Overview

Semiconductors are usually thought of in connection with electronic devices which exhibit physics of the highest reproducibility. However, it was nonequilibrium semiconductor systems and their precision that led the authors of this textbook to the phenomena of chaos. In the first part of the book, they show that chaos is the rule, rather than the result, of exotic working conditions, and discuss in detail the representative example of low-temperature impact ionization breakdown in extrinsic semiconductor crystals, which display several interesting nonlinear phenomena. The final chapter presents the necessary mathematical background. Attention is focused on the interplay between spatial and temporal degrees of freedom, making use of advanced high-resolution experimental techniques and various numerical approaches based on a generalized thermodynamic formalism.

Full Product Details

Author:   Joachim Peinke ,  Jurgen Parisi ,  Otto E. Rossler ,  Ruedi Stoop
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.590kg
ISBN:  

9783540556473

ISBN 10:   3540556478
Pages:   299
Publication Date:   05 December 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Introductory Remarks.- Problems.- 2 Semiconductor Physics.- 2.1 Fundamentals of Nonlinear Dynamics.- 2.1.1 Historical Remarks.- 2.1.2 Plasma Ansatz.- 2.1.3 Negative Differential Conductivity.- 2.1.4 Transport Mechanisms.- 2.2 Recent Experimental Progress.- 2.3 Model Experimental System.- 2.3.1 Material Characterization.- 2.3.2 Experimental Set-up.- 2.4 Experimental Results.- 2.4.1 Static Current-Voltage Characteristics.- 2.4.2 Temporal Instabilities.- 2.4.3 Spatial Structures.- 2.4.4 Spatio-Temporal Behavior.- Problems.- 3 Nonlinear Dynamics.- 3.1 Basic Ideas and Definitions.- 3.2 Fixed Points.- 3.2.1 Fundamental Bifurcations.- 3.2.2 Catastrophe Theory.- 3.2.3 Experiments.- 3.3 Periodic Oscillations.- 3.3.1 The Periodic State.- 3.3.2 Bifurcations to Periodic States.- 3.3.3 Experiments.- 3.4 Quasiperiodic Oscillations.- 3.4.1 The Quasiperiodic State.- 3.4.2 Bifurcations to Quasiperiodic States.- 3.4.3 Influence of Nonlinearities.- 3.4.4 Experiments.- 3.5 Chaotic Oscillations and Hierarchy of Dynamical States.- 3.5.1 The Chaotic State.- 3.5.2 Characterization Methods.- 3.5.3 Bifurcations to Chaotic States.- 3.6 Spatio-Temporal Dynamics.- Problems.- 4 Mathematical Background.- 4.1 Basic Concepts in the Theory of Dynamical Systems.- 4.1.1 Dissipative Dynamical Systems and Attractors.- 4.1.2 Invariant Probability Measures.- 4.1.3 Invariant Manifolds.- 4.1.4 Chaos.- 4.2 Scaling Behavior of Attractors of Dissipative Dynamical Systems.- 4.2.1 Scale Invariance.- 4.2.2 Symbolic Dynamics.- 4.2.3 Analogy with Statistical Mechanics.- 4.2.4 Partition Function for Chaotic Attractors of Dissipative Dynamical Systems.- 4.2.5 Discussion of the Partition Function.- 4.3 Generalized Dimensions, Lyapunov Exponents, Entropies.- 4.3.1 Definition of the Scaling Functions for Sampling Processes.- 4.3.2 Relation Between the Scaling Functions and a Thermodynamical Formalism.- 4.3.3 Relation Between the Scaling of the Support and the Scaling of the Measure (Generic Case).- 4.3.4 Discussion of Nonanalyticities.- 4.3.5 Evidence of Phase-Transition-Like Behavior in Experimental Observations.- 4.4 Evaluation of Experimental Systems.- 4.4.1 Embedding of a Time Series.- 4.4.2 Lyapunov Exponents from the Dynamical Equations and from Time Series.- 4.4.3 Results and Stability of Results.- 4.4.4 Comparison with Other Methods.- 4.5 High-Dimensional Systems.- 4.5.1 Singular-Value Decomposition.- 4.5.2 The Modified Approach.- 4.5.3 Results on Simulated Data.- 4.6 Lyapunov Exponents, Rotation Numbers and the Degree of Mappings.- 4.6.1 Characterization of Solutions of Dynamical Systems via the Degree of Mapping.- 4.6.2 Riemannian Motions on Manifolds of Constant Negative Curvature.- 4.7 Conclusions.- Problems.- References.

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