Nonlinear Wave Methods for Charge Transport

  • ID: 1199908
  • Book
  • 287 Pages
  • John Wiley and Sons Ltd
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The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering. The practice of implementing these techniques and their value are largely realized by showing their application to problems of nonlinear wave phenomena in electronic transport in solid state materials, especially bulk semiconductors and semiconductor superlattices. The authors are recognized leaders in this field, with more than 30 combined years of contributions.

From the contents:

  • Dynamical Systems, Bifurcations, and the Chapman–Enskog Method
  • Excitable Media I: Continuum Systems
  • Excitable Media II: Discrete Systems
  • Electronic Transport in Condensed Matter: From Quantum Kinetics to Drift–diffusion Models
  • Electric Field Domains in Bulk Semiconductors I: the Gunn Effect
  • Electric Field Domains in Bulk Semiconductors II: Trap–mediated Instabilities
  • Nonlinear Dynamics in Semiconductor Superlattices
  • Nonlinear Wave Methods for Related Systems in the Physical World
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1. Introduction

2. Ordinary Differential Equations and Asymptotic Methods

3. Excitable Media 1: Pulses, Fronts, Wave Trains in Continuous Media

4. Excitable Media 2: Discrete Systems

5. Electronic Transport in Condensed Matter: From Quantum Kinetics to Drift–Diffusion Models

6. Bulk Semiconductor Systems: The Gunn Effect

7. Bulk Semiconductor Systems: The Case of Field–Dependent Trapping

8. Semiconductor Superlattices

9. Application to other Systems and the Road ahead

Appendix A: Review of Basic Concepts of Solid State Physics

Appendix B: Detailed Arguments to go from Quantum Kinetic Equations to Boltzmann Transport

Appendix C: Details and Examples of Numerical Methods employed for Simulation

Appendix D: Glossary of Terms
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"This monograph may be a useful reference for graduate students or researchers from different fields: for condensed matter physicists, applied mathematicians,

engineers working in most fields as well as those interested in applications of nonlinear dynamics ideas to describe and analyse scientific problems." (Contemporary Physics, 8 November 2011)
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