# Fluctuations of two-time quantities and non-linear response functions

Source: [Fluctuations of two-time quantities and non-linear response functions](<https://www.sota2.com/research/paper/68fa2f391e209131ce86a426>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:29:03.912Z

Authors: Federico Corberi, Eugenio Lippiello, Alessandro Sarracino, Marco Zannetti

Published: 2010-03-04T15:35:31.000Z

## Abstract

We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond-linear order relating it to the other variances. In a second part of the paper we apply the formalism to the study to non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length $\\xi$ in equilibrium, and with respect to the growing length $L(t)$ after a quench, similarly to what is known for the autocorrelation and the autoresponse functions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1003.1065>)

[PDF](<https://arxiv.org/pdf/1003.1065.pdf>)