论文标题
研究经典和量子三体问题的新概念：基本的不可逆性和动态系统的时间箭头
New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time's Arrow of Dynamical Systems
论文作者
论文摘要
该文章提出了共同欧几里得空间（Riemannian歧管）中经典的三体问题，并且在数学上证明了它与牛顿三体问题的等效性。结果表明，具有局部坐标系的弯曲空间使我们能够检测动态系统内部运动的新隐藏对称性，这使我们能够将三体问题减少到6 \ emph {th}订单系统。一种新方法使地球方程系统相对于动态系统的演化参数（\ emph {internal Time}）\ emph {根本上是不可逆的}。为了描述在不同随机环境中三体系统的运动，获得了相应的随机微分方程（SDE）。使用这些SDE，获得了Fokker-Planck-type方程，以描述相相和配置空间中测量流的关节概率分布。该论文还提出了保形 - 欧几里德空间中的量子三体问题。特别是，已经获得了用于研究三体结合状态的相应波程，以及在内部时间概念的框架中研究多通道量子散射。这使我们能够解决动态庞加莱系统的极其重要的量子古典对应问题。
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6\emph{th} order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (\emph{internal time}) \emph{fundamentally irreversible}. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincaré systems.
