Using Annular Josephson Tunnel Junctions to Monitor Causal Horizon

If systems change as fast as possible as they pass through a phase transition then the initial domain structure is constrained by causality. We shall show how we can trace these causal horizons by measuring the spontaneous production of flux in annular Josephson Tunnel Junctions as a function of the quench time $\tau_{Q}$ into the superconducting phase. A specific test of our analysis is that the probability P$_{1}$ to trap a single fluxon at the N-S transition clearly follows an allometric dependence on $\tau_{Q}$ as $P_1 = a \tau_Q^{-\sigma}$, with a scaling exponent $\sigma = 0.25$, in agreement with the data.