Weighted Modal Transition Systems

Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore fragile in the sense that the inevitable approximation of systems by models, combined with the fundamental unpredictability of hardware platforms, makes it difficult to transfer conclusions about the behavior, based on models, to the actual system. Hence this approach is arguably unsuited for modern software systems. We propose here the first specification theory which allows to capture quantitative aspects during the refinement and implementation process, thus leveraging the problems of the qualitative setting. Our proposed quantitative specification framework uses weighted modal transition systems as a formal model of specifications. These are labeled transition systems with the additional feature that they can model optional behavior which may or may not be implemented by the system. Satisfaction and refinement is lifted from the well-known qualitative to our quantitative setting, by introducing a notion of distances between weighted modal transition systems. We show that quantitative versions of parallel composition as well as quotient (the dual to parallel composition) inherit the properties from the Boolean setting.Comment: Submitted to Formal Methods in System Desig

Two-photon transport through a waveguide coupling to a whispering gallery resonator containing an atom and photon-blockade effect

We investigate the two-photon transport through a waveguide side-coupling to a whispering-gallery-atom system. Using the Lehmann-Symanzik-Zimmermann (LSZ) reduction approach, we present the general formula for the two-photon processes including the two-photon scattering matrices, the wavefunctions and the second order correlation functions of the out-going photons. Based on the exact results of the second order correlation functions, we analyze the quantum statistics behaviors of the out-going photons for two different cases: (a) the ideal case without the inter-modal coupling in the whispering gallery resonator; (b) the case in the presence of the inter-modal coupling which leads to more complex nonlinear behavior. In the ideal case, we show that the system consists of two independent scattering pathways, a free pathway by a cavity mode without atomic excitation, and a "Jaynes-Cummings" pathway described by the Jaynes-Cummings Hamiltonian of a single-mode cavity coupling to an atom. The free pathway does not contribution to correlated two-photon processes. In the presence of intermodal mixing, the system no longer exhibit a free resonant pathway. Instead, both the single-photon and the two photon transport properties depend on the position of the atom. Thus, in the presence of intermodal mixing one can in fact tune the photon correlation properties by changing the position of the atom. Our formalism can be used to treat resonator and cavity dissipation as well.Comment: 9 pages, 7 figure

The non-relativistic limit of (central-extended) Poincare group and some consequences for quantum actualization

The nonrelativistic limit of the centrally extended Poincar\'e group is considered and their consequences in the modal Hamiltonian interpretation of quantum mechanics are discussed [ O. Lombardi and M. Castagnino, Stud. Hist. Philos. Mod. Phys 39, 380 (2008) ; J. Phys, Conf. Ser. 128, 012014 (2008) ]. Through the assumption that in quantum field theory the Casimir operators of the Poincar\'e group actualize, the nonrelativistic limit of the latter group yields to the actualization of the Casimir operators of the Galilei group, which is in agreement with the actualization rule of previous versions of modal Hamiltonian interpretation [ Ardenghi et al., Found. Phys. (submitted)