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

在本国际科学研究计划中，考虑到化学反应系统的多维性，重点研究了以下两点：(a)随时间变化的量子动力学过程和(b)非线性、非平衡和非平稳过程。首先，(1)目前一些理论模型是用粗粒化的多自由度系统，即化学反应系统来建立的。进一步，(2)阐明了经典不可积动力系统中微观耗散过程的产生机理。由于Nagaoka不能出国，通过电子邮件沟通，与Gaspard博士一起推动了关于量子扩散的波函数方法（量子态扩散模型）的合作，推导了一个非马尔可夫随机薛定谔方程，并将其应用于自旋玻色子模型。在访问比利时布鲁塞尔自由大学期间（1999年6月30日至7月26日），Tasaki博士与Gaspard博士合作，推进了关于多贝克变换中的微观耗散机制的联合研究，包括能量坐标和显示间歇性的地图生成算子的频谱分解。Nagaoka和Tasaki在一些研讨会和研究论文中发表了通过本研究获得的一些结果。

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.