scholarly journals A discrete Schrödinger equation via optimal transport on graphs

2019 ◽  
Vol 276 (8) ◽  
pp. 2440-2469 ◽  
Author(s):  
Shui-Nee Chow ◽  
Wuchen Li ◽  
Haomin Zhou
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Optimal Transport ◽  
Discrete Schrödinger Equation

Schrödinger dynamics and optimal transport of measures

2021 ◽  
pp. 2150016
Author(s):  
Lorenzo Zanelli
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Time Dependent ◽  
Probability Measures ◽  
Flat Torus ◽  
Optimal Transport Theory

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.

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