Pancharatnam Phase of Non-Hermitian Hamiltonian

Ali Mostafazadeh

Nimrod Moiseyev

Xiaodong Cui, Yujun Zheng

We generally derive complex geometric phases in non-Hermitian quantum mechanics. The formalism of complex geometric phases for non-Hermitian quantum systems is general and can be applied in the cases of cyclic and noncyclic states in non-Hermitian quantum mechanics. As an example, we show the interpretation of complex geometric phases by a generalized density matrix defined on a two-level non-Hermitian quantum system and the two-level Bethe-Lamb model. Also, in the Hermitian case, our theoretical framework of a complex geometric phase reduces to the counterpart of the Pancharatnam phase.

Fabio Bagarello, Roberto Passante, Camillo Trapani

Tetsuo Deguchi, Pijush K. Ghosh

We show that a Dicke-type non-Hermitian Hamiltonian admits entirely real spectra by mapping it to the "dressed Dicke model" through a similarity transformation. We find a positive-definite metric in the Hilbert space of the non-Hermitian Hamiltonian so that the time evolution is unitary and allows a consistent quantum description. We then show that this non-Hermitian Hamiltonian describing nondissipative quantum processes undergoes quantum phase transition. The exactly solvable limit of the non-Hermitian Hamiltonian has also been discussed.