Hasan Abdur Rahman

• The research work presented in this thesis concerns the improvement of several theoretical techniques for describing quantum systems coupled to fermionic or bosonic reservoirs. The validity of the aforementioned developments is then numerically investigated to obtain the time-dependent quantum transport of charges or excitons through molecular junctions or aggregates, respectively. The former are single or a short chain of conducting, conjugated molecules wedged between two inert electrodes, acting as active circuit elements, while the latter can be comprehended as light absorbing pigments containing conjugated chains residing within fluctuating protein environments. The model used to describe the quantum transport is a linear chain or aggregates of tight-binding sites coupled to external fermionic or bosonic baths. The three main formalisms that are presented in this work include quantum master equations (QME), in second order perturbation theory in the system-reservoir coupling, the hierarchical equations of motion (HEOM) scheme for multi-particle bosonic systems as well as a scheme based on time-dependent nonequilibrium Green's functions (NEGF) for non-interacting fermionic systems. The NEGF scheme for time-dependent quantum transport of charge provides the time-dependent current through the systems of sites as well as the on-site population dynamics, while the QME and HEOM schemes for energy transfer dynamics deliver information only about the population or occupation number dynamics for systems coupled to bosonic baths.