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Fractional kinetics in solidsanomalo...

Sibatov, Renat.

Fractional kinetics in solidsanomalous charge transport in semiconductors, dielectrics, and nanosystems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fractional kinetics in solidsVladimir Uchaikin, Renat Sibatov.
Reminder of title:	anomalous charge transport in semiconductors, dielectrics, and nanosystems /
Author:	Uchaĭkin, V. V.
other author:	Sibatov, Renat.
Published:	Singapore ;World Scientific,c2013.
Description:	1 online resource (xvi, 257 p.) :ill.
Subject:	Solid state physicsMathematics.
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/8185#t=toc
ISBN:	9789814355438 (electronic bk.)

Fractional kinetics in solidsanomalous charge transport in semiconductors, dielectrics, and nanosystems /
Uchaĭkin, V. V.

Fractional kinetics in solidsanomalous charge transport in semiconductors, dielectrics, and nanosystems /[electronic resource] :Vladimir Uchaikin, Renat Sibatov. - Singapore ;World Scientific,c2013. - 1 online resource (xvi, 257 p.) :ill.

Includes bibliographical references (p. 237-256) and index.

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 behaviour 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.

ISBN: 9789814355438 (electronic bk.)Subjects--Topical Terms:

220429
Solid state physics
--Mathematics.Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QC176.8.E35 / U34 2013eb

Dewey Class. No.: 530.4/16

Fractional kinetics in solidsanomalous charge transport in semiconductors, dielectrics, and nanosystems /
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245 1 0 $a Fractional kinetics in solids $h [electronic resource] : $b anomalous charge transport in semiconductors, dielectrics, and nanosystems / $c Vladimir Uchaikin, Renat Sibatov.
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300 $a 1 online resource (xvi, 257 p.) : $b ill.
504 $a Includes bibliographical references (p. 237-256) and index.
520 $a 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 behaviour 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.
588 $a Description based on print version record.
650 0 $a Solid state physics $x Mathematics. $3 220429
650 0 $a Electric discharges $x Mathematical models. $3 648066
650 0 $a Fractional calculus. $3 208302
650 0 $a Semiconductors $x Electric properties. $3 184524
650 0 $a Electron transport $x Mathematical models. $3 648067
650 0 $a Chemical kinetics $x Mathematics. $3 648068
655 0 $a Electronic books. $2 local. $3 214472
700 1 $a Sibatov, Renat. $3 648065
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/8185#t=toc