Fluctuations of the Casimir-like force between two membrane inclusions

TL;DR

This paper investigates the fluctuations of membrane-mediated Casimir-like forces between inclusions, revealing that force fluctuations dominate the force itself and decrease with the inverse square of the distance between inclusions.

Contribution

The study introduces a membrane stress tensor approach to analyze force fluctuations, providing new insights into the variance and distance dependence of Casimir-like forces in soft matter.

Findings

Casimir force fluctuations dominate the force magnitude.

Variance of the force decreases as -1/d^2 with distance.

Force fluctuations share a common physical origin with the Casimir force.

Abstract

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d^2. This distance dependence shares a common physical origin with the Casimir force itself.