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.      Thermal Casimir force:   

 Critical Casimir force observed for colloids in a binary mixture    

III.    Repulsion/Levitation?

 Metamaterials, las invisibility cloaks:     

 Geometry: 

IV.   Earnshaw's theorem:             

  No levitation is possible with electrostatic interactions:  

 No levitation is possible with Casimir forces with dielectric composites: 

V.     Membranes inclusionse: 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.   

Repulsion and stability with wedges:                     

 Experimental demonstrations?

IV.   Out of equilibrium levitation is possible:

 Classical radiation pressure:                                

                  Non-classical (near field) counterpart

Acknowledgments

Thosten Emig, Giuseppe Bimonte, Noah Graham, Robert Jaffe

Jamal Rahi, Mohammad Maghrebi

Vlad Golyk, Matthias Krüger

M. Hertzberg, A. Scardicchio, A. Rodriguez, S. Johnson, U. Mohideen, R. Zandi

Next (Outline) Outline Casimir force Thermal Casimir Repulsion? Earnshaw's theorem Membrane inclusions Out of equilibrium Summary