skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

Journal Article · · Physical Review A
 [1]; ORCiD logo [2];  [1]
  1. Univ. of Oregon, Eugene, OR (United States). Oregon Center for Optical, Molecular and Quantum Science, Dept. of Physics
  2. Santa Fe Inst., Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE; National Science Foundation (NSF)
Grant/Contract Number:
AC52-06NA25396; PHY-1068583; PHY-1505118
OSTI ID:
1414127
Report Number(s):
LA-UR-16-24039; PLRAAN; TRN: US1800653
Journal Information:
Physical Review A, Vol. 94, Issue 4; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

References (46)

Scattering theory approach to electrodynamic Casimir forces journal October 2009
On explicit occupation time distributions for Brownian processes journal February 2002
Field theory without Feynman diagrams: One-loop effective actions journal October 1992
The Casimir effect within scattering theory journal October 2006
The Influence of Retardation on the London-van der Waals Forces journal February 1948
Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties journal July 2011
Casimir Edge Effects journal November 2006
Casimir Effect for Curved Geometries: Proximity-Force-Approximation Validity Limits journal June 2006
Step Options journal January 1999
Macroscopic Quantum Electrodynamics and Duality journal April 2009
Worldline numerics for energy-momentum tensors in Casimir geometries journal February 2016
Ground state energy for a penetrable sphere and for a dielectric ball journal March 1999
Nonmonotonic Thermal Casimir Force from Geometry-Temperature Interplay journal July 2010
Efficient Computation of Casimir Interactions between Arbitrary 3D Objects journal July 2009
Casimir energy for dielectrics. journal May 1992
Electromagnetic fluctuations in matter and molecular (Van-der-Waals) forces between them journal May 1975
Strong interactions of single atoms and photons near a dielectric boundary journal November 2010
Casimir-Polder interaction between an atom and a cavity wall under the influence of real conditions journal October 2004
Perturbative quantum field theory in the string-inspired formalism journal December 2001
Path-integral quantization of electrodynamics in dielectric media journal March 1998
Neumann Casimir effect: A singular boundary-interaction approach journal June 2010
Casimir energy between a plane and a sphere in electromagnetic vacuum journal July 2008
Opposites Attract: A Theorem about the Casimir Force journal October 2006
On Some Relations between the Laplace and Mellin Transforms journal November 1975
Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques journal September 2007
Quantum energies with worldline numerics journal May 2006
Energy-Momentum Tensors with Worldline Numerics journal January 2012
Quantum electrodynamics of the dispersive dielectric medium–a path integral approach journal April 1999
Interplay between geometry and temperature for inclined Casimir plates journal September 2009
Electromagnetic energy, absorption, and Casimir forces. II. Inhomogeneous dielectric media journal November 2011
Fluctuating surface currents: An algorithm for efficient prediction of Casimir interactions among arbitrary materials in arbitrary geometries journal August 2013
Casimir Forces between Arbitrary Compact Objects journal October 2007
The Distribution of the Sojourn Time for the Brownian Excursion journal January 1999
Numerical and semiclassical analysis of some generalized Casimir pistons journal May 2009
General theory of van der Waals' forces [Общая теория ван-дер-ваальсовых сил] journal January 1961
Worldline algorithms for Casimir configurations journal August 2006
Handbook of Brownian Motion - Facts and Formulae book January 2002
Numerical methods for fluctuation-driven interactions between dielectrics journal January 2008
Casimir effect in dielectrics journal September 1978
Electromagnetic energy, absorption, and Casimir forces: Uniform dielectric media in thermal equilibrium journal March 2010
Casimir effect on the worldline journal June 2003
Quantization of the electromagnetic field in dielectrics journal October 1992
Stiction, adhesion energy, and the Casimir effect in micromechanical systems journal January 2001
Casimir forces in the time domain: Theory journal July 2009
Geothermal Casimir phenomena journal April 2008
Trapped atoms in one-dimensional photonic crystals journal August 2013

Cited By (1)

Worldline formalism for a confined scalar field journal August 2019

Similar Records

Casimir forces in multilayer magnetodielectrics with both gain and loss
Journal Article · Fri Jul 15 00:00:00 EDT 2011 · Physical Review. A · OSTI ID:1414127
+1 more
Casimir-Polder interaction between an atom and a small magnetodielectric sphere
Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. A · OSTI ID:1414127
Casimir force in presence of multi layer magnetodielectric slabs
Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Annals of Physics (New York) · OSTI ID:1414127

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS