Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract
Bandelow, Uwe
The presence of quantum wells in laser diodes introduces a new length scale, being in the order of the Fermi-wavelength of the carriers. This induces a mixed spectral density, where the carriers localizing within the quantum wells belong to the discrete spectrum and the free-roaming carriers belong to the continuous spectrum. Consequently, this divides the carriers into species which exhibit different properties. In particular, the latter species is viewed as a ”classical” species, carrying classical transport on a large scale (some $mu$m). By quantum well design the properties of the localized ”quantum” species can be tuned and optimized for applications. Due to their localized nature the above ”quantum” species cannot carry a current within a single-particle approach and therefore acts as a null-space for the transport. In consequence, their occupation remains fixed forever - which is contradicting to physics. Interaction as phonon-carrier and carrier-carrier scattering will change this simplified picture and causes kinetical processes for all the species. Among others, carriers can then migrate from one species to another. Above a certain time-scale such processes can be modeled in some approximation in terms of a dynamics which effectively counts the amount of carriers being captured by the quantum wells as well as the amount of carriers escaping from the quantum wells.