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Title: Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of)
  2. Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm (Germany)
  3. (Finland)
  4. Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)
Publication Date:
OSTI Identifier:
22251043
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CORRELATION FUNCTIONS; FLUCTUATIONS; HARMONIC OSCILLATORS; HARMONIC POTENTIAL; LANGEVIN EQUATION; NOISE; OSCILLATORS; STOCHASTIC PROCESSES