynamical barrier. The spectral statistics of such systems is of great interest, since it is anomalous and deviates from standard ensembles of Random Matrix Theory (RMT).The second part of the project deals with the problem of eigenfunction distributions in chaotic systems. In ergodic systems almost all eigenfunctions are equidistributed in phase space, but exceptional sequences of localised states (scars) might still exist. The main objective is to understand the restriction on the possible “strength” of such a localisation in chaotic systems by proving lower bounds on the metric entropies of the corresponding semiclassical measures.The third part of the project is devoted to many-particle systems. The main new phenomenon appearing here is coexistence of (typically) chaotic single particle and (typically) regular collective dynamics. My long term goal is to develop a semiclassical theory for collective spectral excitations which properly catches both dynamical phenomena.

近年来，由于经典混沌系统周期轨道相关性定量估计技术的发展，半经典理论取得了长足的进展。本项目的第一部分着重于将半经典理论应用于一类具有两种运动类型的单粒子混沌系统，这两种运动类型被动力学屏障分开。这类系统的谱统计是非常有趣的，因为它是反常的，偏离了随机矩阵理论（RMT）的标准系综。本项目的第二部分涉及混沌系统的本征函数分布问题。在遍历系统中，几乎所有的本征函数在相空间中都是等分布的，但例外的局域态序列（疤痕）可能仍然存在。主要目标是通过证明相应的半经典测度的度量熵的下界来理解混沌系统中这种局部化的可能“强度”的限制。该项目的第三部分致力于多粒子系统。这里出现的主要新现象是（典型的）混沌单粒子和（典型的）规则集体动力学的共存。我的长期目标是发展一个半经典理论的集体光谱激发，适当捕捉两个动力学现象。