Scale-Invariant Shapes


Method

red ball Casimir force between multiple objects of different shapes and material properties can be related to scattering amplitudes of electromagnetic fields from individual bodies.

yellow ball "Scattering theory approach to electrodynamic Casimir forces,"

S.J. Rahi, T. Emig, N. Graham, R.L. Jaffe, and M. Kardar, Phys. Rev. D 80, 085021 (2009)

red ball  Shapes amenable to exact treatment of electromagnetic scattering:

yellow ball Plane, sphere, cylinder (circular, parabolic, elliptic), and

yellow ball Sharp shapes wedge, and cone,

"Analytical results on Casimir forces for conductors with edges and tips,"

M.F. Maghrebi, S.J. Rahi, N. Graham, T. Emig, R.L. Jaffe, & M. Kardar, PNAS 108, 6867 (2011)

red ball Wedge:

red ball Cone:

yellow ball For a thin cone (needle), the force vanishes as the inverse logarithm of the opening angle

yellow ball There is a strong temperature dependence (above figure is at a distance of 1 micrometer)

yellow ball The force is of the order of femto Newtons at this separation, but increases rapidly at shorter separations.