The $A$ phase and the $B$ phase of superfluid He-3 are well studied, both theoretically and experimentally. The decay time scale of the $A$ phase to the $B$ phase of a typical supercooled superfluid $^3$He-A sample is calculated to be $10^{20,000}$ years or longer, yet the actual first-order phase transition of supercooled $A$ phase happens very rapidly (in seconds to minutes) in the laboratory. We propose that this very fast phase transition puzzle can be explained by the resonant tunneling effect in field theory, which generically happens since the degeneracies of both the $A$ and the $B$ phases are lifted by many small interaction effects. This explanation predicts the existence of peaks in the $A to B$ transition rate for certain values of the temperature, pressure, and magnetic field. Away from these peaks, the transition simply will not happen.
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