Journal of Statistical Physics

, Volume 122, Issue 4, pp 557–595 | Cite as

Kramers Equation and Supersymmetry

  • Julien Tailleur
  • Sorin Tănase-Nicola
  • Jorge Kurchan


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 introduced, together with strategies for its computation.

Key Words

Kramers equation Supersymmetry Reaction paths Morse theory Stochastic methods 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Julien Tailleur
    • 1
  • Sorin Tănase-Nicola
    • 1
    • 2
  • Jorge Kurchan
    • 1
  1. 1.PMMH UMR 7636 CNRS-ESPCIParis Cedex 05France
  2. 2.FOM Institute for Atomic and Molecular PhysicsSJ AmsterdamThe Netherlands

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