Sharp Shapes

Method

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

 "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)

  Shapes amenable to exact treatment of electromagnetic scattering:

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

 Sharp shapes wedge, and cone,

[M.F. Maghrebi, S.J. Rahi, N. Graham, T. Emig, R.L. Jaffe, & M. Kardar, preprint (2010)]

 Wedge:

 Cone:

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

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

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

Next (Polymer force) Outline QED Casimir force Sharp Shapes Polymer force Phantom polymer Self-avoiding polymer Many polymers Summary