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We show that the adiabatic approximation for nonselfadjoint hamiltoniansseems to induce two non-equal expressions for the geometric phase. The firstone is related to the spectral projector involved in the adiabatic theorem, theother one is the adiabatic limit of the nonadiabatic geometric phase. Thisapparent inconsistency is resolved by observing that the difference between thetwo expressions is compensated by a small deviation in the dynamical phases.

Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians