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Schrödinger dynamics and optimal transport of measures

Lorenzo Zanelli

Department of Mathematics “Tullio Levi-Civita”, University of Padova, Via Trieste, 63, 35121 Padova, Italy

E-mail Address: lorenzo.zanelli@unipd.it

https://doi.org/10.1142/S0219025721500168Cited by:0 (Source: Crossref)

Abstract

In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrödinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.

Communicated by K. B. Sinha

Keywords:

AMSC: 81Q20, 49Q20, 58J40

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