Generalized phase-space kinetic and diffusion equations for classical and dispersive transport
We formulate and solve a physically-based, phase space kinetic equation for transport in the presence of trapping. Trapping is incorporated through a waiting time distribution function. From the phase-space analysis, we obtain a generalized diffusion equation in configuration space. We analyse the i...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/7/073040 |
| _version_ | 1797751400805957632 |
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| author | Bronson Philippa R E Robson R D White |
| author_facet | Bronson Philippa R E Robson R D White |
| author_sort | Bronson Philippa |
| collection | DOAJ |
| description | We formulate and solve a physically-based, phase space kinetic equation for transport in the presence of trapping. Trapping is incorporated through a waiting time distribution function. From the phase-space analysis, we obtain a generalized diffusion equation in configuration space. We analyse the impact of the waiting time distribution, and give examples that lead to dispersive or non-dispersive transport. With an appropriate choice of the waiting time distribution, our model is related to fractional diffusion in the sense that fractional equations can be obtained in the limit of long times. Finally, we demonstrate the application of this theory to disordered semiconductors. |
| first_indexed | 2024-03-12T16:48:58Z |
| format | Article |
| id | doaj.art-c78de7c68bc4486594db6ee153f8c4b2 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:48:58Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-c78de7c68bc4486594db6ee153f8c4b22023-08-08T11:28:35ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116707304010.1088/1367-2630/16/7/073040Generalized phase-space kinetic and diffusion equations for classical and dispersive transportBronson Philippa0R E Robson1R D White2ARC Centre for Antimatter-Matter Studies, School of Engineering and Physical Sciences, James Cook University, Townsville 4810, AustraliaARC Centre for Antimatter-Matter Studies, School of Engineering and Physical Sciences, James Cook University, Townsville 4810, AustraliaARC Centre for Antimatter-Matter Studies, School of Engineering and Physical Sciences, James Cook University, Townsville 4810, AustraliaWe formulate and solve a physically-based, phase space kinetic equation for transport in the presence of trapping. Trapping is incorporated through a waiting time distribution function. From the phase-space analysis, we obtain a generalized diffusion equation in configuration space. We analyse the impact of the waiting time distribution, and give examples that lead to dispersive or non-dispersive transport. With an appropriate choice of the waiting time distribution, our model is related to fractional diffusion in the sense that fractional equations can be obtained in the limit of long times. Finally, we demonstrate the application of this theory to disordered semiconductors.https://doi.org/10.1088/1367-2630/16/7/073040kinetic theorydispersive transportfractional diffusion equation |
| spellingShingle | Bronson Philippa R E Robson R D White Generalized phase-space kinetic and diffusion equations for classical and dispersive transport New Journal of Physics kinetic theory dispersive transport fractional diffusion equation |
| title | Generalized phase-space kinetic and diffusion equations for classical and dispersive transport |
| title_full | Generalized phase-space kinetic and diffusion equations for classical and dispersive transport |
| title_fullStr | Generalized phase-space kinetic and diffusion equations for classical and dispersive transport |
| title_full_unstemmed | Generalized phase-space kinetic and diffusion equations for classical and dispersive transport |
| title_short | Generalized phase-space kinetic and diffusion equations for classical and dispersive transport |
| title_sort | generalized phase space kinetic and diffusion equations for classical and dispersive transport |
| topic | kinetic theory dispersive transport fractional diffusion equation |
| url | https://doi.org/10.1088/1367-2630/16/7/073040 |
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