Non-Markovian Effects in Open Quantum Systems

Over recent years, a growing interest in the properties of molecular junction, typically described by coupling of individual molecules (quantum dots) to macroscopic electrodes under nonequilibrium conditions, has raised fundamental and conceptual issues regarding the physics of nanometer scale systems, as well as those of the low dimensional mesoscopic systems in which they share certain qualities. Theory faces several important challenges: first, the existence of more than one steady-state in these type of systems has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. Second, characterization of the relevant time scales under the role of molecular vibrations, environmental disorder and dissipation is not yet fully understood. In order to address these issues, I will present an exact theory which enable us to study both dynamical and steady state properties. The theory, based on the Nakajima-Zwanzig equations, relies on the fact that out of equilibrium system posses a so called memory terms. Apparently, this memory term, also known in the literature as a non-Markovian effect, holds a significant amount of information regarding transient properties as well as those of the system's relaxation. This would facilitate our understanding of elastic and inelastic transport phenomena, where the nature of both coherent and incoherent transport is crucial for a complete picture.