Title: The multiple Davydov D2 Ansatz and its applications
Abstract: In order to accurately characterize dynamics of the Holstein polaron with simultaneous diagonal and off-diagonal exciton-phonon coupling, a series of multiple Davydov trial states, i.e., the multiple Davydov D 1 , D 1.5 , D 2 , and D ansätze, are formulated as superpositions of the correspondingly single Davydov D 1 , D 1.5 , D 2 , and D ansätze.In this thesis, the multiple Davydov D 2 ansatz, also known as the multi-D 2 ansatz, is demonstrated to enable numerically exact dynamics for various open quantum systems with off-diagonal coupling and is applied to study complicated dynamical quantum behaviours, such as the exciton transport in conducting polymers, Bloch oscillations dynamics in semiconductor superlattices and organic materials, singlet fission processes, and the Landau-Zener transitions in circuit quantum electrodynamics devices.We first use the Dirac-Frenkel time-dependent variational principle combined with the multi-D 2 ansatz to fully quantum mechanically investigate dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling, which is treated traditionally by the Ehrenfest approximation for the description of the exciton transport in the conducting polymers.It is shown that the Ehrenfest method is equivalent to our variational method with the single D 2 ansatz, and with the multi-D 2 ansatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics.The multi-D 2 ansatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation.The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of thetransfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions.We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations.Finally, the variational method with importance sampling is employed to investigate temperature effects on the exciton transport using the multi-D 2 ansatz, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.i