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Control of Partial Differential Equations
About this book
Physics of Optoelectronics focuses on the properties of optical fields and their interaction with matter. Understanding that lasers, LEDs, and photodetectors clearly exemplify this interaction, the author begins with an introduction to lasers, LEDs, and the rate equations, then describes the emission and detection processes.The book summarizes and reviews the mathematical background of the quantum theory embodied in the Hilbert space. These concepts highlight the abstract form of the linear algebra for vectors and operators, supplying the "pictures" that make the subject more intuitive. A chapter on dynamics includes a brief review of the formalism for discrete sets of particles and continuous media. It also covers the quantum theory necessary for the study of optical fields, transitions, and semiconductor gain. This volume supplements the description of lasers and LEDs by examining the fundamental nature of the light that these devices produce. It includes an analysis of quantized electromagnetic fields and illustrates inherent quantum noise in terms of Poisson and sub-Poisson statistics. It explains matter-light interaction in terms of time-dependent perturbation theory and Fermi's golden rule, and concludes with a detailed discussion of semiconductor emitters and detectors.
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Information
Table of contents
- Cover Page
- Halftitle Page
- PURE AND APPLIED MATHEMATICS
- Title Page
- Copyright Page
- Preface
- Contents
- Contributors
- control of partial differential equations
- Null Controllability for a Class of Implicit Differential Equations in Banach Spaces
- Results on Stochastic Navier-Stokes Equations
- A Hyperbolic Problem with Boundary Control: A Solution through Parabolic Regularization
- Flat Cone Condition and Shape Analysis
- Dynamic Programming for an Abstract Second Order Evolution Equation with Convex State Constraints
- Boundary Stabilization of a Nonlinear String with Aerodynamic Force
- Existence of Optimal Controls for Stochastic Evolution Systems
- An Approximation Scheme for the Variational Solutions of the Hamilton-Jacobi Equation of Control Theory
- Global Existence and Uniqueness of Regular Solutions to the Dynamic von Kármán System with Nonlinear Boundary Dissipation
- A State-Space Approach to the Mixed-Sensitivity Minimization Problem for Delay Systems
- The Role of Smoothing in Boundary Control
- Exact Controllability of the Wave Equation in a Polygonal Domain with Cracks
- From Singular to Regular Control Problems
- Feedback Laws via a Trotter Product Formula Treatment of the Dynamic Programming Equation
- Existence of Optimal Controls for Some Nonlinear Systems
- Control Problems for Shape Memory Alloys with Constraints on the Shear Strain
- Linear Quadratic Boundary Control for an Age Equation Perturbed by Noise
- Optimal Quadratic Boundary Control Problem for Wave- and Plate-like Equations with High Internal Damping: An Abstract Approach
- Approximation for the Wave Equation in a Moving Domain