Supersymmetric theory of stochastic dynamics: Difference between revisions

Revision as of 11:59, 6 June 2025

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From an [[algebraic topology]] perspective, the wavefunctions are [[differential forms]]<ref name=":6"/> and [[dynamical systems theory]] defines their dynamics by the generalized transfer operator (GTO)<ref name=":0"/><ref name=":19"/> -- the [[pullback]] averaged over noise. GTO commutes with the [[exterior derivative]], which is the topological supersymmetry (TS) of STS.

The presence of TS arises from the fact that continuous-time dynamics preserves the [[Topological space|topology]] of the [[phase]]/[[State-space representation|state]] space: trajectories originating from close initial conditions remain close over time for any noise configuration. If TS is spontaneously broken, this property no longer holds on average in the limit of infinitely long evolution, meaning the system exhibits a stochastic variant of the butterfly effect. In other words, STS reveals that chaos is a spontaneous long-range order -- a perspective long anticipated withinin theearly conceptdiscussions of [[complexity]]: as pointed out in Ref.

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| last = Uthamacumaran