Optimized Hierarchical Equations Of Motion Theory With Its Applications To Reaction Mechanism Study And Nonlinear Optical Spectroscopies

The thesis aims at the developments and applications of quantum dissipation the-ory. The main content focuses on the optimized construction of hierarchical equations of motion (HEOM) that subjects to the Brownian oscillators bath environment (widely used in reality), together with its applications to the reaction mechanism study and non-linear optical spectroscopies. Both the pump-probe transient absorption spectrum and the coherent two-dimensional spectrum are considered in the simulations of nonlinear optical spectroscopies. In order to evaluate the nonlinear optical response function more efficiently, we propose a mixed Heisenberg-Schrodinger scheme with block-matrix im-plementation. The contents of the thesis are as follows.Chapter1is the introduction of this thesis. In Chapter2, we give a comprehensive account of the HEOM approach to the characterization of stationary and dynamic prop-erties of open quantum systems. This approach is rooted at the Feynman-Vernon in-fluence functional path integral formalism, but much more implementable numerically and operationally for the study of various complex molecular dynamics problems. By construction, HEOM resolves nonperturbatively the combined effects of many-particle interaction, system-bath coupling, and non-Markovian memory.In Chapter3, we present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the opti-mal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some se-lected Pade spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also ana-lytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. The resulting hierarchical dynamics under the apriori convergence criterion are exemplified with a benchmark spin-boson system. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocaliza-tion. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the corre-lated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.In Chapter4, to advance HEOM as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-Schrodinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. The apriori convergence criterion on HEOM dynamics is again exemplified with the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system.In Chapter5, we conclude the thesis, and discuss some future work.