Worldline algorithms for Casimir configurations

2006/05/16 by Holger Gies, Klaus Klingmüller, Klaus Klingmuller · 10 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #cond-mat.stat-mech #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevd.74.045002

published as Phys.Rev.D74:045002,2006 · 23 pages, 9 figures

arxiv created 2006/05/16 · openalex publication_date 2006/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present improved worldline numerical algorithms for high-precision calculations of Casimir interaction energies induced by scalar-field fluctuations with Dirichlet boundary conditions for various Casimir geometries. Significant reduction of numerical cost is gained by exploiting the symmetries of the worldline ensemble in combination with those of the configurations. This facilitates high-precision calculations on standard PCs or small clusters. We illustrate our strategies using the experimentally most relevant sphere-plate and cylinder-plate configuration. We compute Casimir curvature effects for a wide parameter range, revealing the tight validity bounds of the commonly used proximity force approximation (PFA). We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA. Revisiting the parallel-plate configuration, we find a mapping between the D-dimensional Casimir energy and properties of a random-chain polymer ensemble.

Citations

• Dirichlet Spheres in Continuum Quantum Field Theory
• Worldline Approach To The Casimir Effect
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Stronger constraints for nanometer scale Yukawa-type hypothetical interactions from the new measurement of the Casimir force
• New Developments in the Casimir Effect
• Scalar Casimir effect between Dirichlet spheres or a plate and a sphere

Cited by

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• Exact Results for Casimir Interactions between Dielectric Bodies: The Weak-Coupling or van der Waals Limit
• Casimir effect for a sphere and a cylinder in front of a plane and corrections to the proximity force theorem
• The Casimir effect in microstructured geometries
• Casimir Physics