Fluctuation-Induced Interaction

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


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 relevant

classical interactions emerge when inter-particle forces 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)