A stochastic model for the semiclassical collective dynamics

In this paper we brieey review the main aspects of a recent proposal to simulate semiclassical corrections to classical dynamics by suitable classical stochastic uctuations, and we apply it to the spe-ciic instance of charged beams in particle accelerators. The resulting picture is that the collective beam dynamics, at the leading semiclassi-cal order in Planck constant can be described by a particular diiusion process, the Nelson process, that is time{reversal invariant. Its diffusion coeecient p N c represents a semiclassical unit of emittance (here N is the number of particles in the beam, and c is the Comp-ton wavelength). The stochastic dynamics of the Nelson type can be easily recast in the form of a Schroedinger equation, with the semi-classical unit of emittance replacing Planck constant. Therefore we provide a physical foundation to the several quantum{like models of beam dynamics proposed in recent years. We also brieey touch upon applications of the Nelson and Schroedinger formalisms to incorporate the description of coherent collective eeects.