Kramers Equation and Supersymmetry

@article{Tailleur2005KramersEA,
  title={Kramers Equation and Supersymmetry},
  author={Julien Tailleur and Sorin Tanase-Nicola and Jorge Kurchan},
  journal={Journal of Statistical Physics},
  year={2005},
  volume={122},
  pages={557-595}
}
Hamilton’s equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories in an elementary way. From a more practical point of view, the formalism provides new tools to study the reaction paths in systems with separated time scales. A ‘reduced current’ which contains the relevant part of the phase space probability current is… 
Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau
In this talk we review some old and new results about the use of supersymmetric structures in semi-classical problems. Necessary and sufficient conditions are obtained for a real semiclassical
A Quantum field theory as emergent description of constrained supersymmetric classical dynamics
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. --
A particle in equilibrium with a bath realizes worldline supersymmetry
We study the relation between the partition function of a non--relativistic particle, in one spatial dimension, that describes the equilibrium fluctuations implicitly, and the partition function of
Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications
In the first part of this work, we consider second order supersymmetric differential operators in the semiclassical limit, including the Kramers-Fokker-Planck operator, such that the exponent of the
Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only
Supersymmetric structures for second order differential operators
Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of
Tunnel effect and symmetries for non-selfadjoint operators
We study low lying eigenvalues for non-selfadjoint semiclassical differential operators, where symmetries play an important role. In the case of the Kramers-Fokker-Planck operator, we show how the
Transfer operators and topological field theory
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
How quantum mechanics probes superspace
We study quantum mechanics in one space dimension in the stochastic formalism. We show that the partition function of the theory is, in fact, equivalent to that of a model, whose action is explicitly
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.
...
1
2
3
4
...

References

SHOWING 1-10 OF 19 REFERENCES
Stochastic and Non-Stochastic Supersymmetry
In this paper we review the supersymmetries discovered some time ago both in Langevin equations and in Hamilton's canonical equations. Of these two supersymmetries we mainly study the physical
Metastable States, Transitions, Basins and Borders at Finite Temperatures
Langevin/Fokker-Planck processes can be immersed in a larger frame by adding fictitious fermion variables. The (super) symmetry of this larger structure has been used to derive Morse theory in an
Quasisymplectic integrators for stochastic differential equations.
  • R. Mannella
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate
...
1
2
...