Generalized macroscopic Schrodinger equation in scale relativity

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dc.creatorCelerier, Marie-Noelle
dc.creatorNottale, Laurent
dc.date2005-05-02
dc.date.accessioned2026-07-07T03:29:41Z
dc.date.available2026-07-07T03:29:41Z
dc.descriptionThe scale transformation laws produce, on the motion equations of gravitating bodies and under some peculiar assumptions, effects which are anologous to those of a "macroscopic quantum mechanics". When we consider time and space scales such that the description of the trajectories of these bodies (planetesimals in the case of planetary system formation, interstellar gas and dust in the case of star formation, etc...) is in the shape of non-differentiable curves, we obtain fractal curves of fractal dimension 2. Continuity and non-differentiability yield a fractal space and a symmetry breaking of the differential time element which gives a doubling of the velocity fields. The application of a geodesics principle leads to motion equations of Schrodinger-type. When we add an outside gravitational field, we obtain a Schrodinger-Poisson system. We give here the derivation of the Schrodinger equation for chaotic systems, i.e., with time scales much longer than their Lyapounov chaos-time.
dc.description4 pages, oral communication in the framework of the 4eme Semaine de l'Astrophysique Francaise, Paris, 2004
dc.identifierhttps://arxiv.org/abs/gr-qc/0505012
dc.identifierhttp://arxiv.org/abs/gr-qc/0505012
dc.identifierCelerier M. N. and Nottale, L., in "Scientific Highlights 2004", Proceedings of the 4eme Semaine de l'Astrophysique Francaise held in Paris, France, June 14-18, 2004, eds Combes, F., Barret, D., Contini, T., Meynadier, F. and Pagani, L., EDP Sciences, Les Ullis, 2004, p. 649
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/35276
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleGeneralized macroscopic Schrodinger equation in scale relativity
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