Fractional oscillator process with two indices

Details Fractional oscillator process with two indices Fractional oscillator process with two indices

2008-04-24

arxiv.org/abs/0804.3906v1

J. Phys. A: Math. Theor. 42 (2009), 065208

Physics

Mathematical Physics

32 pages

Scientific paper

10.1088/1751-8113/42/6/065208

We introduce a new fractional oscillator process which can be obtained as 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. The fluctuation--dissipation relation of the process is investigated. The fractional oscillator process can be regarded as 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.

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