Fractional kinetics in solids: anomalous charge transport in semiconductors, dielectrics, and nanosystems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ
World Scientific
c2013
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 237-256) and index 1. Statistical grounds. 1.1. Levy stable statistics. 1.2. Random flight models. 1.3. Some properties of the fractional Poisson process. 1.4. Random flights on a one-dimensional Levy-Lorentz gas. 1.5. Subdiffusion -- 2. Fractional kinetics of dispersive transport. 2.1. Macroscopic phenomenology. 2.2. Microscopic backgrounds of dispersive transport. 2.3. Fractional formalism of multiple trapping. 2.4. Some applications -- 3. Transient processes in disordered semiconductor structures. 3.1. Time-of-flight method. 3.2. Non-homogeneous distribution of traps. 3.3. Transient processes in a diode under dispersive transport conditions. 3.4. Frequency properties of disordered semiconductor structures -- 4. Fractional kinetics in quantum dots and wires. 4.1. Fractional optics of quantum dots. 4.2. Charge kinetics in colloidal quantum dot arrays. 4.3. Conductance through fractal quantum conductors -- 5. Fractional relaxation in dielectrics. 5.1. The relaxation problem. 5.2. Fractional approach. 5.3. The Cole-Cole kinetics. 5.4. The Havriliak-Negami kinetics. 5.5. The Kohlrausch-Williams-Watts kinetics -- 6. The scale correspondence principle. 6.1. Finity and infinity. 6.2. Intermediate space-asymptotics. 6.3. Intermediate time-asymptoics. 6.4. Concluding remarks 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 |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 1283899981 9781283899987 9789814355421 9789814355438 9814355429 9814355437 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043127496 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2013 |||| o||u| ||||||eng d | ||
| 020 | |a 1283899981 |9 1-283-89998-1 | ||
| 020 | |a 9781283899987 |9 978-1-283-89998-7 | ||
| 020 | |a 9789814355421 |9 978-981-4355-42-1 | ||
| 020 | |a 9789814355438 |c electronic bk. |9 978-981-4355-43-8 | ||
| 020 | |a 9814355429 |9 981-4355-42-9 | ||
| 020 | |a 9814355437 |c electronic bk. |9 981-4355-43-7 | ||
| 035 | |a (OCoLC)827472818 | ||
| 035 | |a (DE-599)BVBBV043127496 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 530.4/16 |2 23 | |
| 100 | 1 | |a Uchaĭkin, V. V., (Vladimir Vasilʹevich) |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fractional kinetics in solids |b anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| 264 | 1 | |a Hackensack, NJ |b World Scientific |c c2013 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (pages 237-256) and index | ||
| 500 | |a 1. Statistical grounds. 1.1. Levy stable statistics. 1.2. Random flight models. 1.3. Some properties of the fractional Poisson process. 1.4. Random flights on a one-dimensional Levy-Lorentz gas. 1.5. Subdiffusion -- 2. Fractional kinetics of dispersive transport. 2.1. Macroscopic phenomenology. 2.2. Microscopic backgrounds of dispersive transport. 2.3. Fractional formalism of multiple trapping. 2.4. Some applications -- 3. Transient processes in disordered semiconductor structures. 3.1. Time-of-flight method. 3.2. Non-homogeneous distribution of traps. 3.3. Transient processes in a diode under dispersive transport conditions. 3.4. Frequency properties of disordered semiconductor structures -- 4. Fractional kinetics in quantum dots and wires. 4.1. Fractional optics of quantum dots. 4.2. Charge kinetics in colloidal quantum dot arrays. 4.3. Conductance through fractal quantum conductors -- 5. Fractional relaxation in dielectrics. 5.1. The relaxation problem. 5.2. Fractional approach. 5.3. The Cole-Cole kinetics. 5.4. The Havriliak-Negami kinetics. 5.5. The Kohlrausch-Williams-Watts kinetics -- 6. The scale correspondence principle. 6.1. Finity and infinity. 6.2. Intermediate space-asymptotics. 6.3. Intermediate time-asymptoics. 6.4. Concluding remarks | ||
| 500 | |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. | ||
| 500 | |a 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. | ||
| 500 | |a 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 | ||
| 650 | 7 | |a Fractional calculus |2 fast | |
| 650 | 7 | |a Solid state physics / Mathematics |2 fast | |
| 650 | 7 | |a SCIENCE / Physics / Condensed Matter |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Solid state physics |x Mathematics | |
| 650 | 4 | |a Fractional calculus | |
| 650 | 0 | 7 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transportprozess |0 (DE-588)4185932-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kinetik |0 (DE-588)4030665-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kondensierte Materie |0 (DE-588)4132810-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kondensierte Materie |0 (DE-588)4132810-3 |D s |
