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Random-matrix theory for the Lindblad master equation
Open quantum systems with Markovian dynamics can be described by the Lindblad equation. The quantity governing the dynamics is the Lindblad superoperator. We apply random-matrix theory to this superoperator to elucidate its spectral properties. The distribution of eigenvalues and the correlations of neighboring eigenvalues are obtained for the cases of purely unitary dynamics, pure dissipation, and the physically realistic combination of unitary and dissipative dynamics. © 2021 Author(s).
Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.