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We consider a non-Hermitian Hamiltonian in order to effectively describe atwo-level system coupled to a generic dissipative environment. The totalHamiltonian of the model is obtained by adding a general anti-Hermitian part,depending on four parameters, to the Hermitian Hamiltonian of a tunnelingtwo-level system. The time evolution is formulated and derived in terms of thenormalized density operator of the model, different types of decays arerevealed and analyzed. In particular, the population difference and coherenceare defined and calculated analytically. We have been able to mimic variousphysical situations with different properties, such as dephasing, vanishingpopulation difference and purification.

Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments