Solution of a generalized Boltzmann's equation for nonequilibrium charged-particle transport via localized and delocalized states

Stokes, Peter W., Philippa, Bronson, Cocks, Daniel, and White, Ronald D. (2016) Solution of a generalized Boltzmann's equation for nonequilibrium charged-particle transport via localized and delocalized states. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 93. 032119.

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Abstract

We present a general phase-space kinetic model for charged-particle transport through combined localized and delocalized states, capable of describing scattering collisions, trapping, detrapping, and losses. The model is described by a generalized Boltzmann equation, for which an analytical solution is found in Fourier-Laplace space. The velocity of the center of mass and the diffusivity about it are determined analytically, together with the flux transport coefficients. Transient negative values of the free particle center-of-mass transport coefficients can be observed due to the trapping to, and detrapping from, localized states. A Chapman-Enskog-type perturbative solution technique is applied, confirming the analytical results and highlighting the emergence of a density gradient representation in the weak-gradient hydrodynamic regime. A generalized diffusion equation with a unique global time operator is shown to arise, reducing to the standard diffusion equation and a Caputo fractional diffusion equation in the normal and dispersive limits. A subordination transformation is used to solve the generalized diffusion equation by mapping from the solution of a corresponding standard diffusion equation.

Item ID: 43626
Item Type: Article (Research - C1)
ISSN: 1550-2376
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A version of this publication was included as Chapter 3 of the following PhD thesis: Stokes, Peter (2018) Anomalous charged-particle transport in organic and soft-condensed matter. PhD thesis, James Cook University, which is available Open Access in ResearchOnline@JCU. Please see the Related URLs for access.

Funders: Australian Research Council (ARC), Queensland State Government
Date Deposited: 09 Aug 2016 04:19
FoR Codes: 02 PHYSICAL SCIENCES > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020204 Plasma Physics; Fusion Plasmas; Electrical Discharges @ 50%
02 PHYSICAL SCIENCES > 0203 Classical Physics > 020304 Thermodynamics and Statistical Physics @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100%
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