Microscopic theory of energy dissipation and decoherence in solid-state systems: A reformulation of the conventional Markov limit

In this article we provide a detailed comparison of two possible approaches to the study of the long time behavior of an electronic system, namely, the conventional BornMarkov approach and an alternative (symmetrized) Markov procedure recently proposed by our group. To this end, as prototypical device, we consider a quantum dot electronic transition weakly coupled to the lattice vibrations. Our results show highly unphysical behaviors of the conventional approach in the long time limit, under small perturbation of the equilibrium electronic distribution. The alternative procedure, on the contrary, provides the expected energy relaxation within a T1T2 paradigm. Our findings are sharper than the somewhat more naive, and only transient, possible lack of positivity of the conventional Markov approach, already known in the literature. While only mentioning the important advantages of our symmetrized version with respect to already known secular approximation, and postponing further analysis to future works, we hereby stress how the commonly employed conventional strategy may seriously fail to model realistic nanostructures, whereas the new approach gives the expected physical behavior.