Breakdown of the Fluctuation-Dissipation Theorem for fast superdiffusion

TL;DR

This paper investigates anomalous diffusion in one-dimensional systems, revealing that the Fluctuation-Dissipation Theorem fails in fast superdiffusion and characterizing the response function's asymptotic behavior.

Contribution

It classifies superdiffusion into slow and fast types and proves the breakdown of the Fluctuation-Dissipation Theorem in fast superdiffusion.

Findings

Fluctuation-Dissipation Theorem does not hold in fast superdiffusion.

Response function exhibits stretched exponential decay in anomalous diffusion.

Normal diffusion shows exponential decay in response function.

Abstract

We study anomalous diffusion for one-dimensional systems described by a generalized Langevin equation. We show that superdiffusion can be classified in slow superdiffusion and fast superdiffusion. For fast superdiffusion we prove that the Fluctuation-Dissipation Theorem does not hold. We show as well that the asymptotic behavior of the response function is a stretched exponential for anomalous diffusion and an exponential only for normal diffusion.