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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态。（1）非线性双曲系统的统计行为（a）双曲系统：对于一个无限扩展的双曲系统的非平衡定态，即多面包师映射，比较了Gaspard等人的相对熵产生和粗粒熵产生，并证明了它们在适当的标度极限下是一致的，而且与热力学是一致的。（B）非双曲系统：对于单位区间上的分段线性间歇映射，证明了相关性的多项式衰减是由Frobenius-Perron算子的连续谱所表征的。另一方面，对于空间扩展的分段线性间歇映射表现出超扩散，Frobenius-Perron算子的特征值接近1被发现控制异常扩散。（2）无限扩展量子系统的非平衡态（a）C ~* 动力学系统：将C ~* 代数方法应用于一维晶格导体，严格构造了非平衡定态，证明了Landauer公式的正确性和相对熵产生的正性。另一方面，对于渐近阿贝尔C* 动力系统，我们证明了非平衡定态的存在性，Gallavotti-Cohen涨落定理的有效性以及与Zubarev MacLennan系综的等价性。（B）退相干控制：在开放系统中，与环境的相互作用降低了量子相干（退相干）。针对一个与环境场耦合的三能级系统，研究了动态解耦控制和量子Zeno控制，并证明了非理想控制可以增强退相干。