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Phys. Rev. E 73, 016111 (2006) [4 pages]

Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle

A. D. Viñales1 and M. A. Despósito1,2
1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
2Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Received 18 August 2005; published 12 January 2006

We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.

©2006 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.73.016111
DOI: 10.1103/PhysRevE.73.016111
PACS: 02.50.-r; 05.40.-a; 02.50.Ey
  • 02.50.-r
    Probability theory, stochastic processes, and statistics
  • 05.40.-a
    Fluctuation phenomena, random processes, noise, and Brownian motion
  • 02.50.Ey
    Stochastic processes
  • YEAR: 2006
KEYWORDS: diffusion, fractals, harmonic oscillators, stochastic processes

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