Low frequency limit for thermally activated escape with periodic driving
arXiv:cond-mat/0602232
Abstract
The period-average rate in the low frequency limit for thermally activated escape with periodic driving is derived in a closed analytical form. We define the low frequency limit as the one where there is no essential dependence on frequency so that the formal limit in the appropriate equations can be taken. We develop a perturbation theory of the action in the modulation amplitude and obtain a cumbersom but closed and tractable formula for arbitrary values of the modulation ampitude to noise intensity ratio except a narrow region near the bifurcation point and a simple analytical formula for the limiting case of moderately strong modulation. The present theory yields analytical description for the retardation of the exponential growth of the escape rate enhancement (i.e., transition from a log-linear regime to more moderate growth and even reverse behavior). The theory is developed for an arbitrary potential with an activation barrier but is exemplified by the cases of cubic (metastable) and quartic (bistable) potentials.
arXiv comment26 LaTex pages, 4 eps figures
References in corpus (12)
- Strong friction limit in quantum mechanics: the Quantum Smoluchowski equation
- Surmounting Oscillating Barriers
- Noise-Activated Escape from a Sloshing Potential Well
- Activated escape of periodically driven systems
- Quantum Brownian Motion With Large Friction
- Rate description of Fokker-Planck processes with time dependent parameters
- Activated escape of periodically modulated systems
- Quantum decay rates for driven barrier potentials in the strong friction limit
- Dynamical contribution into enzyme catalytic efficiency
- Scaling and crossovers in activated escape near a bifurcation point
- Notes on Brownian motion and related phenomena
- Discrete breathers in protein secondary structure