拓扑超对称破缺是蝴蝶效应的起源
Topological Supersymmetry Breaking as the Origin of the Butterfly Effect
摘要：
以前，没有明确的解释为什么混沌动力学总是伴随着被称为蝴蝶效应（BE）的扰动（和/或初始条件）的无限长记忆。在本文中，它表明，在最近提出的近似自由的超对称理论的随机（偏）微分方程（SDES），BE是一个可导出的后果（随机）混沌，严格的定义是自发击穿的拓扑超对称性，所有的SDES拥有。本文还讨论了当模型具有多重本征值的“物理”态时，遍历性的概念必须在伪时间反演对称性自发破裂的条件下加以完善，这些本征值能在无限长时间传播的物理极限下存活。
英文摘要：
Previously, there existed no clear explanation why chaotic dynamics is always accompanied by the infinitely long memory of perturbations (and/or initial conditions) known as the butterfly effect (BE). In this paper, it is shown that within the recently proposed approximation-free supersymmetric theory of stochastic (partial) differential equations (SDE), the BE is a derivable consequence of (stochastic) chaos, a rigorous definition of which is the spontaneous breakdown of topological supersymmetry that all SDEs possess. It is also discussed that the concept of ergodicy must be refined under the condition of the spontaneous breakdown of pseudo-time-reversal symmetry when the model has "physical" states of multiple eigenvalues that survive the physical limit of the infinitely long temporal propagation.
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