论文标题
部分可观测时空混沌系统的无模型预测
Analytic continuation over complex landscapes
论文作者
论文摘要
在本文中，我们跟踪了许多复杂变量的“复杂景观”的研究。与真实的景观不同，指数对马鞍的分类是微不足道的。取而代之的是，固定点波动的频谱决定了在该理论的分析延续下它们的拓扑稳定性。拓扑变化发生在所谓的斯托克斯点，在边缘（平坦）方向的马鞍之间扩散，否则会被抑制。这可以直接解释差距或“阈值”能量（在实际情况下，将马鞍与minima分开），因为固定点的Hessian矩阵频谱会形成差距。这会导致对具有不同结构的真实景观的分析延续的不同后果：“一步副本对称性”的全球最小值构成破碎的景观，其景观超出了阈值，它们的hessians被盖住了，并在stokes上受到了局部保护，并从斯托克斯角度受到了保护，而“许多步骤replica-smymmmetry brogelly brogelly opplica-smmetsry broken”却是无与伦比的，那些是无与伦比的黑典和斯特牛皮的点。发现了一个新的矩阵合奏，扮演着Goe在确定马鞍的拓扑性质中扮演的角色。
In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at stationary points determines their topological stability under analytic continuation of the theory. Topological changes, which occur at so-called Stokes points, proliferate among saddles with marginal (flat) directions and are suppressed otherwise. This gives a direct interpretation of the gap or 'threshold' energy -- which in the real case separates saddles from minima -- as the level where the spectrum of the hessian matrix of stationary points develops a gap. This leads to different consequences for the analytic continuation of real landscapes with different structures: the global minima of 'one step replica-symmetry broken' landscapes lie beyond a threshold, their hessians are gapped, and are locally protected from Stokes points, whereas those of 'many step replica-symmetry broken' have gapless hessians and Stokes points immediately proliferate. A new matrix ensemble is found, playing the role that GOE plays for real landscapes in determining the topological nature of saddles.
