In this chapter, we overview recent developments of a simulation framework capable of capturing the highly nonequilibrium physics of the strongly coupled electron and phonon systems in quantum cascade lasers (QCLs). In midinfrared (mid-IR) devices, both electronic and optical phonon systems are largely semiclassical and described by coupled Boltzmann transport equations, which we solve using an efficient stochastic technique known as ensemble Monte Carlo. The optical phonon system is strongly coupled to acoustic phonons, the dominant carriers of heat, whose dynamics and thermal transport throughout the whole device are described via a global heat-diffusion solver. We discuss the roles of nonequilibrium optical phonons in QCLs at the level of a single stage , anisotropic thermal transport of acoustic phonons in QCLs, outline the algorithm for multiscale electrothermal simulation, and present data for a mid-IR QCL based on this framework.

This chapter is an overview, placing the body of work described in this book in perspective and describing its overarching structure, namely, how the three levels of structure are related: quantum field theory in curved spacetime established in the 1970s, semiclassical gravity developed in the 80s and stochastic gravity introduced in the 90s, a manifestation of the almost ubiquitous existence of a semiclassical and a stochastic regime in relation to quantum and classical in the description of physical systems. We describe the main physical issues in semiclassical and stochastic gravity, namely, backreaction and fluctuations, the mathematical tools used, and their applications to physical problems in early universe cosmology and black hole physics. In terms of connection to related disciplines, it is pointed out that the popular Newton–Schrödinger equation cherished in alternative quantum theories does not belong to semiclassical gravity, as it is not derivable from quantum field theory and general relativity. However, stochastic gravity is needed for quantum information issues involving gravity. These theories enter even in the low-energy, weak-gravity realm where laboratory experiments are carried out. We finish with a summary of the contents of each chapter and a guide to readers.