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Dynamical formulation of Gaussian white noise
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Paper Abstract

We study the connection between Hamiltonian dynamics and irreversible, stochastic equations, such as the Langevin equation. We consider a simple model of a harmonic oscillator (Brownian particle) coupled to a field (heat bath). We introduce an invertible transformation operator Λ that brings us to a new representation where dynamics is decomposed into independent Markovian components, including Brownian motion. The effects of Gaussian white noise are obtained by the non-distributive property of Λ with respect to products of dynamical variables. In this way we obtain an exact formulation of white noise effects. Our method leads to a direct link between dynamics of Poincaré nonintegrable systems, probability and stochasticity.

Paper Details

Date Published: 7 May 2003
PDF: 12 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.500170
Show Author Affiliations
Gonzalo E Ordonez, Univ. of Texas at Austin (United States)
Sungyun Kim, Univ. of Texas at Austin (United States)

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)

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