Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics
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Aleksander Stanislavsky
Abstract
Motion of charges, their accumulation, and discharge arise in many physical, chemical, and biological processes in nature. The simplest theoretical description of the relaxation phenomenon as a function of time is the exponential law. However, the relaxation properties of various physical systems (dielectrics, amorphous semiconductors and insulators, ferroelectrics, polymers, and others) strongly deviate from the classical exponential decay. They relax in a nonexponential fashion and have attracted an immediate interest of scientists and technologists for a long time. A theoretical description of the nonexponential relaxation is one of the most important problems of modern physics. In this chapter, we show the role played by the fractional calculus tools in a realistic physical treatment of dielectric relaxation.
Abstract
Motion of charges, their accumulation, and discharge arise in many physical, chemical, and biological processes in nature. The simplest theoretical description of the relaxation phenomenon as a function of time is the exponential law. However, the relaxation properties of various physical systems (dielectrics, amorphous semiconductors and insulators, ferroelectrics, polymers, and others) strongly deviate from the classical exponential decay. They relax in a nonexponential fashion and have attracted an immediate interest of scientists and technologists for a long time. A theoretical description of the nonexponential relaxation is one of the most important problems of modern physics. In this chapter, we show the role played by the fractional calculus tools in a realistic physical treatment of dielectric relaxation.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
