Path integral representation of fractional harmonic oscillator
Fractional oscillator process can be obtained as the solution to the fractional Langevin equation. There exist two types of fractional oscillator processes, based on the choice of fractional integro-differential operators (namely Weyl and Riemann-Liouville). An operator identity for the fractional d...
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ELSEVIER SCIENCE BV
2006
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| Online Access: | http://shdl.mmu.edu.my/3262/ |
| _version_ | 1848790279284326400 |
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| author | EAB, C LIM, S |
| author_facet | EAB, C LIM, S |
| author_sort | EAB, C |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | Fractional oscillator process can be obtained as the solution to the fractional Langevin equation. There exist two types of fractional oscillator processes, based on the choice of fractional integro-differential operators (namely Weyl and Riemann-Liouville). An operator identity for the fractional differential operators associated with the fractional oscillators is derived; it allows the solution of fractional Langevin equations to be obtained by simple inversion. The relationship between these two fractional oscillator processes is studied. The operator identity also plays an important role in the derivation of the path integral representation of the fractional oscillator processes. Relevant quantities such as two-point and n-point functions can be calculated from the generating functions. (c) 2006 Elsevier B.V. All rights reserved. |
| first_indexed | 2025-11-14T18:10:05Z |
| format | Article |
| id | mmu-3262 |
| institution | Multimedia University |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:10:05Z |
| publishDate | 2006 |
| publisher | ELSEVIER SCIENCE BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | mmu-32622011-10-18T00:09:39Z http://shdl.mmu.edu.my/3262/ Path integral representation of fractional harmonic oscillator EAB, C LIM, S T Technology (General) QA75.5-76.95 Electronic computers. Computer science Fractional oscillator process can be obtained as the solution to the fractional Langevin equation. There exist two types of fractional oscillator processes, based on the choice of fractional integro-differential operators (namely Weyl and Riemann-Liouville). An operator identity for the fractional differential operators associated with the fractional oscillators is derived; it allows the solution of fractional Langevin equations to be obtained by simple inversion. The relationship between these two fractional oscillator processes is studied. The operator identity also plays an important role in the derivation of the path integral representation of the fractional oscillator processes. Relevant quantities such as two-point and n-point functions can be calculated from the generating functions. (c) 2006 Elsevier B.V. All rights reserved. ELSEVIER SCIENCE BV 2006-11 Article NonPeerReviewed EAB, C and LIM, S (2006) Path integral representation of fractional harmonic oscillator. Physica A: Statistical and Theoretical Physics, 371 (2). pp. 303-316. ISSN 03784371 http://dx.doi.org/10.1016/j.physa.2006.03.029 doi:10.1016/j.physa.2006.03.029 doi:10.1016/j.physa.2006.03.029 |
| spellingShingle | T Technology (General) QA75.5-76.95 Electronic computers. Computer science EAB, C LIM, S Path integral representation of fractional harmonic oscillator |
| title | Path integral representation of fractional harmonic oscillator |
| title_full | Path integral representation of fractional harmonic oscillator |
| title_fullStr | Path integral representation of fractional harmonic oscillator |
| title_full_unstemmed | Path integral representation of fractional harmonic oscillator |
| title_short | Path integral representation of fractional harmonic oscillator |
| title_sort | path integral representation of fractional harmonic oscillator |
| topic | T Technology (General) QA75.5-76.95 Electronic computers. Computer science |
| url | http://shdl.mmu.edu.my/3262/ http://shdl.mmu.edu.my/3262/ http://shdl.mmu.edu.my/3262/ |