Guangqi Li

• The goal of this thesis is to investigate the electron transport through molecular junctions or wires which have recently attracted much attention experimentally as well as theoretically. Under the influence of a bias voltage and the coupling to the leads which act as electron source and drain, a current through the molecular junction is established. When an external time-dependent field, such as a laser field or an additional AC voltage is applied to the molecular junction, new features can be observed. One phenomenon is the well-known photon-assisted tunneling (PAT) which means that an external field periodic in time with frequency $omega$ can induce inelastic tunneling events when the electrons exchange energy quanta $hbar omega$ with the external field. Another important effect is the famous phenomenon of coherent destruction of tunneling (CDT) which exhibits the unusual effect of quenching the tunneling dynamics at specific values of the field amplitude. In the present thesis the theoretical foundation for these investigations is a density matrix formalism where the full system is partitioned into a relevant part, i.e. the molecular junctions and fermionic reservoirs mimicking the leads. By using a perturbative approach in the system-reservoir coupling strength, it is possible to establish a quantum master equation (QMEs) for the population dynamics of the wire states and an equation for the current through the wire. By combining the theory of optimal control and assuming a predefined target current, a laser field can be obtained which does generate a predefined current pattern. The same technique can be applied to minimize the shot noise. Besides of using QMEs to study electron transport through molecular junctions with the affection of a coupling to leads, it is also possible to apply QMEs to investigate the electron transfer through DNA which is coupled to a phonon-bath.