WAVE OPERATORS IN CHARGE
DYNAMICS
In nonautonomous transport problems, like those concerning the modelization of charge exchange dynamics in a monoatomic ionized gas, scattering theory may be applied. Usually one considers as free dynamics that of the total distribution of particles and as perturbed dynamics that of one type of particles ( for instance, in the case of charge exchange the distribution of neutral particles). The evolution equation for this distribution results to be nonautonomous.
The problem of the existence of time dependent wave operators was dealt in reference Howland`s formalism in constructing a time independent (otherwise called stationary) scattering theory for nonautonomous problem is suitably applied in reference 2 obtaining the proof of existence of wave operators and relations of similarity between perturbed and unperturbed wave operators. Two models for the evolution of the distributions in a plasma having low densities are presented in reference 3. Techniques similar to those of the scattering theory in quantum mechanics are used to study asymptotics of the models.
G. Busoni, Asymptotic behaviour and wave operators charge exhange, J. Math. Anal. Appl., 212, 190-208 (1997)
G. Busoni, H. Emamirad, Stationary scattering theory for a charged particles transport problem, J. Stat.Phys. 96(1-2), 377-401 (1999)
G.Busoni, S.Matucci, Asymptotic behaviour and wave operators in charge exchange, Atti XIV Congresso Nazionale Aimeta, Como (1999) - Ed. Elettronica - 9 pag.
Last Updated: 27 settembre 2000, by Giovanni Frosali