Arbitrary compact shapes

Spheres

"Casimir Forces between Arbitrary Compact Objects,"

Emig, Graham, Jaffe, & Kardar, Phys. Rev. Lett. 99, 170403 (2007)

Generalizes the multi-pole expansion from electrostatics to fluctuating sources

Full results are available for (frequency-dependent) dielectrics, as well as metals

Can be generalized to arbitrary compact shapes:

The shape and material properties are encoded in the scattering properties of the object.

Orientation dependence

  Forces and torques between non-spherical compact objects; e.g. prolate and oblate spheroids:

Two prolate (metallic) spheroids (cigar-shaped)

Two oblate (metallic) spheroids (pancake shaped)

  The leading asymptotic behavior is dictated by the polarizability of the object, and is implicit in

R. Balian and B. Duplantier, Ann. Phys. 104, 300 (1977).

There is no leading orientation dependence for a spheroid above a (perfect reflector) plate:

Numerical results indicate that a Neumann spheroid flips its orientation on moving away from the surface!