  Quantum tunneling introduces a fundamental difference between classical and
quantum mechanics. Whenever the classical ground state is non-unique
(degenerate), quantum mechanics restore uniqueness thanks to tunneling. A
condensate in a rotating trap with a vortex can have such a degenerate
classical ground state, a degeneracy that is excluded in the absence of
rotation at least when the Gross-Pitaevskii equation applies. If the rotating
trap has a center of symmetry, like a figure eight (a peanut), the vortex may
be on either side with the same energy yielding a degenerate ground state, a
degeneracy lifted by quantum tunneling. We explain how to compute the rate of
tunneling in the WKB limit by estimating the action of the trajectory in the
Euclidean version of the dynamics.
