LEADER 05959nam 2200757Ia 450 001 9910788622503321 005 20230803033502.0 010 $a1-283-89998-1 010 $a981-4355-43-7 035 $a(CKB)3280000000002153 035 $a(EBL)1109702 035 $a(OCoLC)826853968 035 $a(SSID)ssj0000782540 035 $a(PQKBManifestationID)12406278 035 $a(PQKBTitleCode)TC0000782540 035 $a(PQKBWorkID)10745655 035 $a(PQKB)11730825 035 $a(MiAaPQ)EBC1109702 035 $a(WSP)00002848 035 $a(Au-PeEL)EBL1109702 035 $a(CaPaEBR)ebr10640621 035 $a(CaONFJC)MIL421248 035 $a(EXLCZ)993280000000002153 100 $a20121119d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractional kinetics in solids$b[electronic resource] $eanomalous charge transport in semiconductors, dielectrics, and nanosystems /$fVladimir Uchaikin, Ulyanovsk State University, Russia, Renat Sibatov, Ulyanovsk State University, Russia 210 $aSingapore $cWorld Scientific$d2013 215 $a1 online resource (274 p.) 300 $aDescription based upon print version of record. 311 $a981-4355-42-9 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; 1. Statistical grounds; 1.1 Levy stable statistics; 1.1.1 Generalized limit theorems; 1.1.2 Two subclasses of stable distributions; 1.1.3 Fractional stable distributions; 1.1.4 Self-similar processes: Brownian motion and Levy motion; 1.1.5 Space-fractional equations; 1.2 Random flight models; 1.2.1 Continuous time random flights; 1.2.2 Counting process for number of jumps; 1.2.3 The Poisson process; 1.2.4 The Fractional Poisson process; 1.2.5 Simulation of waiting times; 1.3 Some properties of the fractional Poisson process; 1.3.1 The nth arrival time distribution 327 $a1.3.2 The fractional Poisson distribution1.3.3 Limit fractional Poisson distributions; 1.3.4 Fractional Furry process; 1.3.5 Time-fractional equation; 1.4 Random flights on a one-dimensional Levy-Lorentz gas; 1.4.1 One-dimensional Levy-Lorentz gas; 1.4.2 The flight process on the fractal gas; 1.4.3 Propagators; 1.4.4 Fractional equation for flights on fractal; 1.5 Subdiffusion; 1.5.1 Integral equations of diffusion in a medium with traps; Necessary and sufficient condition for subdiffusion; 1.5.2 Differential equations of subdiffusion; 1.5.3 Subdiffusion distribution density 327 $a1.5.4 Analysis of subdiffusion distributions1.5.5 Discussion; 2. Fractional kinetics of dispersive transport; 2.1 Macroscopic phenomenology; 2.1.1 A role of phenomenology in studying complex systems; 2.1.2 Universality of transient current curves; 2.1.3 From self-similarity to fractional derivatives; 2.1.4 From transient current to waiting time distribution; 2.2 Microscopic backgrounds of dispersive transport; 2.2.1 From the Scher-Montroll model to fractional derivatives; 2.2.2 Physical basis of the power-law waiting time distribution; 2.2.3 Multiple trapping regime 327 $a2.2.4 Hopping conductivity2.2.5 Bassler's model of Gaussian disorder; 2.3 Fractional formalism of multiple trapping; 2.3.1 Prime statements; 2.3.2 Multiple trapping regime and Arkhipov-Rudenko approach; 2.3.3 Fractional equations for delocalized carriers; 2.3.4 Fractional equation for the total concentration; 2.3.5 Two-state dynamics; 2.3.6 Delocalized carrier concentration; 2.3.7 Percolation and fractional kinetics; 2.3.8 The case of Gaussian disorder; 2.4 Some applications; 2.4.1 Dispersive diffusion; 2.4.2 Photoluminescence decay; 2.4.3 Including recombination; 2.4.4 Including generation 327 $a2.4.5 Bipolar dispersive transport2.4.6 The family of fractional dispersive transport equations; 3. Transient processes in disordered semiconductor structures; 3.1 Time-of-flight method; 3.1.1 Transient current in disordered semiconductors; 3.1.2 Transient current for truncated waiting time distributions; 3.1.3 Distributed dispersion parameter; 3.1.4 Transient current curves in case of Gaussian disorder; 3.1.5 Percolation in porous semiconductors; 3.1.6 Non-stationary radiation-induced conductivity; 3.2 Non-homogeneous distribution of traps 327 $a3.2.1 Non-uniform spatial distribution of localized states 330 $aThe 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 derivative 606 $aSolid state physics$xMathematics 606 $aElectric discharges$xMathematical models 606 $aFractional calculus 606 $aSemiconductors$xElectric properties 606 $aElectron transport$xMathematical models 606 $aChemical kinetics$xMathematics 615 0$aSolid state physics$xMathematics. 615 0$aElectric discharges$xMathematical models. 615 0$aFractional calculus. 615 0$aSemiconductors$xElectric properties. 615 0$aElectron transport$xMathematical models. 615 0$aChemical kinetics$xMathematics. 676 $a530.4/16 676 $a530.416 676 $a531.3 700 $aUchai?kin$b V. V$g(Vladimir Vasil?evich)$0520680 701 $aSibatov$b Renat$01510459 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788622503321 996 $aFractional kinetics in solids$93743146 997 $aUNINA