The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable. In this talk, I will first show that a periodic driving field may stabilize the non-unitary dynamics for a continuous range of system parameters. I will show that the stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of Hamiltonians. Then I will give a new definition of Aharonov-Anandan phase which is always real and gauge invariant. The adiabatic theorem will be discussed using two toy models. Finally I will present a surprising hopping phenomenon in which the adiabatic following does not occur no matter how slow the evolution is. This work shows the rich geometric features of non-unitary dynamics.

Coffee: 2:30 pm, 241 Compton