Abstract
We propose a functional framework for some nonlinear dynamics, where the nonlinearities are (very) short-range perturbation of a given Hamiltonian. In this framework one can prove the global in time existence and uniqueness of a solution for the time dependent problem and the existence of steady states of the form which can be specified. This problem arises from the modeling of semiconductors and covers different applications.
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Nier, F. (1999). The dynamics of some quantum open systems with short-range nonlinearities. In: Leach, P.G.L., Bouquet, S.E., Rouet, JL., Fijalkow, E. (eds) Dynamical Systems, Plasmas and Gravitation. Lecture Notes in Physics, vol 518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105920
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DOI: https://doi.org/10.1007/BFb0105920
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