A Are there conditions for the vanishing of geometrical phases in QM?

andresB
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Are there theorems for sufficient and necessary conditions for the vanishing of Berry and/or Wilzeck-Zee phases for a given quantum mechanical system?
 
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No, there are no theorems for sufficient and necessary conditions for the vanishing of Berry and/or Wilczek-Zee phases for a given quantum mechanical system. However, there are general conditions that can be used to determine whether these phases vanish or not. In particular, if the Hamiltonian of the system is time-independent, the Berry phase will always vanish. If the Hamiltonian is time-dependent, the Wilczek-Zee phase may vanish if the Hamiltonian is periodic in time.
 

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