Splitting of the superconducting transition in the two weakly coupled 2D XY models

The frequency $\omega$ and temperature T dependent complex conductivity $\sigma$ of two weakly coupled 2D XY models subject to the RSJ dynamics is studied through computer simulations. A double dissipation-peak structure in $Re[\omega\sigma]$ is found as a function of T for a fixed frequency. The characteristics of this double-peak structure, as well as its frequency dependence, is investigated with respect to the difference in the critical temperatures of the two XY models, originating from their different coupling strengths. The similarity with the experimental data in Festin {\it et al.} [Physica C 369, 295 (2002)] for a thin YBCO film is pointed out and some possible implications are suggested.