Harmonic oscillator with non-Gaussian frequency fluctuations

Author

Dubkov, Alexander

Author_Institution

Radiophys. Fac., Lobachevsky State Univ., Nizhny Novgorod, Russia

fYear

2011

fDate

12-16 June 2011

Firstpage

45

Lastpage

48

Abstract

The moment and probability characteristics of harmonic oscillator with white non-Gaussian frequency fluctuations are investigated. Using a functional approach we derive the integro-differential Kolmogorov equation for the joint probability density function of oscillator coordinate and velocity. Since it is difficult to find a solution of this equation in the steady state the set of equations for joint moments and the hypothesis of time-reversal symmetry which is valid for zero friction are applied. For the case of small friction we obtain the approximate probability distributions of oscillator coordinate and velocity which transform into exact stable Cauchy distributions in the limit of zero friction.

Keywords

fluctuations; harmonic oscillators; integro-differential equations; probability; exact stable Cauchy distributions; harmonic oscillator; integrodifferential Kolmogorov equation; joint probability density function; moment characteristics; oscillator coordinate; oscillator velocity; probability characteristics; probability distributions; time-reversal symmetry; white nonGaussian frequency fluctuations; Fluctuations; TV;

fLanguage

English

Publisher

ieee

Conference_Titel

Noise and Fluctuations (ICNF), 2011 21st International Conference on

Conference_Location

Toronto, ON

Print_ISBN

978-1-4577-0189-4

Type

conf

DOI

10.1109/ICNF.2011.5994369

Filename

5994369