Time evolution of non-hermitian hamiltonian systems using Krein Spaces

We discuss the time evolution of non-hermitian hamiltonians in the frame of Krein Space Theory. We analyse both the regime of real and of complex conjugate spectrum. Also, our proposal is applied to the understanding of exceptional points. As an example, we study the stationary behavior of a non hermitian One Axis Twisting Hamiltonian. We discussed the effect of decoherence in the different coupling schemes.