Schrödinger dynamics and optimal transport of measures on the torus

2018/04/10 by L. Zanelli, Zanelli, L.
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1804.06302

arxiv created 2018/04/10 · arxiv updated 2018/04/18

Abstract

The aim of this paper is to recover displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by semiclassical measures associated with solutions of Schrödinger equations defined on the flat torus. Under an additional assumption, we show the completing viewpoint by proving that a family of displacement interpolations can always be viewed as these time dependent semiclassical measures.

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