Energy Dissipation and Decoherencein Solid-State Quantum Devices:Markovian versus non-Markovian Treatments

The design and optimization of new-generation solid-state quantum hardware absolutelyrequires reliable dissipation versus decoherence models. Depending on the device operationalcondition, the latter may range from Markov-type schemes (both phenomenological- and microscopiclike)to quantum-kinetic approaches. The primary goal of this paper is to review in a cohesive wayvirtues versus limitations of the most popular approaches, focussing on a few critical issues recentlypointed out (see, e.g., Phys. Rev. B 90, 125140 (2014); Eur. Phys. J. B 90, 250 (2017)) and linkingthem within a common framework. By means of properly designed simulated experiments ofa prototypical quantum-dot nanostructure (described via a two-level electronic system coupledto a phonon bath), we shall show that both conventional (i.e., non-Lindblad) Markov modelsand density-matrix-based non-Markov approaches (i.e., quantum-kinetic treatments) may lead tosignificant positivity violations. While for the former case the problem is easily avoidable by choosinggenuine Lindblad-type dissipation models, for the latter, a general strategy is still missing.