Non-Equilibrium Force

  Consider forces between two spheres at different temperatures:

 "Non-equilibrium Casimir forces: Spheres and sphere-plate,"

M. Krüger, T. Emig,G. Bimonte and M. Kardar, Europhys. Lett. 95, 21002 (2011)

 Whereas the nonequilibrium force falls off as 1/d⁶, the non-equilibrium force decays as 1/d². ( * )

 The non-equilibrium force can be attractive and repulsive.  ( * )

 Unlike in thermal equilibrium, there are points of stable levitation.  ( * )

 Forces are not equal and opposite, with points of equal force in the same direction!  ( * )

  Example of non-equilibrium Casimir levitation:

 A hot microsphere can levitate on top of a cold plate.

 If it cools down (including heat transfer) the sphere will fall down.

 

Next (Dynamic) Outline Casimir force Repulsion? Scattering approach Earnshaw's theorem Out of equilibrium Heat Radiation Force Dynamic Summary