Casimir interaction of arbitrarily shaped conductors

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• The Casimir effect describes an attractive force between uncharged conductors in vacuum.
• Calculating Casimir interactions for arbitrary shapes is computationally challenging.

Purpose of the Study:

• To present a practical implementation of the Balian-Duplantier multiple scattering formalism.
• To calculate Casimir interactions for arbitrarily shaped smooth conductors.

Main Methods:

• Systematic implementation of the Balian-Duplantier multiple scattering theory.
• Evaluation of the leading two-point scattering term for computational efficiency.
• Analysis of higher-order terms for accuracy checks and screening phenomena.

Main Results:

• The two-point scattering approximation provides a compact and accurate method for many geometries.
• The method was validated by re-evaluating sphere-sphere and sphere-plane interactions.
• Novel calculations include the Casimir interaction between a hyperboloid and a plane.

Conclusions:

• The Balian-Duplantier formalism offers a versatile and accurate approach to Casimir calculations.
• The two-point approximation is effective for most scenarios, with analytical solutions for specific cases.
• The theory is extended to finite temperatures, maintaining computational tractability.