A model of atomic radiation

We consider a non-relativistic quantum mechanical particle in an external potential well, coupled to an infinite free quantum field. We prove rigorously that with certain cut-offs and in the weak coupling limit, the particle decays exponentially between its bound states as predicted by perturbation theory. We also prove the existence of a « dynamical phase transition » for a particle attracted to two widely separated potential wells and also weakly coupled to an infinite reservoir. RESUME. 2014 Nous considerons une particule quantique non-relativiste dans un potentiel, couplee a un champ libre infini. Avec certaines regularisations et dans une limite faible, nous montrons que la particule passe exponentiellement entre ses etats lies selon les predictions de la theorie des perturbations. Nous montrons 1’existence d’une « transition de phase dynamique » pour une particule attractee par deux potentiels tres éloignés et aussi couplee faiblement a un reservoir infini. §1 DESCRIPTION OF THE MODEL We consider a single quantum mechanical particle with Hilbert space ~f = L 2(1R3) and Hamiltonian where so that HS may be easily defined as a self-adjoint operator on ~ as described in [11] ] [18]. Annales de l’Institut Henri Poincare Section A Vol. XXVIII, n° 1 1978.