Effective dynamics for particles coupled to a quantized scalar field

We consider a system of N non-relativistic spinless quantum particles (``electrons'') interacting with a quantized scalar Bose field (whose excitations we call ``photons''). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c= epsilon << 1). We show that dressed particle states exist (particles surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)^{2}. Beyond that order the effective dynamics are expected to be dissipative. The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum, which is not an eigenvalue. Nevertheless we construct approximate dressed electrons subspaces, which are adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln (v/c)^{-1}}. We also give an explicit expression for the non adiabatic transitions corresponding to emission of free photons. For the radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in Communications in Mathematical Physic

SimParc, un jeu sérieux pour la gestion participative des espaces protégés pour la conservation de la biodiversité et l'inclusion sociale

International audienceThe objective of this paper is to reflect on our experience in a serious game research project, named SimParc, about multi-agent support for participatory management of protected areas for biodiversity conservation and social inclusion. Our project has a clear filiation with the MAS-RPG (Multi-Agent-Simulation – Role-Playing Games) methodology developed by the ComMod action-research community about participatory management of renewable resources, where multi-agent simulation (MAS) computes the dynamics of the resources and role-playing game (RPG) represents the actions and dialogue between stakeholders about the resources. Meanwhile, we have explored some specific directions, such as: dialogue support for negotiation; argumentation-based decision making and its explanation; technical assistance to the players based on viability modeling. In fact, in our project multi-agent based simulation focuses on the negotiation process itself, performed by human players and some artificial participants/agents, rather than on the simulation of the resources dynamics. Meanwhile, as we will see, we have also reintroduced the modeling of the socioecosystem dynamics, but as a local technical assistance/analysis tool for the players and not as a global system modeling. In this proposed chapter, we aim at discussing the rationales for these specificities and for the whole project, as well as summarizing the architecture of our prototype system, current results and experience produced and, last but not the least, lessons learned and prospects for future works