The power spectrum of the circular noise

TL;DR

This paper analytically derives the power spectrum of circular noise detected by a detector in Trocheries-Takeno motion, exploring its distribution, energy density, and implications for equilibrium and temperature distribution.

Contribution

It provides the first analytical expression for the power spectrum of circular noise in this specific motion, linking it to fundamental physics concepts.

Findings

Derived an infinite series expression for the power spectrum.

Obtained a mean distribution function and energy density.

Discussed non-constant temperature distribution and equilibrium conditions.

Abstract

The circular noise is important in connection to Mach's principle, and also as a possible probe of the Unruh effect. In this letter the power spectrum of the detector following the Trocheries-Takeno motion in the Minkowski vacuum is analytically obtained in the form of an infinite series. A mean distribution function and corresponding energy density are obtained for this particular detected noise. The analogous of a non constant temperature distribution is obtained. And in the end, a brief discussion about the equilibrium configuration is given.