Supersymmetric theory of stochastic dynamics: Difference between revisions

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Revision as of 11:59, 6 June 2025

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[[stochastic differential equation]]s (SDE),

[[Topological quantum field theories|topological field theories]],

and the theory of pseudo-Hermitian operators. It can be seen as an algebraic dual to the traditional set-theoretic framework of the dynamical systems theory, with its added algebraic structure and an inherent [[Supersymmetry#Supersymmetry in dynamical systems|topological supersymmetry]] (TS) enabling the generalization of certain concepts from [[Deterministic system|deterministic]] to [[Stochastic process|stochastic]] models. At the same time, it can be looked upon as a [[Topological quantum field theories|topological field theory]] of stochastic dynamics that reveals various topological aspects.

STS seeks to give a rigorous mathematical derivation to several [[Universality class|universal]] phenomena of [[Stochastic process|stochastic dynamical systems]]., Itusing identifiestools of [[SpontaneousTopological symmetryquantum breakingfield theories|spontaneoustopological breakdownfield of TStheory]], presentoriginally developed in all stochastic models, as the stochastic generalization of [[chaosParticle theoryphysics|chaoshigh-energy physics]]. InThe this view, STStheory reveals that dynamical chaos is a formsort of long-range [[Topological ordertopology|topological]] order originating from the [[supersymmetry]] hidden in all stochastic models. The theory also provides the lowest level classification of stochastic chaos which has a potential to explain [[Self-organized criticality|self-organized criticality]].

== Overview ==