大葉大學圖書館 |

Fractional kinetics in solids[electronic resource] :anomalous charge transport in semiconductors, dielectrics, and nanosystems /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	530.4/16
書名/作者:	Fractional kinetics in solids : anomalous charge transport in semiconductors, dielectrics, and nanosystems // Vladimir Uchaikin, Renat Sibatov.
作者:	Uchaĭkin, V. V.
其他作者:	Sibatov, Renat.
出版者:	Singapore ; : World Scientific,, c2013.
面頁冊數:	1 online resource (xvi, 257 p.) : : ill.
標題:	Solid state physics - Mathematics.
標題:	Electric discharges - Mathematical models.
標題:	Fractional calculus.
標題:	Semiconductors - Electric properties.
標題:	Electron transport - Mathematical models.
標題:	Chemical kinetics - Mathematics.
ISBN:	9789814355438 (electronic bk.)
ISBN:	9814355437 (electronic bk.)
書目註:	Includes bibliographical references (p. 237-256) and index.
摘要、提要註:	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.
電子資源:	http://www.worldscientific.com/worldscibooks/10.1142/8185#t=toc

Fractional kinetics in solids[electronic resource] :anomalous 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:

556669
Solid state physics
--Mathematics.Index Terms--Genre/Form:

336502
Electronic books.

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

Dewey Class. No.: 530.4/16

Fractional kinetics in solids[electronic resource] :anomalous charge transport in semiconductors, dielectrics, and nanosystems /
LDR:03579cam a2200277Ma 4500 001 400009
006 m o d
007 cr |n|||||||||
008 140123s2013 si a ob 001 0 eng d
020 $a 9789814355438 (electronic bk.)
020 $a 9814355437 (electronic bk.)
020 $z 9814355429
020 $z 9789814355421
020 $z 9781283899987
020 $z 1283899981
035 $a ocn822655790
040 $a CDX $b eng $c CDX $d OCLCO $d HKP $d YDXCP $d UKMGB $d OCLCQ $d DEBSZ $d STF $d IDEBK $d E7B
049 $a FISA
050 4 $a QC176.8.E35 $b U34 2013eb
082 0 4 $a 530.4/16 $2 23
100 1 $a Uchaĭkin, V. V. $q (Vladimir Vasilʹevich) $3 556667
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.
260 $a Singapore ; $a Hackensack, NJ : $b World Scientific, $c c2013.
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 556669
650 0 $a Electric discharges $x Mathematical models. $3 556670
650 0 $a Fractional calculus. $3 405623
650 0 $a Semiconductors $x Electric properties. $3 556671
650 0 $a Electron transport $x Mathematical models. $3 556672
650 0 $a Chemical kinetics $x Mathematics. $3 556673
655 0 $a Electronic books. $2 local $3 336502
700 1 $a Sibatov, Renat. $3 556668
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/8185#t=toc