Path integral representation of fractional harmonic oscillator

被引:15
作者
Eab, Chai Hok
Lim, S. C. [1 ]
机构
[1] Multimedia Univ, Fac Engn, Selangor 63100, DE, Malaysia
[2] Chulalongkorn Univ, Fac Sci, Dept Chem, Bangkok 10330, Thailand
关键词
fractional oscillator process; path integral; partition function;
D O I
10.1016/j.physa.2006.03.029
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页码:303 / 316
页数:14
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