An approach to dynamical description of dissipative systems

Jiushu Shao

Hans Cruz-Prado, Alessandro Bravetti, Angel García-Chung

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.

Benjamin Fain, S. H. Lin

Irène Burghardt, Klaus B. Møller

This paper explores the hydrodynamic description of quantum densities evolving under the effects of dissipation. For illustration, we refer to analytical solutions for a harmonic system and Markovian dissipation, and derive expressions for the hydrodynamic moments and a hydrodynamic force that represents a generalization of the quantum force of Bohmian dynamics. Beyond this, we draw general conclusions on the dynamical transition, induced by dissipation, to a classical-like regime. In this context, the relation between the quantum-mechanical hydrodynamic picture and its classical-statistical analogue is investigated. This has some bearing upon mixed quantum-classical schemes emerging from the hydrodynamic description.

Kentaro Urasaki

We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it causes destructive interference to suppress the quantum fluctuation. Using the variational method, we confirm that this dissipation term is a reasonable extension of the standard (Schrödinger) description for isolated systems, from which we also derive the classical action. Consequently, in macroscopic systems, the states whose time-integrated dissipation takes an extreme value come true. This description, which is consistent with our sense of reality, coexists with the usual linear-time-dependent description.

Peter P. Orth, Adilet Imambekov, Karyn Le Hur