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We derive higher-order macroscopic transport models for semiconductor device simulation from Boltzmann's transport equation using the method of moments. To obtain a tractable equation set suitable for numerical implementation the validity of the diffusion limit will be assumed which removes the convective terms from the equation system. The infinite hierarchy of equations is then truncated at the orders two ͑drift-diffusion model͒, four ͑energy-transport model͒, and six. Nonparabolicity correction factors are included in the streaming terms. Closure relations for the highest-order moments are obtained from a cold Maxwell distribution ͑drift-diffusion͒ and a heated Maxwell distribution ͑energy-transport͒. For the six moments model this issue is more complicated. In particular, this closure relation is identified to be crucial both in terms of accuracy and in terms of numerical stability. Various possible closure relations are discussed and compared. In addition to the closure of the highest-order moment, various transport parameters such as mobilities and relaxation times appear in the models and need to be accurately modeled. Particularly for higher-order transport models this is a complicated issue and since the analytical models used in our previous attempts did not deliver satisfactory results we extract all these parameters using homogeneous Monte Carlo simulations. Since all macroscopic transport models are based on rather stringent assumptions a practical evaluation is mandatory. Therefore, the proposed six moments model, a corresponding energy-transport model, and the drift-diffusion model are carefully compared to self-consistent Monte Carlo simulations.

Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

Two popular approaches to formalize adequate reasoning with vague propositions are usually deemed incompatible: On the one hand, there is supervaluation with respect to precisification spaces, which consist in collections of classical interpretations that represent admissible ways of making vague atomic statements precise. On the other hand, t-norm based fuzzy logics model truth functional reasoning, where reals in the unit interval [0, 1] are interpreted as degrees of truth. We show that both types of reasoning can be combined within a single logic SŁ, that extends both: Łukasiewicz logic Ł and (classical) S5, where the modality corresponds to '. . . is true in all complete precisifications'. Our main result consists in a game theoretic interpretation of SŁ, building on ideas already introduced by Robin Giles in the 1970s to obtain a characterization of Ł in terms of a Lorenzen style dialogue game combined with bets on the results of binary experiments that may show dispersion. In our case the experiments are replaced by random evaluations with respect to a given probability distribution over permissible precisifications. upwards and downwards Löwenheim-Skolem, and recursive axiomatizability fail for 'natural' supervaluation based consequence relations.

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