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Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in $Nb-Al/Al_{ox}/Nb$ Josephson Tunnel Junctions: New Theory and Experiment

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched $Nb-Al/Al_{ox}/Nb$ annular Josephson tunnel junctions as a function of the quench time, $τ_{Q}$. The probability $f_{1}$ to trap a single defect during the N-S phase transition clearly follows an allometric dependence on $τ_{Q}$ with a scaling exponent $σ= 0.5$, as predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealised model was used that predicted $σ= 0.25$, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.