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Center for Nonlinear Studies |
We present a mixed quantum-classical (MQC) particle method based on the theory of Koopman wavefunctions in classical mechanics. 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 Hamiltonian dynamics. 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 that allows to introduce 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 fully quantum hydrodynamic 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. Depending on time, higher-dimensional extensions will be also discussed.
Host: Sergei Tretiak (T-1) and Alexander White (T-1)