From geometry to coherent dissipative dynamics in quantum mechanics

Abstract

Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal consists on extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation using an appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation that the resulting dynamics constitutes a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.