Koopmon trajectories in nonadiabatic quantum-classical dynamics

TL;DR

This paper introduces a Koopman wavefunction-based mixed quantum-classical method for nonadiabatic dynamics that improves accuracy and computational efficiency over traditional approaches, successfully handling complex quantum regimes.

Contribution

It develops a novel Koopman wavefunction approach blending classical mechanics with symplectic geometry, enabling accurate, efficient simulations of nonadiabatic quantum dynamics.

Findings

Reproduces fully quantum results in Tully's problems with higher accuracy than Ehrenfest methods.

Achieves computational advantages over fully quantum approaches.

Successfully handles ultrastrong and deep strong coupling regimes.

Abstract

In order to alleviate the computational costs of fully quantum nonadiabatic dynamics, we present a mixed quantum-classical (MQC) particle method based on the theory of Koopman wavefunctions. Although conventional MQC models often suffer from consistency issues such as the violation of Heisenberg's principle, we overcame these difficulties by blending Koopman's classical mechanics on Hilbert spaces with methods in symplectic geometry. The resulting continuum model enjoys both a variational and a Hamiltonian structure, while its nonlinear character calls for suitable closures. Benefiting from the underlying action principle, here we apply a regularization technique previously developed within our team. This step allows for a singular solution ansatz which introduces the trajectories of computational particles - the koopmons - sampling the Lagrangian classical paths in phase space. In the case of Tully's nonadiabatic problems, the method reproduces the results of fully quantum simulations with levels of accuracy that are not achieved by standard MQC Ehrenfest simulations. In addition, the koopmon method is computationally advantageous over similar fully quantum approaches, which are also considered in our study. As a further step, we probe the limits of the method by considering the Rabi problem in both the ultrastrong and the deep strong coupling regimes, where MQC treatments appear hardly applicable. In this case, the method succeeds in reproducing parts of the fully quantum results.