Decay of Complex Metastable States

Participating group members: Peter Reimann, Mykhaylo Evstigneev, Sebastian Getfert
Main cooperation partners: Roger Filliger, Clemens Bechinger, Peter Hänggi, Jörg Lehmann, Peter Talkner

Along the general lines of Kramers reaction rate theory in far from equilibrium systems, three main directions are pursued.

(i) Escape/decay in the presence of randomly fluctuating potential-barriers, of great interest for instance in the context of complex biochemical reactions and transport processes.

(ii) Thermally activated escape over periodically oscillating potential-barriers, a basic scenario in a variety of driven experimental systems.

(iii) Escape rate theory for systems in discrete time. The methodological framework are extensions of path-integral and WKB-type methods in the spirit of a singular perturbation theory for weak noise both for time-continuous and time-discrete non-linear dynamical systems.

These general methods also find applications in our projects on ratchet effects, friction phenomena on the nanometer scale, dynamic force spectroscopy on single biomolecules, stochastic resonance, nonlinear dynamics and chaos. The quantum mechanical counterpart of this research represents the project on open quantum systems.

Main publications on fluctuating and oscillating barriers:

P. Reimann
Thermally Driven Escape with Fluctuating Potentials: A new Type of Resonant Activation
Phys. Rev. Lett. 74, 4576 (1995)

P. Reimann and P. Hänggi
Surmounting Fluctuating Barriers: Basic Concepts and Results
p. 127 in "Stochastic Dynamics", Lecture Notes in Physics, Vol. 484
edited by L. Schimansky-Geier and T. Pöschel, Springer, Berlin 1997

J. Lehmann, P. Reimann, and P. Hänggi
Surmounting Oscillating Barriers
Phys. Rev. Lett. 84, 1639 (2000)

J. Lehmann, P. Reimann, and P. Hänggi
Activated escape over oscillating barriers: The case of many dimensions
phys. stat. sol. (b) 237, 53 (2003)

M. Evstigneev and P. Reimann
Probability densities of periodically driven noisy systems: An approximation scheme incorporating linear-response and adiabatic theory
Phys. Rev. E 72, 045101(R) (2005)

S. Bleil, P. Reimann, and C. Bechinger
Directing Brownian motion by oscillating barriers
Phys. Rev. E 75, 031117 (2007)

S. Getfert and P. Reimann
Suppression of thermally activated escape by heating
Phys. Rev. E 80, 030101(R) (2010)

Main publications on path-integral- and WKB-methods:

P. Reimann
Thermally Activated Escape with Potential Fluctuations driven by an Ornstein-Uhlenbeck Process
Phys. Rev. E 52, 1579 (1995)

P. Reimann and T. C. Elston
Kramers Rate for Thermal plus Dichotomous Noise applied to Ratchets
Phys. Rev. Lett. 77, 5328 (1996)

B. Lindner, L. Schimansky-Geier, P. Reimann, P. Hänggi, and M. Nagaoka
Inertia Ratchets: A Numerical Study Versus Theory
Phys. Rev. E. 59, 1417 (1999)

J. Lehmann, P. Reimann, and P. Hänggi
Surmounting Oscillating Barriers: Path-integral Approach for Weak Noise
Phys. Rev. E 62, 6282 (2000)

R. Filliger and P. Reimann
Kramers escape rate for a charged particle in a magnetic field
Europhys. Lett. 77, 30008 (2007)

S. Getfert and P. Reimann
Thermally activated escape far from equilibrium: A unified path-integral approach
Chem. Phys. 375, 386 (2010)

Main publications on systems in discrete time:

P. Reimann and P. Talkner
Invariant Densities for Noisy Maps
Phys. Rev. A 44, 6348 (1991)

P. Reimann, R. Müller, and P. Talkner
Decay of Metastable States with Discrete Dynamics
Phys. Rev. E 49, 3670 (1994)

P. Reimann and P. Talkner
Escape Rates for Noisy Maps
Phys. Rev. E 51, 4105 (1995)

P. Reimann and E. Lootens
Escape Rates for Noisy Maps with Anomalous Prefactors
Europhys. Lett. 34, 1 (1996)

Last modified on 2010-11-03