Schrödinger equation on graphs via optimal transport

Schrödinger equation on graphs via optimal transport

In 1966, Nelson derived Schrödinger equation by diffusion process. Nowadays this approach connects with the theory of optimal transport. We consider similar matters on finite graphs. We propose a discrete Schrödinger equation from Nelson’s idea and optimal transport. The proposed equation enjoys several dynamical features. Many numerical examples are also presented.


Wuchen Li

May 09, 2017