Related Experiment Video
Updated: Jul 12, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Surmounting oscillating barriers: path-integral approach for weak noise
1Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1, D-86135 Augsburg, Germany.
Abstract:
We consider the thermally activated escape of an overdamped Brownian particle over a potential barrier in the presence of periodic driving. A time-dependent path-integral formalism is developed which allows us to derive asymptotically exact weak-noise expressions for both the instantaneous and the time-averaged escape rate. Our results comprise a conceptually different, systematic treatment of the rate prefactor multiplying the exponentially leading Arrhenius factor. Moreover, an estimate for the deviations at finite noise strengths is provided and a supersymmetry-type property of the time-averaged escape rate is verified. For piecewise parabolic potentials, the rate expression can be evaluated in closed analytical form, while in more general cases, as exemplified by a cubic potential, an action-integral remains to be minimized numerically. Our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies.
Related Concept Videos
Oscillations about an Equilibrium Position
Damped Oscillations
Although friction and other non-conservative...
Forced Oscillations
Sound Waves: Interference
Interference: Path Lengths
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Limits with Oscillating Discontinuities

