论文标题
部分可观测时空混沌系统的无模型预测
Semiclassical Formulae For Wigner Distributions
论文作者
论文摘要
在本文中，我们概述了混乱的混乱的现代数学理论的某些方面，即统一的双曲线，动力学系统及其在物理学中的含义。首先，我们回想起共振数学理论的最新发展，特别是作为加权Zeta函数的残基而不变的ruelle分布。然后，我们在负弯曲表面的设置中得出了加权和半经典Zeta函数之间的对应关系。将其与Hilgert，Guillarmou和Weich的结果相结合，可以将不变的Ruelle分布作为恒定负曲率中的量子机械矩阵系数的高频解释。我们通过在3盘散射系统的更多物理设置中介绍相空间分布的数值计算来结束。
In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.
