Stochastic Theories and Deterministic Differential Equations
We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory wi...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/749306 |
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| _version_ | 1832561417468772352 |
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| author | John F. Moxnes Kjell Hausken |
| author_facet | John F. Moxnes Kjell Hausken |
| author_sort | John F. Moxnes |
| collection | DOAJ |
| description | We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared. |
| format | Article |
| id | doaj-art-3938bffe959049a49ef57a7de6ceb500 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3938bffe959049a49ef57a7de6ceb5002025-02-03T01:24:58ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/749306749306Stochastic Theories and Deterministic Differential EquationsJohn F. Moxnes0Kjell Hausken1Department for Protection, Norwegian Defence Research Establishment, P.O. Box 25, 2007 Kjeller, NorwayFaculty of Social Sciences, University of Stavanger, 4036 Stavanger, NorwayWe discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared.http://dx.doi.org/10.1155/2010/749306 |
| spellingShingle | John F. Moxnes Kjell Hausken Stochastic Theories and Deterministic Differential Equations Advances in Mathematical Physics |
| title | Stochastic Theories and Deterministic Differential Equations |
| title_full | Stochastic Theories and Deterministic Differential Equations |
| title_fullStr | Stochastic Theories and Deterministic Differential Equations |
| title_full_unstemmed | Stochastic Theories and Deterministic Differential Equations |
| title_short | Stochastic Theories and Deterministic Differential Equations |
| title_sort | stochastic theories and deterministic differential equations |
| url | http://dx.doi.org/10.1155/2010/749306 |
| work_keys_str_mv | AT johnfmoxnes stochastictheoriesanddeterministicdifferentialequations AT kjellhausken stochastictheoriesanddeterministicdifferentialequations |