Abstract
Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant ℏ→0 and large quantum number N→∞, with ℏ N kept fixed. In a suitable topology, the limit is the discontinuous symbol pχ_D(x,p) where χ_D is the characteristic function of the classically permitted region D in phase space. A refined analysis shows that the symbol is asymptotically close to the function pχ_D^(N)(x,p), where χ_D^(N) is a smooth version of χ_D related to the integrated Airy function. We also discuss the limit from a dynamical point of view.