Geometry and spectrum of Casimir forces

Area of Science:

• Physics
• Quantum Field Theory
• Condensed Matter Physics

Background:

• The Casimir effect describes an attractive force between closely spaced surfaces.
• Calculating this force for arbitrarily shaped boundaries and general conditions is complex.
• Existing methods often struggle with nonperturbative regimes and complex geometries.

Purpose of the Study:

• To introduce a novel approach for the Helmholtz spectrum applicable to arbitrary boundaries.
• To derive nonperturbative results for the Casimir interaction between rigid surfaces.
• To compute the Casimir force between corrugated surfaces and identify universal behaviors.

Main Methods:

• Derivation of the boundary-induced change in the density of states.
• Utilizing the free Green's function for calculations.
• Applying the method to compute the lateral electrodynamic force between corrugated surfaces.

Main Results:

• A new, nonperturbative method for calculating the Helmholtz spectrum and Casimir interaction.
• Precise calculation of the lateral Casimir force between corrugated surfaces.
• Identification of universal behavior at large separations, dependent only on the largest surface wavelength component.

Conclusions:

• The presented approach offers a powerful tool for Casimir force calculations with complex geometries.
• The findings provide new insights into the behavior of the Casimir effect in nonperturbative regimes.
• The method successfully reproduces known short-distance expansions with high accuracy.