Quasi-classical coherent states of a charged particle in a magnetic field with accounting for viscous losses

Abstract

A quasi-classical approach is proposed for describing the motion of a charged particle in a magnetic field, taking into account irreversible losses due to the macroscopic viscosity of the medium. The wave function of a charged particle corresponding to its quasi-classical coherent state is found. It is shown that viscosity leads to an irreversible collapse of the wave function in directions perpendicular to the magnetic field. At the same time along the magnetic field the wave function experiences irreversible spreading up to a certain static limit. Thus, in the transverse directions a viscous medium and a magnetic field behave like a classical measuring device. In the longitudinal directions the signs of the quantum Zeno effect are visible. As a result of such anisotropic quantum dynamics the wave packet of the probability density takes the form of a thin filament wound around a magnetic field. The length of the filament is determined by the limiting value of the uncertainty of the longitudinal coordinate of the particle. In turn, this asymptotic uncertainty contains the information about its initial value, about the mass of the particle, and about the properties of the viscous medium.