No abstract

PrefaceThe operational principle of modern semiconductor nanostructures, such as quantum wells, quantum wires, or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nanostructures is threefold: First, they are needed for a deeper understanding of experimental data and of the operational principle. Second, is to predict and optimize in advance qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nanostructures are embedded as an active region in semiconductor devices. Finally, the results of quantum mechanical simulations of semiconductor nanostructures can be used by upscaling methods to deliver parameters needed in semi-classical models for semiconductor devices such as quantum well lasers. This book covers in detail all these three aspects using a variety of illustrating examples.Multi-band effective mass approximations have been increasingly attracting interest over the last decades, since it is an essential tool for effective models in semiconductor materials. This book is concerned with several mathematical models from the most relevant class of k p-Schrödinger Systems. We will present both mathematical models and state-of-the-art numerical methods to solve adequately the arising systems of differential equations. The designated audience is graduate and Ph.D. students of mathematical physics, theoretical physics and people working in quantum mechanical research or semiconductor/opto-electronic industry who are interested in new mathematical aspects.The principal audience of this book is graduate and Ph.D. students of (mathematical) physics, research lecturer of mathematical physics, and research people working in semiconductor, opto-electronic industry for a professional reference.

The velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D. C. electric field is studied. A simplified one-dimensional Boltzmann model of the Kač type is adopted. Necessary conditions and sufficient conditions are established for the existence, uniqueness, and attractivity of a stationary non-negative distribution corresponding to a specified concentration level. Conditions for the onset of the runaway process are established.

No abstract

We consider a class of abstract evolution problems characterized by the sum of two unbounded linear operators $A$ and $B$, where $A$ is assumed to generate a positive semigroup of contractions on an $L^1$-space and $B$ is positive. We study the relations between the semigroup generator $G$ and the operator $A + B$. $A$ characterization theorem for $G =A+B$ is stated. The results are based on the spectral analysis of $B(\lambda-A)^{-1}$. The main point is to study the conditions under which the value 1 belongs to the resolvent set, the continuous spectrum, or the residual spectrum of \ud $B(\lambda - A)^{-1}$

·Giovanni FrosaliAbstract We derive semiclassical diffusive equations for the densities of electrons in the two energy bands of a semiconductor, as described by a k·p Hamiltonian. The derivation starts from a quantum kinetic (Wigner) description and resorts to the Chapman-Enskog method as well as to the quantum version of the minimum entropy principle. Four different regimes are investigated, according to different scalings of the k·p band-coupling and band-gap parameters with respect to the scaled Planck constant.

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu in Ref.[2], we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner-Fokker-Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of gaussian solutions. It is shown that the addition of a Caldeira-Legget friction term provides the asymptotic behaviour that one expects on the basis of physical considerations.

No abstract