Abstract
Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using 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 constitute 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.
Highlights
The structure of this work is as follows: after a brief review of the standard geometric description of n-level quantum systems in Section 2, we introduce our approach in Section 3, and we show that, by choosing the contact Hamiltonian appropriately, the dynamics on CP(H0 ) × R is projectable onto the proper dynamics on CP(H0 ), preserving the purity of states while at the same time dissipating the expected value of the energy of the reference system
We have put forward a novel approach to the description of dissipative quantum systems based on the geometric approach to quantum mechanics and on the analogy with the description of classical dissipative systems based on contact Hamiltonian dynamics
We have considered here, in particular, the important case of radiative decay for a 2-level system, both because of its theoretical importance in understanding quantum mechanics and because of recent experiments that point to an explanation in terms of the existence of coherent quantum trajectories for these systems [5,6]
Summary
The structure of this work is as follows: after a brief review of the standard geometric description of n-level quantum systems, we introduce our approach, and we show that, by choosing the contact Hamiltonian appropriately, the dynamics on CP(H0 ) × R is projectable onto the proper dynamics on CP(H0 ), preserving the purity of states while at the same time dissipating the expected value of the energy of the reference system. In this manner, we obtain a dissipative dynamics on the manifold of physical quantum states.
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