Quantum energies with worldline numerics

TL;DR

This paper introduces worldline numerics as a versatile computational method to calculate Casimir forces in complex geometries, providing both accurate results and intuitive insights into quantum fluctuation phenomena.

Contribution

It applies worldline numerics to new Casimir geometries, demonstrating its effectiveness and expanding the toolkit for quantum fluctuation calculations.

Findings

Casimir force calculations for sphere-plate geometry

Results for perpendicular-plates configuration

Validation of worldline numerics in complex geometries

Abstract

We present new results for Casimir forces between rigid bodies which impose Dirichlet boundary conditions on a fluctuating scalar field. As a universal computational tool, we employ worldline numerics which builds on a combination of the string-inspired worldline approach with Monte-Carlo techniques. Worldline numerics is not only particularly powerful for inhomogeneous background configurations such as involved Casimir geometries, it also provides for an intuitive picture of quantum-fluctuation-induced phenomena. Results for the Casimir geometries of a sphere above a plate and a new perpendicular-plates configuration are presented.