Títol:
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Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
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Autor/a:
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Guerrero, Pilar; López, J. L.; Montejo-Gámez, J.; Nieto, J.; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker-Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial-boundary value problem. This simplification requires the performance of the polar (modulus-argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions. |
Matèries:
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-Equacions no lineals -Quàntums, Teoria dels -Logaritmes |
Drets:
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open access
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:
https://creativecommons.org/licenses/by-nc-nd/3.0/ |
Tipus de document:
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Article Prepublicació |
Publicat per:
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Centre de Recerca Matemàtica
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Compartir:
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Uri:
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https://ddd.uab.cat/record/181520
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