Koopman analysis of quantum systems*

Abstract Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, control. There is an intricate connection between dynamical systems driven by stochastic differential equations quantum mechanics. In this paper, we compare the ground-state transformation Nelson’s mechanics demonstrate how data-driven methods developed for approximation of can be used analyze physics problems. Moreover, exploit relationship Schrödinger operators control show that modern solve stationary imaginary-time equation. Our findings open up a new avenue toward solving Schrödinger’s equation using recently tools data science.