Analytical Study on the State-Evolution Operator and Nonequilibrium States for Nonlinear Dynamical Systems including Chaotic Systems

包括混沌系统在内的非线性动力系统的状态演化算子和非平衡状态的解析研究

基本信息

批准号：
12640375
负责人：
TASAKI Shuichi
金额：
$ 2.3万
依托单位：
Waseda University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2003
项目状态：
已结题

项目摘要

We have mainly investigated nonequilibrium states for nonlinear dynamical systems and, infinitely extended quantum systems. The results are summarized as follows :(1)STATISTICAL BEHAVIOR OF NONLINEAR DYNAMICAL SYSTEMS (a)Hyperbolic Systems : For nonequilibrium steady states of an infinitely extended hyperbolic system, called a multibaker map, the relative entropy production and a coarse-grained entropy production of Gaspard et al. are is compared and are shown to be consistent with each other and with thermodynamics in an appropriate scaling limit. (b)Nonhyperbolic Systems : For a piecewise linear intermittent map on the unit interval, the polynomial decay of correlation is shown to be characterized by a continuous spectrum of the Frobenius-Perron operator. On the other hand, for a spatially extended piecewise linear intermittent map exhibiting super diffusion, eigenvalues near 1 of the Frobenius-Perron operator are found to control the anomalous diffusion. (2)NONEQUILIBRIUM STATES OF INFINITELY EXTENDED QUANTUM SYSTEMS (a) C* Dynamical Systems : Applying the C* algebraic method to a 1-d lattice conductor, nonequilibrium steady states are rigorously constructed and the validity of Landauer formula & the positivity of the relative entropy production are shown. On the other hand, for asymptotically abelian C* dynamical systems, we have shown the existence of nonequilibrium steady states, the validity of Gallavotti-Cohen fluctuation theorem and the equivalence with the Zubarev-MacLennan ensembles, (b)Decoherence Control : In open systems, the interaction with environment reduces quantum coherence (decoherence). For a three-level system coupled with an environmental field, the dynamical decoupling control and quantum Zeno control are investigated and non-ideal controls are shown to enhance decoherence.

我们主要研究了非线性动力学系统和无限扩展量子系统的非平衡状态。结果总结如下：（1）非线性动力学系统的统计行为（a）双曲线系统：对于无限扩展的双曲线系统的非平衡稳态，称为多生物图，相对熵产生和Gasspard等人的粗粒熵产生。进行比较，并显示出彼此一致，并与适当的缩放限制的热力学一致。（b）非输液系统：对于单位间隔上的分段线性间歇地图，相关的多项式衰减显示为以Frobenius-Perron oberon的连续光谱为特征。另一方面，对于表现出超级扩散的空间扩展线性间歇地图，发现特征值在Frobenius-Perron operator中的1个附近可以控制异常扩散。（2）无限扩展的量子系统的非平衡状态（a）C*动力学系统：将C*代数方法应用于1-D晶格导体，严格构建非平衡稳态以及Landauer公式的有效性和相对生产的积极性。另一方面，对于渐近的阿贝里安c*动力系统，我们显示了非平衡稳态的存在，Gallavotti-Cohen波动定理的有效性以及与Zubarev-Maclennan ensembles的等效性，（b）含量控制：在开放系统中：与环境量化量子的相互作用（在环境中的相互作用）（在环境量相互作用）中（REDUCES REDUSUM CORESICE（REDUSUM CORESICE）（RECORESERICE（RECO）。对于三级系统，结合环境场，研究了动力学去耦控制和量子ZENO控制，并显示非理想的对照可提高反熔。