Casimir effect as a sum over modes in dissipative systems

2012/09/30 by Francesco Intravaia, F. Intravaia, Ryan O. Behunin +1 · 1 citation
Physics and Astronomy · #Mechanical and Optical Resonators #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #quant-ph

paper · pdf · doi:10.1103/physreva.86.062517

published as Phys. Rev. A 86, 062517 (2012) · 20 pages, 3 figures

arxiv created 2012/11/14 · openalex publication_date 2012/12/28 · arxiv updated 2013/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to show that within the open-system framework the sum-over-modes approach of Casimir leads to the Lifshitz formula for the Casimir free energy. A general result applicable to arbitrary geometries is obtained through the use of Ford, Lewis, and O'Connell's remarkable formula. Additionally, we address the possibility of obtaining the Casimir energy as a sum over complex ``modes.'' We show in this case that the standard sum-over-modes formula must be suitably generalized to avert unphysical complex energies. Finally, we apply our results to several standard examples.

Citations

• The theory of molecular attractive forces between solids
• Density-matrix operatorial solution of the non-Markovian master equation for quantum Brownian motion
• New Developments in the Casimir Effect
• Thermal Agitation of Electric Charge in Conductors
• The Casimir effect within scattering theory
• The Casimir effect: Recent controversies and progress
• Comment on the sign of the Casimir force

Cited by

• Casimir effect [wikipedia]