Universality in the point discretization method for calculating Casimir interactions with classical Gaussian fields

Abstract

We study how universality arises when computing Casimir interactions between arbitrary bodies by discretizing their boundaries into pointlike constraints viewed as pointlike inclusions. Introducing ad hoc cutoff and regularization for the field's correlation function, we find that universality arises when i) the separation δ between the pointlike inclusions is less than the cutoff Λ−1, and ii) the bodies are much larger than the cutoff. A sharp transition from discrete to continuous boundaries occurs at δ = π/Λ in the thermodynamic limit for rods at large separation. We illustrate our findings in two dimensions with rodlike bodies and more complex bodies shaped as moons.

Membrane-Mediated Interactions

“…5b, and a non-rigid "ribbon" only imposing ∂ x ∂ x h = 0 along it), which is reminiscent of results obtained in critical binary mixtures [23]. In addition, the interaction energy was studied numerically versus d/L, thanks to a discretization scheme [59], showing the transition between the asymptotic behaviors at large d/L [27] and at small d/L [58] were recovered. Finally, the bending and coming into contact of the rods due to the fluctuation-induced interaction was discussed: it was predicted to occur below a certain value of d [58].…”

Universal amplitudes of the Casimir-like interactions between four types of rods in fluid membranes

“…The idea is to discretize the functional integral over the auxiliary fields ψ i that enforce the constraints. Using a discretization scheme that will be discussed elsewhere [20], we have calculated the Casmir interaction between two rigid "ct" rods at any separation (fig. 3).…”