Dynamics of finite dimensional non-hermitian systems with indefinite metric

We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to construct metric operators and well-defined inner products. As an application, we study the stationary behaviour of dissipative One Axis Twisting Hamiltonians. We discuss the effect of decoherence under different coupling schemes.