THEORICAL STUDY ON FUNDAMENTAL THEORIES ON MULTI-DIMENSIONAL CHEMICALLY REACTING SYSTEMS

多维化学反应系统基础理论的理论研究

• 批准号: 10044106
• 负责人: NAGAOKA Masataka
• 金额: $ 2.43万
• 依托单位: NAGOYA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10044106/
• 关键词: QUANTUM DIFFUSION; NONLINEAR EFFECT; QUANTUM CHAOS; DIFFUSION PROCESS; NONINTEGRABLE SYSTEM; DISSIPATION PROCESS; NONEQUILIBRIUM STATIONARY STATE; RELAXATION PROCESS

In this International Scientific Research Program, notifying the multidimensionality of chemically reacting systems, the research was executed focusing the following two points : (a) they are time-dependent quantum dynamical processes and (b) nonlinear, nonequilibrium and nonstationary processes. First of all, (1) some theoretical models were constructed by coarse-graining such many-degrees-of-freedom systems, i. e. chemically reacting systems, presently. Further, (2) the emerging mechanism of the microscopic dissipative processes was clarified in the classical nonintegrable dynamical systems.1. Since Nagaoka was not able to go abroad, by e-mail for communication, the collaboration was promoted together with Dr. Gaspard with respect to the wave-function approach of quantum diffusion (the quantum state diffusion model), derived a non-markovian stochastic Schrodinger equation and applied it to the spin-boson model.2. During the visit of Tasaki to Free University of Brussels (Belgium) (Jun. 30 - Jul. 26, 1999), by collaboration with Dr. Gaspard, Tasaki has advanced the joint study with respect to the microscopic dissipative mechanism in the multibaker transformation including the energy coordinate and the spectral decomposition of the generating operator of the map showing intermittency.3. Nagaoka and Tasaki published some of the results obtained through the present research at some symposia and some as research articles.

在这个国际科学研究计划中，注意到化学反应体系的多维性，研究集中在以下两点：(A)它们是依赖时间的量子动力学过程，(B)非线性、非平衡和非稳态过程。首先，(1)通过粗粒化这类多自由度体系，即化学反应体系，建立了一些理论模型。进一步，(2)阐明了经典不可积动力系统中微观耗散过程的显现机制。由于长冈不能出国，通过电子邮件进行交流，与Gaspard博士在量子扩散的波函数方法(量子态扩散模型)方面进行了合作，推导了一个非马尔科夫随机薛定谔方程，并将其应用于自旋玻色子模型。在Tasaki访问比利时布鲁塞尔自由大学期间(1999年6月30日-7月26日)，Tasaki与Gaspard博士合作，推进了关于多面包客变换中微观耗散机制的联合研究，包括间歇性地图生成算子的能量坐标和谱分解。Nagaoka和Tasaki在一些研讨会和一些研究文章中发表了通过本研究获得的一些结果。

项目成果

Masataka Nagaoka: "Slippage of Initial Conditions for the Redfield Master Equation"J. Chemical Physics. 111. 5668-5675 (1999)

长冈正孝：“雷德菲尔德主方程初始条件的滑移”J.

Shuichi Tasaki: "An Analytical Construction of the SRB Measuresfor Baker-type Maps" Chaos. 8. 424-443 (1998)

Shuichi Tasaki：“贝克型地图的 SRB 措施的分析构建”混沌。

Masataka Nagaoka: "Quantum Mechanical Transition Amplitude and Characteristic of Numerical Solutions and Stochastic Partial Differential Equation" Int.J.Quantum Chemistry. (in press). (1999)

长冈正孝：“量子力学跃迁幅度和数值解的特征以及随机偏微分方程”Int.J.Quantum Chemistry。

Shuichi Tasaki: "Thermodynamic Behavior of an Area-Preserving Multibaker Map with Energy"Theoretical Chemistry Accounts. 102. 385-396 (1999)

Shuichi Tasaki：“具有能量的保面积 Multibaker 图的热力学行为”理论化学帐户。

Shuichi Tasaki: "Thermodynamic Behavior of an Area-Preserving Multi Baker Map with Energy" Theoretical Chemistry Accounts. (in press). (1999)

Shuichi Tasaki：“具有能量的保面积多贝克图的热力学行为”理论化学帐户。