**Fluctuation-Induced Interaction**

**Radiation:** Virtual photons (QED fluctuations) at low temperatures:

"On the attraction between two perfectly conducting plates,"

Quantum fluctuations of electromagnetic field in the vacuum between leads to an

attractive forcebetween perfect mirrors

"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.

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

Attractive

Strongly dependent on the shape of the container

Now confirmed in myriad experiments.

**Particles:** 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.)

Finite-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)Goldstone 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

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