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Zbl 1156.82010
Lim, S.C.; Teo, L.P.
The fractional oscillator process with two indices. (English)
[J] J. Phys. A, Math. Theor. 42, No. 6, Article ID 065208, 34 p. (2009). ISSN 1751-8113; ISSN 1751-8121/e

Summary: We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique.

MSC 2000:: *82C31 Stochastic methods in time-dependent statistical mechanics

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