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We discuss the time evolution of physical finite dimensional systems whichare modelled by non-hermitian Hamiltonians. We address both generalnon-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory ofKrein Spaces to construct metric operators and well-defined inner products. Asan application, we study the stationary behaviour of dissipative One AxisTwisting Hamiltonians. We discuss the effect of decoherence under differentcoupling schemes.

Dynamics of finite dimensional non-hermitian systems with indefinite metric