2007/10/31 by Serge Reynaud, Paulo A. Maia Neto, Astrid Lambrecht
Engineering · Physics and Astronomy · #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #Thermal Radiation and Cooling Technologies #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/16/164004
published as Journal of Physics A 41 (2008) 164004 · corrected typos, added references, QFEXT'07 special issue in J. Phys. A
arxiv created 2008/01/22 · openalex publication_date 2008/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We review the relation between the Casimir effect and geometry, emphasizing deviations from the commonly used proximity force approximation (PFA). We use, to this aim, the scattering formalism which is nowadays the best tool available for accurate and reliable theory–experiment comparisons. We first recall the main lines of this formalism when the mirrors can be considered to obey specular reflection. We then discuss the more general case where non-planar mirrors give rise to non-specular reflection with wavevectors and field polarizations mixed. The general formalism has already been fruitfully used for evaluating the effect of roughness on the Casimir force as well as the lateral Casimir force or Casimir torque appearing between corrugated surfaces. In this paper, we focus our attention to the case of the lateral force which should make possible in the future an experimental demonstration of the nontrivial (i.e. beyond PFA) interplay of the geometry and Casimir effect.