# Introduction to Supersymmetric Theory of Stochastics

@article{Ovchinnikov2016IntroductionTS, title={Introduction to Supersymmetric Theory of Stochastics}, author={Igor V. Ovchinnikov}, journal={Entropy}, year={2016}, volume={18}, pages={108} }

Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, $1/f$ noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale…

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## References

SHOWING 1-10 OF 140 REFERENCES

Topological Supersymmetry Breaking as the Origin of the Butterfly Effect

- Physics
- 2012

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…

Kinematic dynamo, supersymmetry breaking, and chaos

- Physics
- 2016

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an…

Topological field theory of dynamical systems.

- PhysicsChaos
- 2012

It is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry), which stands behind spatio-temporal self-similarity of Q-broken phases.

Transfer operators and topological field theory

- Physics
- 2013

The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed supersymetric theory of stochastic differential equations (SDE). It…

Ergodic theory of chaos and strange attractors

- Physics
- 1985

Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the…

Stochastic and parastochastic aspects of supersymmetric functional measures: A new non-perturbative approach to supersymmetry

- Mathematics
- 1983

Topological field theory of dynamical systems. II.

- MathematicsChaos
- 2013

It is discussed that the stochastic expectation values of a DS must be complemented on the TFT side by (-1)(F^), where F^ is the ghost number operator and the role of this inclusion is to unfold the natural path-integral representation of the T FT.

Stochastic processes, slaves and supersymmetry

- Mathematics
- 2012

We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external…

Topological analysis of chaotic dynamical systems

- Mathematics
- 1998

Topological methods have recently been developed for the analysis of dissipative dynamical systems that operate in the chaotic regime. They were originally developed for three-dimensional dissipative…

Self-organized criticality as Witten-type topological field theory with spontaneously broken Becchi-Rouet-Stora-Tyutin symmetry.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC and suggests that there may in principle exist a connection between some SOC's and the concept of topological quantum computing.