Johnson noise and the thermal Casimir effect

TL;DR

This paper investigates the thermal electromagnetic interactions between metallic wires, revealing that Johnson currents induce a repulsive force through inductive coupling, and highlights the importance of capacitive effects in resolving related theoretical puzzles.

Contribution

It introduces a simple model demonstrating how capacitive effects resolve longstanding puzzles in the thermal Casimir effect related to inductive coupling.

Findings

Johnson currents cause repulsive forces via inductive coupling

Capacitive effects at wire endpoints resolve theoretical inconsistencies

Finite-size effects are crucial in understanding thermal electromagnetic interactions

Abstract

We study the thermal interaction between two nearby thin metallic wires, at finite temperature. It is shown that the Johnson currents in the wires give rise, via inductive coupling, to a repulsive force between them. This thermal interaction exhibits all the puzzling features found recently in the thermal Casimir effect for lossy metallic plates, suggesting that the physical origin of the difficulties encountered in the Casimir problem resides in the inductive coupling between the Johnson currents inside the plates. We show that in our simple model all puzzles are resolved if account is taken of capacitive effects associated with the end points of the wires. Our findings suggest that capacitive finite-size effects may play an important role in the resolution of the analogous problems met in the thermal Casimir effect.