随机模拟中的中间时间尺度运动表示：与测量缺陷有关的经典哈密顿动力学的随机描述分析
Representation of intermediate time-scale motions in stochastic modeling: Analysis on stochastic description of classical Hamiltonian dynamics in relation with measurement imperfection
摘要：
这是一个公认的结果，在经典的动力系统具有足够的时间尺度分离，快速混沌自由度很好地模拟（高斯）白噪声。在本文中，我们提出的随机动力学描述的中间时间尺度运动的时间尺度分离不足的慢动力系统。首先，我们分析了如何快速确定性动力学可以被视为随机动力学在实验观测的测量的内在误差。然后，我们提出了如果存在中间时间尺度运动，应该如何修改随机动力学描述：将噪声的时间相关性修改为<f（t）f（t '）> = C（x，p）δ（t-t'），其中C（x，p）是慢坐标（x，p）的平滑函数，并且通常除了其平均值之外，f的累积量作为慢坐标（x，p）的平滑函数而变化。在这项工作中给出的分析实际上表明，无论时间尺度分离的充分性，任何复杂的（混沌和遍历）动力系统可以很好地描述使用马尔可夫过程，如果我们完美地构建（扩展）随机动力学的确定性部分。
英文摘要：
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical description for intermediate time-scale motions with insufficient time-scale separation from the slow dynamical system. First, we analyze how the fast deterministic dynamics can be viewed as stochastic dynamics under experimental observation by intrinsic errors of measurement. Then, we present how the stochastic dynamical description should be modified if intermediate time-scale motions exist: the time correlation of the noise ξis modified to <ξ(t)ξ(t')> = C(x,p)δ(t-t'), where C(x,p) is a smooth function of the slow coordinate (x,p), and generally the cumulants of ξexcept its average vary as a smooth function of the slow coordinates (x,p). The analysis given in this work actually shows that, regardless of the sufficiency of time-scale separation, any complex (chaotic and ergodic) dynamical system can be well described using Markov process, if we perfectly construct the deterministic part of (extended) stochastic dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
