Fluctuation-Induced Force


red ballRadiation: Virtual photons (QED fluctuations) at low temperatures:                    

yellow ball"On the attraction between two perfectly conducting plates,"

H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

yellow ball Quantum fluctuations of electromagnetic field in the vacuum between leads to an attractive force between perfect mirrors

        

yellow ball"The Theory of Molecular Attractive Forces Between Solids,"

E.M. Lifshitz, Soviet Physics 2, 73 (1956),

 Generalizes the result by considering fluctuating current sources in the bodies, and to finite temperatures.

yellow ball "Pressure" =>"Interaction"; Force per unit area of the wall is

greenarrowAttractive

Strongly dependent on the shape of the container

yellow ball Now confirmed in myriad experiments.


red ballParticles: There are corresponding quantum fluctuations at low temperatures, but more interesting

classical interactions emerge when interactions lead to large correlation lengths  .

(Long ranged, as opposed to short-range depletion forces.)

yellow ballFinite-size behavior of free energy confined between plates takes a universal form at criticality

M.E. Fisher and P.-G. de Gennes, C. R. Acad. Sci. Ser. B 287, 207 (1978)

  

Experimental confirmation for colloidal particles in critical oil/water mixture.

Hertlein, Helden, Gambassi, Dietrich & Bechinger, Nature 451, 172 (2008)

bluearrowGoldstone mode fluctuations following continuous symmetry breaking are long-range correlated

H. Li . Kardar, Phys. Rev. Lett. 67, 3275 (1991)

Experimental confirmation in wetting of superfluid films

yellow ballR. Garcia and M.H.W. Chan, Phys. Rev. Lett. 83, 1187 (1999)