Renat T Sibatov's Books

Fractional Kinetics In Solids: Anomalous Charge Transport In Semiconductors, Dielectrics And Nanosystems

By: Vladimir V Uchaikin,Renat T Sibatov

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Fractional Kinetics In Solids: Anomalous Charge Transport In Semiconductors, Dielectrics And Nanosystems

By: Vladimir V Uchaikin,Renat T Sibatov

The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory.In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher-Montroll and Arkhipov-Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations.It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.

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274

Publisher

World Scientific

Published Date

ISBN 10

9814449601

ISBN 13

9789814449601

Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

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Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

This book is first of its kind describing a new direction in modeling processes taking place in interplanetary and interstellar space (magnetic fields, plasma, cosmic rays, etc.). This method is based on a special mathematical analysis — fractional calculus. The reader will find in this book clear physical explanation of the fractional approach and will become familiar with basic rules in this calculus and main results obtained in frame of this approach. In spite of its profound subject, the book is not overloaded by mathematical details. It contains many illustrations, rich citation and remains accessible to a wide circle of physicists.This book is addressed to graduate and postgraduate students, young and mature researchers specializing in applications of fractional calculus, astrophysics, solar-terrestrial science and physics of cosmic rays.

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Page Count

300

Publisher

World Scientific

Published Date

ISBN 10

9813225440

ISBN 13

9789813225442

Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

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Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory. In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher Montroll and Arkhipov Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations. It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.

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274

Publisher

World Scientific

Published Date

ISBN 10

9814355429

ISBN 13

9789814355421

Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

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Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

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Solve jigsaw puzzle

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Page Count

300

Publisher

World Scientific

Published Date

ISBN 10

9813225440

ISBN 13

9789813225442

Book's by Renat T Sibatov

Fractional Kinetics In Solids: Anomalous Charge Transport In Semiconductors, Dielectrics And Nanosystems

Fractional Kinetics In Solids: Anomalous Charge Transport In Semiconductors, Dielectrics And Nanosystems

Fractional Kinetics In Space: Anomalous Transport Models

Fractional Kinetics In Space: Anomalous Transport Models

Fractional Kinetics in Solids

Fractional Kinetics in Solids

Fractional Kinetics In Space: Anomalous Transport Models

Fractional Kinetics In Space: Anomalous Transport Models

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