Topological field theory of dynamical systems. II.

@article{Ovchinnikov2013TopologicalFT,
  title={Topological field theory of dynamical systems. II.},
  author={Igor V. Ovchinnikov},
  journal={Chaos},
  year={2013},
  volume={23 1},
  pages={
          013108
        }
}
This paper is a continuation of the study [Chaos.22.033134] of the relation between the stochastic dynamical systems (DS) and the Witten-type topological field theories (TFT). Here, 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. The role of this inclusion is to unfold the natural path-integral representation of the TFT, i.e., the Witten index that equals up to a topological constant to the… 
6 Citations

Figures from this paper

Supersymmetric theory of stochastic ABC model
In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics
Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems
We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be
Kinematic dynamo, supersymmetry breaking, and chaos
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
Introduction to Supersymmetric Theory of Stochastics
TLDR
The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS), which may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity.
Topological Field Theory and Computing with Instantons
TLDR
TFTs of another type, specifically the gauge-field-less Witten-type TFTs known as topological sigma models, describe the recently proposed digital memcomputing machines (DMMs) - engineered dynamical systems with point attractors being the solutions of the corresponding logic circuit that solves a specific task.
Information, Thermodynamics and Life: A Narrative Review
TLDR
The present work attempts to build a connection between information and thermodynamics in terms of energy consumption and work production, as well as present some possible applications of these physical quantities.

References

SHOWING 1-10 OF 53 REFERENCES
Topological field theory of dynamical systems.
TLDR
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.
Non-Equilibrium Thermodynamics and Topology of Currents
In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of
Topological sigma models
A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry,
On field theory quantization around instantons
Various aspects of the so-called topological embedding, a procedure recently proposed for quantizing a field theory around a non-discrete space of classical minima, are discussed and collected in a
Periodic orbit spectrum in terms of Ruelle-Pollicott resonances.
  • P. Leboeuf
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
TLDR
A random-matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards, proposing an explicit formula for the density rho(tau) in terms of the zeros and poles of the Ruelle zeta function.
Statistical Dynamics of Classical Systems
The statistical dynamics of a classical random variable that satisfies a nonlinear equation of motion is recast in terms of closed self-consistent equations in which only the observable correlations
Instantons beyond topological theory. I
Abstract Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections
Chaos and Quantum Mechanics
TLDR
The physically more complete treatment reveals the existence of dynamical regimes—such as chaos—that have no direct counterpart in the linear (unobserved) case, and allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions.
DYNAMICAL CHAOS AND NONEQUILIBRIUM STATISTICAL MECHANICS
Chaos in the motion of atoms and molecules composing fluids is a new topic in nonequilibrium physics. Relationships have been established between the characteristic quantities of chaos and the
...
1
2
3
4
5
...