Quantifying stochastic resonance: theory versus experiment

Abstract

We discuss different quantifiers of stochastic resonance (SR) and how far they are mathematically related with each other. Specifically, we address bona fide SR in terms of the areas of the hysteresis loops and of the first peaks in the residence time distributions. We demonstrate a surprisingly good agreement of these two SR quantifiers experimentally for colloidal particles in periodically modulated laser traps. A simple theoretical model is established, which reproduces the experimental observations very well.

Stochastic resonancevs.resonant activation

“…For the sake of simplicity, we only considered a one-dimensional potential which has been demonstrated to describe our experimental situation very well [17].…”

“…The friction coefficient η was estimated from Stokes' formula and then adjusted numerically in order to optimally fit the agreement between experiment and simulation for the MRT. For all simulations presented here we used η = 1.7 × 10 −8 kg s −1 which is slightly higher than the value estimated from Stokes' formula [17]. As a characteristic quantifier of RA we have used up to here the MRT, as determined from the long-time trajectories.…”

“…Our experimental setup consisting of scanned laser tweezers, a sample cell containing a colloidal suspension, and a video microscope was described in [6,17]. For the measurements presented here we used silica beads of diameter 2r = 1.57 µm.…”

Stochastic resonance and heat fluctuations in a driven double-well system

“…Here, noise plays a constructive role of pumping power in a particular mode, that is in consonance with the applied field, at the cost of the entire spectrum of modes present in it. SR, so defined, leaves a lot of liberty as to what is the physical quantity that is to be observed which should show a maximum as a function of noise strength [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In other words, no unique quantifier of SR is specified.…”

Work fluctuations and stochastic resonance

“…Because of its generic nature, this phenomenon, boasts applications in almost all areas of natural sciences. Different quantifiers of SR have been discussed [2][3][4][5][6] as regards to its validity as a bona fide resonance, i.e., the resonance phenomena as a function of noise strength as well as the driving frequency. Hysteresis loop area [2], input energy or the work done on the system per cycle [3,4] and area under the first peak in the residence time distribution [7] have turned out to be good quantifiers characterizing SR as a bona fide resonance.…”