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Improved linear response for stochastically driven systems

Frontiers of Mathematics in China 2012年第2期7卷 199-216页

作者： Rafail V. ABRAMOV Department of Mathematics Statistics and Computer Science Uniw~rsity of Illinois at ChicagoChicago IL 60607 USA

Abstract The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation- dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which mig：ht not be available with sufficient precision in the case of complex dynamics （usually a Gaussian approximation is used）. Here, we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response tiraes before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times.

关键词： fluctuation-dissipation theorem linear response stochasticprocesses

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Ballistic Diffusion of a Charged Particle in a Blackbody Radiation Field

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Chinese Physics Letters 2005年第8期22卷 1845-1847页

作者：包景东白占武 DepartmentofPhysics BeijingNormalUniversityBeijing100875

The generalized Langevin equation is used to describe the motion of a chargedparticle interacting with a black-body radiation held via dipole coupling. The exact expressionsfor the mean-square displacement and velocity of such a particle are obtained, which show aballistic diffusion and a modified Kubo fluctuation-dissipation relation. In particular, avelocity-dependent coupling or force can induce this novel phenomenon.

关键词： fluctuation-dissipation theorem LANGEVIN EQUATION BROWNIAN-MOTION OSCILLATOR SYSTEM

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Short-Time Linear Response with Reduced-Rank Tangent Map

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Chinese Annals of Mathematics,Series B 2009年第5期30卷 447-462页

作者： Rafail V. ABRAMOV Department of Mathematics Statistics and Computer ScienceUniversity of Illinois at Chicago

The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response ***,the computation of the short-time linear response formula with the full rank tangent map can be ***,a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is *** conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established,and two practical situations are examined,where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.

关键词： fluctuation-dissipation theorem Linear response

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