Correlation and response in a driven dissipative model

TL;DR

This paper analyzes a driven dissipative system with spatial structure, deriving correlation and response functions, and explores heat transfer behavior, showing qualitative agreement with granular gas simulations.

Contribution

It explicitly calculates correlation and response functions in a dissipative model, revealing their identical spatial dependence and linking heat transfer to granular gas behavior.

Findings

Correlations exist except at zero and maximal dissipation.

Correlation and response functions share the same spatial pattern.

Heat transfer behavior aligns qualitatively with granular gas simulations.

Abstract

We consider a simple dissipative system with spatial structure in contact with a heat bath. The system always exhibits correlations except in the cases of zero and maximal dissipation. We explicitly calculate the correlation function and the nonlocal response function of the system and show that they have the same spatial dependence. Finally, we examine heat transfer in the model, which agrees qualitatively with simulations of vibrated granular gases.