Casimir forces between cylinders and plates

Sahand Jamal Rahi 1, Thorsten Emig 2, 3, Robert L. Jaffe 4, Mehran Kardar 1

Physical Review A: Atomic, Molecular and Optical Physics 78 (2008) 012104

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.

  • 1. Department of Physics,
    Massachusetts Institute of Technology
  • 2. Institut für Theoretische Physik,
    Universität zu Köln
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. Center for Theoretical Physics and Laboratory for Nuclear Science,
    Massachusetts Institute of Technology