GEOMETRICAL PHASE IN THE CYCLIC EVOLUTION OF NON-HERMITIAN SYSTEMS

We derive, by a biorthonormal state approach, the analogy of Berry's phase factor for open, non-conservative systems, for both adiabatic and non-adiabatic evolution. In the latter case, a (non-unitary) evolution operator method is exploited. An application is given to the optical supermode propagation in the free-electron laser