From geometry to coherent dissipative dynamics in quantum mechanics

TL;DR

This paper introduces a geometric approach to model dissipative quantum processes that preserve coherence by extending the symplectic structure to contact geometry, providing a new framework for finite-level quantum systems.

Contribution

It develops a novel contact geometric framework for dissipative quantum dynamics that maintains coherence, offering an alternative to traditional models.

Findings

Contact Hamiltonian dynamics describe dissipation while preserving coherence.

Finite-level systems can be modeled with a contact master equation.

Application to 2-level systems matches experimental observations.

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.