| 689 | 0 | 1 | |a Kinetik |0 (DE-588)4030665-3 |D s |
| 689 | 0 | 2 | |a Transportprozess |0 (DE-588)4185932-7 |D s |
| 689 | 0 | 3 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028551687 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175563374460928 |
|---|---|
| any_adam_object | |
| author | Uchaĭkin, V. V., (Vladimir Vasilʹevich) |
| author_facet | Uchaĭkin, V. V., (Vladimir Vasilʹevich) |
| author_role | aut |
| author_sort | Uchaĭkin, V. V., (Vladimir Vasilʹevich) |
| author_variant | v v v v u vvvv vvvvu |
| building | Verbundindex |
| bvnumber | BV043127496 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)827472818 (DE-599)BVBBV043127496 |
| dewey-full | 530.4/16 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/16 |
| dewey-search | 530.4/16 |
| dewey-sort | 3530.4 216 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06363nmm a2200625zc 4500</leader><controlfield tag="001">BV043127496</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2013 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1283899981</subfield><subfield code="9">1-283-89998-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781283899987</subfield><subfield code="9">978-1-283-89998-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814355421</subfield><subfield code="9">978-981-4355-42-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814355438</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-981-4355-43-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814355429</subfield><subfield code="9">981-4355-42-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814355437</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">981-4355-43-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)827472818</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043127496</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.4/16</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Uchaĭkin, V. V., (Vladimir Vasilʹevich)</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fractional kinetics in solids</subfield><subfield code="b">anomalous charge transport in semiconductors, dielectrics, and nanosystems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hackensack, NJ</subfield><subfield code="b">World Scientific</subfield><subfield code="c">c2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 237-256) and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">1. Statistical grounds. 1.1. Levy stable statistics. 1.2. Random flight models. 1.3. Some properties of the fractional Poisson process. 1.4. Random flights on a one-dimensional Levy-Lorentz gas. 1.5. Subdiffusion -- 2. Fractional kinetics of dispersive transport. 2.1. Macroscopic phenomenology. 2.2. Microscopic backgrounds of dispersive transport. 2.3. Fractional formalism of multiple trapping. 2.4. Some applications -- 3. Transient processes in disordered semiconductor structures. 3.1. Time-of-flight method. 3.2. Non-homogeneous distribution of traps. 3.3. Transient processes in a diode under dispersive transport conditions. 3.4. Frequency properties of disordered semiconductor structures -- 4. Fractional kinetics in quantum dots and wires. 4.1. Fractional optics of quantum dots. 4.2. Charge kinetics in colloidal quantum dot arrays. 4.3. Conductance through fractal quantum conductors -- 5. Fractional relaxation in dielectrics. 5.1. The relaxation problem. 5.2. Fractional approach. 5.3. The Cole-Cole kinetics. 5.4. The Havriliak-Negami kinetics. 5.5. The Kohlrausch-Williams-Watts kinetics -- 6. The scale correspondence principle. 6.1. Finity and infinity. 6.2. Intermediate space-asymptotics. 6.3. Intermediate time-asymptoics. 6.4. Concluding remarks</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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. </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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. </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fractional calculus</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Solid state physics / Mathematics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE / Physics / Condensed Matter</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Solid state physics</subfield><subfield code="x">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional calculus</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gebrochene Analysis</subfield><subfield code="0">(DE-588)4722475-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Transportprozess</subfield><subfield code="0">(DE-588)4185932-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kinetik</subfield><subfield code="0">(DE-588)4030665-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kondensierte Materie</subfield><subfield code="0">(DE-588)4132810-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kondensierte Materie</subfield><subfield code="0">(DE-588)4132810-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kinetik</subfield><subfield code="0">(DE-588)4030665-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Transportprozess</subfield><subfield code="0">(DE-588)4185932-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Gebrochene Analysis</subfield><subfield code="0">(DE-588)4722475-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028551687</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043127496 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:17Z |
