# 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…

## 36 Citations

Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau

- Physics
- 2015

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

- Physics
- 2005

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

- Physics
- 2014

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

- Mathematics
- 2008

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

- Physics
- 2014

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

- Mathematics
- 2012

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

- Mathematics, Physics
- 2013

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

- 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…

How quantum mechanics probes superspace

- Physics
- 2014

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.

- 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.

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