An Optimal Transport View On Schroedinger's Equation

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dc.creatorvon Renesse, Max-K.
dc.date2008-04-29
dc.date2009-03-12
dc.date.accessioned2026-07-07T12:51:07Z
dc.date.available2026-07-07T12:51:07Z
dc.descriptionWe show that the Schroedinger equation is a lift of Newton's law of motion on the space of probability measures, where derivatives are taken w.r.t. the Wasserstein Riemannian metric. Here the potential is the sum of the total classical potential energy of the extended system and its Fisher information. The precise relation is established via a well known ('Madelung') transform which is shown to be a symplectic submersion of the standard symplectic structure of complex valued functions into the canonical symplectic space over the Wasserstein space. All computations are conducted in the framework of Otto's formal Riemannian calculus for optimal transportation of probability measures
dc.identifierhttps://arxiv.org/abs/0804.4621
dc.identifierhttp://arxiv.org/abs/0804.4621
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222894
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject90C28, 49Q99
dc.titleAn Optimal Transport View On Schroedinger's Equation
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