Koopman analysis of quantum systems

Stefan Klus, Feliks Nüske*, Sebastian Peitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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

Original languageEnglish
Article number314002
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number31
Early online date18 Jul 2022
DOIs
Publication statusPublished - 5 Aug 2022

Keywords

  • Koopman operator
  • machine learning
  • quantum mechanics
  • Schrödinger equation
  • stochastic control
  • stochastic differential equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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