Non-Markovian Stochastic Schr?dinger Equations And Its Applications For Open Quantum Systems

With the burst of newly-fabricated materials and rapid developments of experimental tech-niques,it has been gradually realized by numerous studies that non-Markovian and quan-tum effects indeed play a constructive role in optimizing various photovoltaic and thermo-electric devices.In order to accurately characterize these effects on the dynamical process-es of those various complex systems,we have proposed a new non-Markovian stochastic Schrodinger equation for large-scale open quantum systems in this thesis.In contrast to equations of motion for density matrix,the new method propagates the stochastic wave-function in Hilbert space,and is convenient for considering dynamical and static disorders simultaneously.Thus,it is extremely suitable for simulating quantum dynamics,various linear spectra,as well as a variety of equilibrium transport properties in many complex systems,like photosynthetic systems and organic aggregates.The contents of this thesis are organized as follows:Based on the reduced system density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments,the influence functional therein is divided into the product of two parts:the first part is temperature-dependent and is stochastically unraveled by introducing two correlated Gaussian stochastic process-es,while the rest part is handled with by introducing auxiliary stochastic wavefunctions.In the end,we have established a hierarchical structure of forward-backward stochastic Schrodinger equations.The power of this method is verified by calculating time-dependent population dynamics in the valuable spin-boson model and the realistic Fenna-Matthews-Olson(FMO)complex.Then the method is extended for open quantum dynamics under polarized initial bath conditions.It is confirmed that system dynamics is extremely sen-sitive to the initial bath condition when exposed to an unltraslow bath.The localization tendency is stronger in the polarized initial bath conditions than the unpolarized ones.Be-sides,it is found that the strong non-Markovianity in this case renders oscillatory coherent dynamics persistent even when the system-bath coupling is very strong.The hierarchical stochastic Schrodinger equation is numerically exact,but its numerical efficiency is greatly limited by the specific form of spectral density function and the fac-torial scaling between the number of auxiliary wavefunctions and the system degree of freedom.Making use of the fact that the product of multiple time-dependent operators is automatically time-ordered in the path integral formalism,we have reconstructed the stochastic wave functions in the interaction picture,and finally established a new and dif-ferent non-Markovian stochastic Schrodinger equation(NMSSE)that allows for the sys-tematic perturbation expansion with respect to the system-bath coupling to arbitrary order.Benchmarked by numerically exact results,we have conducted a comparative study of the proposed method in its lowest order approximation with perturbative quantum master e-quations,and found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases.Besides,the method is ap-plicable on an equal footing for any kind of spectral density function.Therefore,it is expected to be a powerful tool to explore the multi-timescale energy relaxation process-es of hot excitons in organic aggregates.The results demonstrate that the fast relaxation time essentially corresponds to the dephasing time of excitonic coherence motion whereas the slow time is related to a hopping migration,which fairly explained an experimental observation of hot exciton energy relaxation in a low energy-gap PBDTTPD polymer.Following the same spirit,a theoretically solid and numerically exact method is also pre-sented in this thesis for the calculation of absorption spectra,linear dichroism spectra,and circular dichroism spectra of molecular aggregates immersed in a harmonic bath consti-tuted as the combination of some prominent quantized vibrational modes and continuous overdamped Brownian oscillators.To go beyond the independent local bath approxima-tion,all the correlations of site energy fluctuations and excitonic coupling fluctuations are included in our strategy.Nevertheless,it is not directly applicable in calculating the e-mission spectra and other equilibrium correlation functions since the system and bath are initially correlated in those cases.Such that,we have extended the traditional stochas-tic hierarchy equations of motion method into the correlated real-time and imaginary-time propagations.The feasibility and validity of the proposed method are justified in the emis-sion spectra of homodimer compared to those obtained through the deterministic hierarchy equations of motion.Besides,it is interesting to find that the complex noises generated from a small portion of real-time and imaginary-time cross terms can be safely dropped to produce the stable and accurate position and flux correlation functions in a broad parameter regime.At last,we summarize the strengths and weaknesses of the method proposed in this paper,and then sketch out its further developments and applications in the future.