Dynamics of Davydov Ansatze

Abstract: Following the Dirac-Frenkel time-dependent variational principle, dynamics of a one-dimensional Holstein polaron is probed by employing the Davydov D2 Ansatz with two sets of variational parameters, one for each constituting particle in the exciton-phonon system, and a simplified variant of the Davydov D1 Ansatz, also known as the $\tilde{D}$ Ansatz, with an additional set of phonon displacement parameters. A close examination of variational outputs from the two trial states reveals fine details of the polaron structure and intricacies of dynamic exciton-phonon interactions. Superradiance coherence sizes, speeds of exciton-induced phonon wave packets, linear optical absorption, and polaron energy compositions are also included in the study.