Corrugated Surfaces
Normal force
A common method
for dealing with non-flat geometries is the Proximity Force
Approximation, which in effect assumes an effective Casimir interactions
between locally parallel pairs on points on the two surfaces, and sums over
all such pairs.
For a sinusoidally
corrugated plate:
"Demonstration
of the Nontrivial Boundary Dependence of the Casimir Force,"
Path-Integral formulation
Integrate over
all configurations of the field in the space between deformed plates (or
other boundaries)
Thermal fluctuations: Scalar field with Dirichlet boundary conditions
TM modes (Dirichlet) + TE modes (Neumann)
"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)
Lateral force
A sideways
force to "align" the two plates at b=λ/2 :
"Demonstration
of the Lateral Casimir Force,"
F. Chen, U. Mohideen, et. al , Phys. Rev. Lett. 88, 101801 (2002)
