论文标题
最大混乱的动力学系统和基本互动
Maximally Chaotic Dynamical Systems and Fundamental Interactions
论文作者
论文摘要
我们对沿阳米尔斯仪场和重力系统动力学的应用的应用进行了一般综述，及其在蒙特卡洛方法和流体动力学中的应用。在奇异理论中，最大混乱的动力学系统（MCD）可以定义为具有非零kolmogorov熵的动力系统。满足ANOSOV C条件的双曲线动力系统属于MCDS，因为它们具有相位轨迹的指数不稳定性和阳性的Kolmogorov熵。因此，C条件定义了一类丰富的MCD，这些MCD跨越了所有动态系统空间中的一个开放集。大型的Anosov-Kolmogorov MCD在负截面曲率和高维托里的Riemannian流形上实现。对MCD的兴趣植根于试图了解放松现象，统计力学的基础，流体动力学中湍流的出现，Yang-Mills场的非线性动力学以及引力N体系统的非线性动力学以及黑洞热力学。我们的目的是研究MCD的经典和量子力学特性及其在基本相互作用理论中的作用。
We give a general review on the application of Ergodic theory to the investigation of dynamics of the Yang-Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In ergodic theory the maximally chaotic dynamical systems (MCDS) can be defined as dynamical systems that have nonzero Kolmogorov entropy. The hyperbolic dynamical systems that fulfil the Anosov C-condition belong to the MCDS insofar as they have exponential instability of their phase trajectories and positive Kolmogorov entropy. It follows that the C-condition defines a rich class of MCDS that span over an open set in the space of all dynamical systems. The large class of Anosov-Kolmogorov MCDS is realised on Riemannian manifolds of negative sectional curvatures and on high-dimensional tori. The interest in MCDS is rooted in the attempts to understand the relaxation phenomena, the foundations of the statistical mechanics, the appearance of turbulence in fluid dynamics, the non-linear dynamics of Yang-Mills field and gravitating N-body systems as well as black hole thermodynamics. Our aim is to investigate classical- and quantum-mechanical properties of MCDS and their role in the theory of fundamental interactions.
