Eur. Phys. J. B (2013) 86: 415
https://doi.org/10.1140/epjb/e2013-40692-y

Regular Article

Influence of nonlinearities on the dynamics of thermally fluctuating systems revealed by the expansion of dynamic observables in powers of the thermal noise strength

¹ Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
² Physics Department, Technische Universität München, 85748 Garching, Germany

^a e-mail: yann.von.hansen@fu-berlin.de

Received: 19 July 2013
Received in final form: 9 August 2013
Published online: 7 October 2013

Abstract

The effects of nonlinearities in the equations of motion of thermally fluctuating systems are investigated based on the Langevin equation. We identify the first terms in the expansions of equilibrium correlation functions and dynamic susceptibilities in powers of the thermal noise strength. The resulting expressions are explicitly evaluated for the case of overdamped diffusion in two monostable but anharmonic potentials, as well as in a double-well potential. The comparison to the results of numerical simulations allows to estimate the range of validity of our analytical results. Moreover, we provide a simple method to detect nonlinearities in the fluctuating time series data of a system in thermal equilibrium and discuss the resulting implications for the dynamics of composite systems. Finally, our findings shed light on the limitations of a recently introduced linear dynamic convolution theory, for which we derive a first-order correction term.