Nonlinear Wave Methods for Charge Transport

Mathematische Verfahren zur Behandlung nichtlinearer Wellen und singuläre Störungsmethoden erläutert dieser Band auf einem Niveau, das für Interessenten aus allen naturwissenschaftlich-technischen Bereichen geeignet ist.

Auteur
Luis L. Bonilla received his Ph.D. in physics from the Universidad Nacional de Educacion a Distancia (UNED), Madrid, in 1981. After conducting postdoctoral research for three years at the Mathematics Department at Stanford University, he took positions as associate professor at the Universities of Sevilla and Barcelona, both Spain. In 1992, he accepted his current post of Professor of Applied Mathematics at the University Carlos III in Madrid. Professor Bonilla's research interests lie in the modeling and asymptotic analysis of nonlinear problems in condensed matter physics, including electronic and mechanical properties. He is the author and co-author of more than 180 research papers and book chapters.

Stephen W. Teitsworth received his Ph.D. in Physics in 1986 from Harvard University, where he also carried out postdoctoral research. For the past several years, he has been a faculty member of the Physics department at Duke University. His current research interests center on experimental and theoretical studies of nonlinear electronic transport and optoelectronic properties of semiconductor-based materials, with a focus on spatially periodic systems such as superlattices.

Résumé
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.

Contenu

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