Brandeis University Physics
Colloquium 24
November 2009
The Shape Dependence of
Fluctuation-Induced Forces
KITP
workshop on: The
Theory and Practice of Fluctuation-Induced Interactions
Summary
I.
Casimir force:
theory and experiment, & application
II. Thermal
fluctuations:
Critical
Casimir force observed for colloids in a binary mixture
The
wetting film of helium becomes thinner, at and below the superfluid transition
Fluctuation-induced
forces from phonons and surface modes account for the thinning in the superfluid
phase
Missing
a quantitative theory (including dimensional crossovers) below the (bulk)
critical temperature
III. Corrugated
surfaces: normal and lateral forces
The
Proximity Force/Pairwise summation breaks down for short-wavelength deformations.
A
lateral force is demonstrated for electromagnetic fluctuations, but more
precise measurements are needed.
The
lateral force from critical fluctuations has been used to manipulate colloidal
particles.
Beyond
the perturbative limit by numerical or analytical schemes.
Precision
experiments of force between an atom and a corrugated surface
(spin ecko measurements by Maarten
De Kievert)
IV. Cylinder-plate:
Importance of dimensionality (for metals)
Exact
expression- dominated at large separations by long wavelength charge fluctuations
Non-monotonic
3-body effects
Carbon nanotubes,
and the importance of material properties
V. Compact
objects
General
scattering-based for dealing with arbitrary shapes and dielectric properties
Complete
expressions for spheres at any separation
Orientation
dependence, torques, ... for spheroids
Applying
the formalism to real materials by including their dielectric properties
(ala Lifshitz), and finite temperatures
New solvable geometries: paraboloids, wedges, cones, ...
VI. Repulsive forces? sphere,
piston
The
force on a rectangular piston is always attractive.
In
the limit of small height, the force can be calculated for a piston of
arbitrary cross section.
Ruling out a "repulsive force" for arbitrary shapes (Earnshaw theorem)
Acknowledgements
Hao Li, Ramin Golestanian
Thorsten Emig,
Andreas Hanke
Roya Zandi, Aviva
Shackell, Lincoln Chayes, Joseph Rudnick
Mark Hertzberg,
Antonello Scardicchio, Noah Graham, Robert Jaffe
Jamal Rahi, Alex
Rodriguez, Steve Johnson
