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系统和无限扩展的量子系统的非平衡态。结果总结如下： (1)非线性动态系统的统计行为 (a)双曲系统：对于无限延伸双曲系统的非平衡稳态，称为多贝克图，相对熵产生和粗粒度熵产生为加斯帕德等人。进行了比较，结果表明它们彼此一致，并且在适当的标度限制下与热力学一致。 (b)非双曲系统：对于单位间隔上的分段线性间歇映射，相关性的多项式衰减由 Frobenius-Perron 算子的连续谱来表征。另一方面，对于表现出超扩散的空间扩展分段线性间歇图，发现 Frobenius-Perron 算子的特征值接近 1 来控制反常扩散。 (2)无限广延量子系统的非平衡态 (a) C* 动力系统：将 C* 代数方法应用于一维晶格导体，严格构造非平衡稳态，以及 Landauer 公式的有效性和相关关系的正性显示了熵的产生。另一方面，对于渐近阿贝尔 C* 动力系统，我们证明了非平衡稳态的存在、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性（退相干）。对于与环境场耦合的三能级系统，研究了动态解耦控制和量子芝诺控制，并证明非理想控制可以增强退相干。