Coupling-Induced Synchronized Motion and Stochastic Resonance in Overdamped Dimers

Abstract

In this study, we explore an overdamped system of a dimer in a bistable potential immersed in a heat bath. The monomers interact via the combination of the Lennard-Jones potential and the harmonic potential. We have introduced a short-range interaction in our model making it more physical. Such a classical system can be used as a model for stochastic resonance (SR) based energy harvesters where the interplay between the noise, coupling and a periodic perturbation leads to a rich class of dynamical behaviours. A key distinction between observing SR in single and coupled particle studies is that a transition between the two wells is only considered successful if both the particles cross a certain threshold position. Although we observe qualitatively a similar peaking behaviour in different quantifiers of SR (like input energy ($W_p$) and hysteresis loop area (HLA)), the effects of the above-mentioned condition on the dynamics of the system remain unaddressed to the best of our knowledge. We study SR using different measures like the input energy per period of the external forcing, the hysteresis loop area as well as quantities like phase lag between the response and the external forcing and the maximum average amplitude of the response. Additionally, we have defined a new quantity called the successful transition ratio. This ratio helps us understand the effects of the dimer's coupling on the number of successful transitions out of the total attempted transitions. The successful transition ratio is almost unity for strongly coupled dimer suggesting most of the transition attempts end up successfully however few they are in numbers. On the other hand, the ratio shows a peaking behaviour with respect to noise for weak and intermediate couplings. We show that only for the weakly coupled dimer, the ratio is maximum around the temperature where SR takes place.