| institution | BVB |
| isbn | 1283899981 9781283899987 9789814355421 9789814355438 9814355429 9814355437 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028551687 |
| oclc_num | 827472818 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Uchaĭkin, V. V., (Vladimir Vasilʹevich) Verfasser aut Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems Hackensack, NJ World Scientific c2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 237-256) and index 1. Statistical grounds. 1.1. Levy stable statistics. 1.2. Random flight models. 1.3. Some properties of the fractional Poisson process. 1.4. Random flights on a one-dimensional Levy-Lorentz gas. 1.5. Subdiffusion -- 2. Fractional kinetics of dispersive transport. 2.1. Macroscopic phenomenology. 2.2. Microscopic backgrounds of dispersive transport. 2.3. Fractional formalism of multiple trapping. 2.4. Some applications -- 3. Transient processes in disordered semiconductor structures. 3.1. Time-of-flight method. 3.2. Non-homogeneous distribution of traps. 3.3. Transient processes in a diode under dispersive transport conditions. 3.4. Frequency properties of disordered semiconductor structures -- 4. Fractional kinetics in quantum dots and wires. 4.1. Fractional optics of quantum dots. 4.2. Charge kinetics in colloidal quantum dot arrays. 4.3. Conductance through fractal quantum conductors -- 5. Fractional relaxation in dielectrics. 5.1. The relaxation problem. 5.2. Fractional approach. 5.3. The Cole-Cole kinetics. 5.4. The Havriliak-Negami kinetics. 5.5. The Kohlrausch-Williams-Watts kinetics -- 6. The scale correspondence principle. 6.1. Finity and infinity. 6.2. Intermediate space-asymptotics. 6.3. Intermediate time-asymptoics. 6.4. Concluding remarks 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 Fractional calculus fast Solid state physics / Mathematics fast SCIENCE / Physics / Condensed Matter bisacsh Mathematik Solid state physics Mathematics Fractional calculus Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Transportprozess (DE-588)4185932-7 gnd rswk-swf Kinetik (DE-588)4030665-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Kinetik (DE-588)4030665-3 s Transportprozess (DE-588)4185932-7 s Gebrochene Analysis (DE-588)4722475-7 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Uchaĭkin, V. V., (Vladimir Vasilʹevich) Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems Fractional calculus fast Solid state physics / Mathematics fast SCIENCE / Physics / Condensed Matter bisacsh Mathematik Solid state physics Mathematics Fractional calculus Gebrochene Analysis (DE-588)4722475-7 gnd Transportprozess (DE-588)4185932-7 gnd Kinetik (DE-588)4030665-3 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4722475-7 (DE-588)4185932-7 (DE-588)4030665-3 (DE-588)4132810-3 |
| title | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_auth | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_exact_search | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_full | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_fullStr | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_full_unstemmed | Fractional kinetics in solids anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| title_short | Fractional kinetics in solids |
| title_sort | fractional kinetics in solids anomalous charge transport in semiconductors dielectrics and nanosystems |
| title_sub | anomalous charge transport in semiconductors, dielectrics, and nanosystems |
| topic | Fractional calculus fast Solid state physics / Mathematics fast SCIENCE / Physics / Condensed Matter bisacsh Mathematik Solid state physics Mathematics Fractional calculus Gebrochene Analysis (DE-588)4722475-7 gnd Transportprozess (DE-588)4185932-7 gnd Kinetik (DE-588)4030665-3 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Fractional calculus Solid state physics / Mathematics SCIENCE / Physics / Condensed Matter Mathematik Solid state physics Mathematics Gebrochene Analysis Transportprozess Kinetik Kondensierte Materie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516997 |
| work_keys_str_mv | AT uchaikinvvvladimirvasilʹevich fractionalkineticsinsolidsanomalouschargetransportinsemiconductorsdielectricsandnanosystems |