Cylinder-Plate geometry


H.B.G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948)

"The Influence of Retardation on the London-van der Waals Forces"

For asymptotically large separations H, the attractive force between a sphere (radius R) and a plate is

Sukenik, Boshier, Cho, Sandoghdar, and Hinds, Phys. Rev. Lett. 70, 560 (1993)

"Measurement of the Casimir-Polder force"

from deflection of sodium atoms passing through a cavity.


What is the force between a cylinder (wire) and a plate?

 Analogy with parallel plates suggests an energy proportional to area:

 Analogy with the Casimir-Polder results suggests (in the limit R << H ):

 Proximity force approximation (exact in the limit R >> H ) gives:

 We find the following exact results (in the limit R >> H ):

due to long wave-length charge fluctuations along the length of the cylinder.

T. Emig, R.L. Jaffe, M. Kardar, and A. Scardicchio, Phys. Rev. Lett. 96, 080403 (2006).

 


Unexpected non-monotonicity due to three-body effects:

"Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders," S.J. Rahi, A. Rodriguez, T. Emig, R.L. Jaffe, S.G. Johnson, M. Kardar, Phys. Rev. A 77, 030101(R) (2008)