On dissipationless decoherence

We consider a model of environment-induced dissipationless decoherence of a quantum system where the system is coupled to the bath degrees of freedom via the system Hamiltonian itself. We solve exactly for the reduced density operator of the system for an arbitrary spectral density of the thermal ba th and also write down an exact master equation in the Lindblad form. We co mpare and contrast the above results with those obtained by considering the system frequencies to be randomly modulated as in stochastic models. We ob serve that a coupling to the bath as above necessarily induces a Kerr-like coherent contribution in the reduced dynamics of the system. This Kerr-like term is a reflection of the quantum nature of the bath and cannot be obtai ned from stochastic models. For the special case of a harmonic oscillator w e consider the influence of decoherence and its relation with phase diffusi on. Our numerical results exhibit oscillations in the evolution of system v ariables which overall is a signature of the quantum nature of the environm ent.