Fluctuation-dissipation in accelerated frames

TL;DR

This paper explores the fluctuation-dissipation relation for particles in an accelerated frame, revealing Brownian-type correlations consistent across different spacetime dimensions, and discusses its implications.

Contribution

It demonstrates the fluctuation-dissipation relation for particles in an accelerated frame, linking Unruh radiation to Brownian motion in both (1+1) and (1+3) dimensions.

Findings

Correlation functions exhibit Brownian motion characteristics.

Fluctuation-dissipation relation holds in accelerated frames.

Results are consistent across different spacetime dimensions.

Abstract

An uniformly accelerated (Rindler) observer will detect particles in the Minkowski vacuum, known as Unruh effect. The spectrum is thermal and the temperature is given by that of the Killing horizon, which is proportional to the acceleration. Considering these particles are kept in a thermal bath with this temperature, we find that the correlation function of the random force due to radiation acting on the particles as measured by the accelerated frame, shows the fluctuation-dissipation relation. It is observed that the correlations, in both ($1+1$) spacetime and ($1+3$) dimensional spacetimes, are of Brownian type. We discuss the implications of this new observation at the end.