Evolution in a Quantum Wire

Abstract

Typical physical scales characterizing quantum electron decoherence are embodied in the femtosecond evolution of optically generated carriers interacting with phonons. A variety of quantum effects can be observed on these scales, such as non- Markovian evolution, giving rise to the Retardation effect, Collision Broadening which is a result of the lack of energy conservation in the early times of the evolution, as well as the Intra-Collisional Field Effect which is the effect of the field on the process of interaction Such effects are accounted by models which are beyond the Boltzmann equation, such as the Levinson and the Barker-Ferry equations, originally devised for homogeneous transport conditions.

Here we first generalize the homogeneous Levinson and Barker-Ferry equations for the case of a quantum wire. The derivation follows the first principles of quantum mechanics, allowing for a detailed analysis of the assumptions and approximations. This gives rise to a heuristic picture providing a deep understanding of the above quantum effects, discussed at the end of the chapter. References to simulation results and the corresponding algorithms based on a backward evolution in time are provided.