Quantum mechanical effects in continuum charge flow models
This paper concerns mathematical modelling of charge transport across a thin poorly conducting layer between two electrodes. We describe and analyse two alternative approaches to model quantum effects within a continuum theory: the Density Gradient Confinement (DGC) and Density Gradient Tunnelling (...
| Κύριοι συγγραφείς: | , , |
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| Μορφή: | Journal article |
| Έκδοση: |
Oxford University Press
2016
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| _version_ | 1826297319006404608 |
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| author | Black, J Breward, C Howell, P |
| author_facet | Black, J Breward, C Howell, P |
| author_sort | Black, J |
| collection | OXFORD |
| description | This paper concerns mathematical modelling of charge transport across a thin poorly conducting layer between two electrodes. We describe and analyse two alternative approaches to model quantum effects within a continuum theory: the Density Gradient Confinement (DGC) and Density Gradient Tunnelling (DGT) theories. In either case, quantum effects are characterised by a small parameter, which we exploit to analyse the problems asymptotically. We thus find simplified approximate solutions which show excellent agreement with numerical solutions of the full models, and demonstrate previously undocumented oscillatory behaviour both in the charge density profile and in the variation of current with applied potential difference. |
| first_indexed | 2024-03-07T04:29:46Z |
| format | Journal article |
| id | oxford-uuid:cde80d5f-aa3e-4c42-acf2-c559ea87c26d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:29:46Z |
| publishDate | 2016 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:cde80d5f-aa3e-4c42-acf2-c559ea87c26d2022-03-27T07:31:57ZQuantum mechanical effects in continuum charge flow modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cde80d5f-aa3e-4c42-acf2-c559ea87c26dSymplectic Elements at OxfordOxford University Press2016Black, JBreward, CHowell, PThis paper concerns mathematical modelling of charge transport across a thin poorly conducting layer between two electrodes. We describe and analyse two alternative approaches to model quantum effects within a continuum theory: the Density Gradient Confinement (DGC) and Density Gradient Tunnelling (DGT) theories. In either case, quantum effects are characterised by a small parameter, which we exploit to analyse the problems asymptotically. We thus find simplified approximate solutions which show excellent agreement with numerical solutions of the full models, and demonstrate previously undocumented oscillatory behaviour both in the charge density profile and in the variation of current with applied potential difference. |
| spellingShingle | Black, J Breward, C Howell, P Quantum mechanical effects in continuum charge flow models |
| title | Quantum mechanical effects in continuum charge flow models |
| title_full | Quantum mechanical effects in continuum charge flow models |
| title_fullStr | Quantum mechanical effects in continuum charge flow models |
| title_full_unstemmed | Quantum mechanical effects in continuum charge flow models |
| title_short | Quantum mechanical effects in continuum charge flow models |
| title_sort | quantum mechanical effects in continuum charge flow models |
| work_keys_str_mv | AT blackj quantummechanicaleffectsincontinuumchargeflowmodels AT brewardc quantummechanicaleffectsincontinuumchargeflowmodels AT howellp quantummechanicaleffectsincontinuumchargeflowmodels |