Electron–phonon dissipation in quantum nanodevices - Limitations of quantum-kinetic treatments

Microscopic modelling of electronic-phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, a variety of simulation strategies have been proposed and employed. The aim of this article is to discuss virtues versus intrinsic limitations of non-Markovian density-matrix approaches. More specifically, we shall show that the usual mean-field treatment employed to derive quantum-kinetic equations may lead to highly unphysical results, like negative distribution functions and non-dissipative carrier–optical phonon couplings. By means of a simple two-level model, we shall show that such limitations are expected to be particularly severe in zero-dimensional electronic systems—like quantum-dot nanostructures, potential constituents of quantum-computation devices—coupled to dispersionless phonon modes. Such a behaviour is in striking contrast with the case of Markovian treatments, where a proper combination of adiabatic limit and mean-field approximation guarantees a physically acceptable solution.