A new class of adiabatic cyclic states and geometric phases for non-Hermitian Hamiltonians

For a T-periodic non-Hermitian Hamiltonian H(t), we construct a class of ad iabatic cyclic states of period T which are not eigenstates of the initial Hamiltonian H(O). We show that the corresponding adiabatic geometric phase angles are real and discuss their relationship with the conventional comple x adiabatic geometric phase angles. We present a detailed calculation of th e new adiabatic cyclic states and their geometric phases for a non-Hermitia n analog of the spin 1/2 particle in a precessing magnetic field. (C) 1999 Elsevier Science B.V. All rights reserved.