Reversing the Critical Casimir force by shape deformation

TL;DR

This paper derives an exact formula for the critical Casimir force between deformed boundaries in 2D systems, showing how shape changes can reverse the force and create stable equilibria.

Contribution

It provides a universal, conformally invariant approach to calculating Casimir forces for arbitrary shapes, including force reversal and stability analysis.

Findings

Shape deformation can reverse the Casimir force direction.

Stable equilibrium points can be induced by shape changes.

The theory applies to various conformally invariant models, including tricritical Ising.

Abstract

The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium points, is demonstrated for certain conformally invariant models, including the tricritical Ising model.