Perturbative Expansions

A systematic perturbative calculation of the Casimir force is possible for gently deformed parallel plates, in the limit

by path integral methods (for thermal scalar fields, and by decomposing the QED field into TE and TM modes).

"Probing the Strong Boundary Shape Dependence of the Casimir Force,"

T. Emig, A. Hanke, R. Golestanian, and M. Kardar, Phys. Rev. Lett. 87, 260402 (2001)

Example: Force between a flat and a sinusoidally corrugated plate:

"Demonstration of the Nontrivial Boundary Dependence of the Casimir Force,"

A. Roy and U. Mohideen, Phys. Rev. Lett. 82, 4380 (1999)

Many further works have explored breakdown of PFA with corrugated plates

 "Measurement of the Casimir Force between a Gold Sphere and a Silicon Surface with Nanoscale Trench Arrays,"

H.B. Chan et. al., Phys. Rev. Lett. 101, 030401 (2008)

 

 What do gentle perturbations have to do with PFA corrections?

Next (Derivative Expansion) Outline Proximity Force Approx. Perturbative Expansion Derivative Expansion Casimir Polder force Spectroscopic probe Summary