The quantum Rabi model is a widespread description for the coupling between two-level system and quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when light-matter interaction reaches so-called ultrastrong regime. Recently, modified able to provide gauge-invariant physical results in any regime was in...

We seek to establish qualitative convergence results a general class of evolution PDEs described by gradient flows in optimal transportation distances. These come from dynamical systems under the name LaSalle Invariance Principle. By combining some basic notions flow theory and systems, we are able reproduce this invariance principle setting assumptions. apply abstract non-exhaustive list examp...

Invariance properties and convergence of solutions of set dynamical systems are studied. Using a framework for systems with set-valued states, notions of stability and detectability, similar to the existing results for classical dynamical systems, are defined and used to obtain information about the convergence properties of solutions. In particular, it is shown that local stability, detectabil...