Path integral representation of fractional harmonic oscillator |
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| Affiliation: | 1. Department of Chemistry, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand;2. Faculty of Engineering, Multimedia University, Cyberjaya 63100, Selangor DE, Malaysia;1. Science Department, Harvard-Westlake School, 3700 Coldwater Canyon, Studio City, 91604, USA;2. Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, CA 90024, USA;3. Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain;1. Dipartimento di Chimica e Farmacia, University of Sassari, Italy;2. POLCOMING Department, Section of Information Engineering, University of Sassari, Italy;3. Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, Italy |
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| Abstract: | 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. |
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