Summary

I.       Casimir force in QED:       

 High precision experimental precision achieved with scanning probes                        

       Applications require control of this force, and its shape dependence                                                            

II.     Casimir force of Critical fluctuations:   

 Critical Casimir force observed for colloids in a binary mixture    

III.     Casimir force of Goldstone modes:   

               The wetting film of helium becomes thinner

 Fluctuation-induced forces from phonons and surface modes        

account for the thinning in the film in the superfluid phase

 Quantitative theory (including dimensional crossovers) below the (bulk) critical temperature

IV.    Membranes inclusions: Forces between inclusions

 Due to membrane shape fluctuations                               

                        Due to membrane concentration fluctuations    

Conformal invariance enables computing forces for arbitrary shapes in any critical system.

 Experimental demonstrations?

V.     Scale-Invariant Shapes:  

 Analytical results for the objects with edges (wedge) and tips (cone)   

 The forces on the cone (AFM tip) are possibly at the edge of experimental sensitivity.

VI.   Entropic Force on Polymers:                                  

 Universal force amplitude for scale-invariant shapes related to other polymer exponents

Phantom polymers: Exact exponent

Self-avoiding polymers: Results from epsilon-expansion

 Potentially measurable force for multiple polymers.         

Acknowledgements

G. Bimonte, T. Emig, N. Graham, R. Jaffe

Jamal Rahi, Mohammad Maghrebi

R. Golestanian, A. Scardicchio, H. Li, Y. Kantor, J. Rudnik, R. Zandi

Next (Off Equilibrium) Outline Casimir force in QED Thermal Casimir Repulsion? Scattering approach Earnshaw's theorem Summary