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Title: Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

Abstract

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.

Authors:
; ; ;  [1];  [2]
  1. Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
  2. Faculty of Sciences, Department of Physics and Department of Astronomy, Vrije Universiteit Amsterdam (Netherlands)
Publication Date:
OSTI Identifier:
21015920
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 76; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.76.032106; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CASIMIR EFFECT; DIELECTRIC MATERIALS; ELECTROMAGNETISM; EVALUATION; FINITE DIFFERENCE METHOD; FLUCTUATIONS; GREEN FUNCTION; METALS; PHOTONS; PLATES; RESOURCES; STRESSES

Citation Formats

Rodriguez, Alejandro, Ibanescu, Mihai, Joannopoulos, J D, Johnson, Steven G, and Iannuzzi, Davide. Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.76.032106.
Rodriguez, Alejandro, Ibanescu, Mihai, Joannopoulos, J D, Johnson, Steven G, & Iannuzzi, Davide. Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques. United States. https://doi.org/10.1103/PHYSREVA.76.032106
Rodriguez, Alejandro, Ibanescu, Mihai, Joannopoulos, J D, Johnson, Steven G, and Iannuzzi, Davide. 2007. "Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques". United States. https://doi.org/10.1103/PHYSREVA.76.032106.
@article{osti_21015920,
title = {Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques},
author = {Rodriguez, Alejandro and Ibanescu, Mihai and Joannopoulos, J D and Johnson, Steven G and Iannuzzi, Davide},
abstractNote = {We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.},
doi = {10.1103/PHYSREVA.76.032106},
url = {https://www.osti.gov/biblio/21015920}, journal = {Physical Review. A},
issn = {1050-2947},
number = 3,
volume = 76,
place = {United States},
year = {Sat Sep 15 00:00:00 EDT 2007},
month = {Sat Sep 15 00:00:00 EDT 2007}
}