On the fluctuation of thermal van der Waals forces due to dipole fluctuations

TL;DR

This paper evaluates the fluctuations of thermal van der Waals forces between dielectric slabs modeled as polarizable dipoles, revealing that these fluctuations scale with area and are independent of microscopic cut-offs.

Contribution

It provides a detailed analysis of force fluctuations due to dipole interactions, highlighting their thermodynamic scaling and independence from microscopic details.

Findings

Force fluctuations scale with the area of the slabs.

Fluctuations are independent of microscopic cut-offs.

Average force and variance serve as unique fingerprints of fluctuation interactions.

Abstract

Fluctuations of the thermal or classical component of the van der Waals force between two dielectric slabs, modelled as an ensemble of polarizable dipoles which interact via the usual electrostatic dipole-dipole interaction, are evaluated. In the model the instantaneous force is a deterministic function of the dipole configurations in the slabs and its fluctuations are purely due to dipole fluctuations (no background thermal fluctuations of the electromagnetic field are considered). The average of the force and its variance are computed. The fluctuations of the force exhibit normal thermodynamic scaling in that they are proportional to the area of the two plates, and even more importantly, do not depend on any microscopic cut-off in the theory. The average and the variance of the thermal van der Waals forces give a unique fingerprint of these fluctuation interactions.