Relaxation in interacting arrays of oscillators

Abstract

We analyze a system of interacting arrays of globally coupled nonlinear oscillators. The relaxation in the interacting arrays with different interaction strengths is compared to that in an array not subject to interaction with others. The relaxation of the latter is found to be an exponential function of time. On the other hand the relaxation of the interacting arrays is slowed down and departs from an exponential of time. There exists a crossover time, $t_c$, before which relaxation of the interacting arrays is still an exponential function. However, beyond $t_c$ relaxation is no longer exponential but well approximated by a stretched exponential $\exp [-{\left(\frac{t}{\tau }\right)}^{\beta }]$. The fractional exponent $\beta$ decreases further from unity with increasing interaction strength. The result bears strong similarity to the basic features suggested by the coupling model and seen experimentally by neutron scattering for relaxation in densely packed interacting molecules in glass-forming liquids.