Two oscillators in a common heat bath

TL;DR

This paper demonstrates that two oscillators in a shared heat bath exhibit unique interactions due to electromagnetic zero-point fluctuations, which cannot be simplified to a single oscillator model, even at zero temperature.

Contribution

It reveals the non-reducibility of two oscillators in a common heat bath and identifies zero-temperature induced interactions from electromagnetic fluctuations.

Findings

Interaction persists at zero temperature

Cannot reduce to an effective one-body problem

Zero-point fluctuations induce oscillator interactions

Abstract

We show that the case of two oscillators in a common heat bath cannot be reduced to an effective one body problem. In addition, there is an interaction between the oscillators, even at zero temperature, due to the fluctuations caused in both oscillators by the zero-point oscillations of the electromagnetic field.