A Crossing degeneracies and geometrical phases

  • Thread starter andresB
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Assume all the usual things for the usual things for the geometric phases: A Hamiltonian that depend on external parameters, Adiabatic evolution, cyclic evolution in parameter space and all that

If through the evolution in parameter space there is no energy level crossing, then a eigenvector of the hamiltonian will acquire a geometric phase; the Berry phase for non-degenerate levels and the Wilzeck-Zee phase otherwise.

Now, what happen when there is a crossing in a energy level?. Suppose we start the adiabatic evolution in point of parameter space that have an accidental degeneracy and that after we leave that point the degeneracy is completely lifted. What happen after a cyclic evolution?
 

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