Modeling a Quantum Hall System via Elliptic Equations
Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework to search for universal principles relevant to nanosystem modeling and nanosystem-specific signal processing. Recently, we have been able to construct a partial dif...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2009/514081 |
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| _version_ | 1849405382291619840 |
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| author | Artur Sowa |
| author_facet | Artur Sowa |
| author_sort | Artur Sowa |
| collection | DOAJ |
| description | Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology.
In particular, it is a good framework to search for universal principles relevant to
nanosystem modeling and nanosystem-specific signal processing. Recently, we have been able
to construct a partial differential equations-based model of a quantum Hall system, which
consists of the Schrödinger equation supplemented with a special-type nonlinear feedback
loop. This result stems from a novel theoretical approach, which in particular brings to
the fore the notion of quantum information. Here we undertake to modify the original model by
substituting the dynamics based on the Dirac operator. This leads to a model that consists
of a system of three nonlinearly coupled first-order elliptic equations in the plane. |
| format | Article |
| id | doaj-art-4e24fe7ef05e4ba38f618751aa1f7bb9 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-4e24fe7ef05e4ba38f618751aa1f7bb92025-08-20T03:36:41ZengWileyAdvances in Mathematical Physics1687-91201687-91392009-01-01200910.1155/2009/514081514081Modeling a Quantum Hall System via Elliptic EquationsArtur Sowa0Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, CanadaQuantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework to search for universal principles relevant to nanosystem modeling and nanosystem-specific signal processing. Recently, we have been able to construct a partial differential equations-based model of a quantum Hall system, which consists of the Schrödinger equation supplemented with a special-type nonlinear feedback loop. This result stems from a novel theoretical approach, which in particular brings to the fore the notion of quantum information. Here we undertake to modify the original model by substituting the dynamics based on the Dirac operator. This leads to a model that consists of a system of three nonlinearly coupled first-order elliptic equations in the plane.http://dx.doi.org/10.1155/2009/514081 |
| spellingShingle | Artur Sowa Modeling a Quantum Hall System via Elliptic Equations Advances in Mathematical Physics |
| title | Modeling a Quantum Hall System via Elliptic Equations |
| title_full | Modeling a Quantum Hall System via Elliptic Equations |
| title_fullStr | Modeling a Quantum Hall System via Elliptic Equations |
| title_full_unstemmed | Modeling a Quantum Hall System via Elliptic Equations |
| title_short | Modeling a Quantum Hall System via Elliptic Equations |
| title_sort | modeling a quantum hall system via elliptic equations |
| url | http://dx.doi.org/10.1155/2009/514081 |
| work_keys_str_mv | AT artursowa modelingaquantumhallsystemviaellipticequations |