Thermal expansion of Josephson junctions as an elastic response to an effective stress field

By introducing a concept of thermal expansion (TE) of a Josephson junction as an elastic response to an effective stress field, we study (both analytically and numerically) the temperature and magnetic field dependence of TE coefficient $\alpha $ in a single small junction and in a square array. In particular, we found that in addition to {\it field} oscillations due to Fraunhofer-like dependence of the critical current, $\alpha $ of a small single junction also exhibits strong flux driven {\it temperature} oscillations near $T_C$. We also numerically simulated stress induced response of a closed loop with finite self-inductance (a prototype of an array) and found that $\alpha $ of a $5\times 5$ array may still exhibit temperature oscillations provided the applied magnetic field is strong enough to compensate for the screening induced effects.