Stationary Scattering Theory for a Charged Particles Transport Problem |
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Authors: | Busoni G Emamirad H |
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Institution: | (1) Dipartimento di Matematica U. Dini, Università di Firenze, I-50134 Florence, Italy;(2) Laboratoire de Modélisation Mécanique et de Mathématiques Appliquées, Université de Poitiers, F 86950 Futuroscope, Cedex, France |
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Abstract: | We consider a nonautonomous transport problem, the modelization of the charge exchange dynamics in a monoatomic ionized gas, and apply scattering theory to its dynamics. The free dynamics corresponds to the evolution of the total distribution of particles (neutral plus ionized particles) and the perturbed dynamics corresponds to the evolution of the neutral particles, which is the solution of a nonautonomous transport problem. The existence of the time-dependent wave operators was proved by the first author. In the present paper we follow Howland's formalism in constructing a stationary scattering theory for this nonautonomous transport problem by studying the evolution equation. We prove the existence of the wave operators and by using the smooth perturbation technique we obtain the similarity between perturbed and unperturbed operators. |
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Keywords: | charged particle transport problem stationary scattering theory wave operators scattering operator smooth perturbation |
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