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-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.

Contracting Forced Lagrangian and Contact Lagrangian Systems: application to nonholonomic systems with symmetries

“…One of its main advantages is the existence of symmetries [15] and the possibility to apply reduction by symmetries techniques. It is worth mentioning that contact systems have also been used to model the evolution of thermodynamic variables [24], [25], quantum mechanics [19] and the evolution of finite state dissipative quantum systems [26].…”