Equilibrium Pressure & Fluctuation-Induced Force


red ball Particles:  Pressure is a function of state.

         

yellow ball Force per unit area of the wall is a bulk property;

independent of the shape of the container and potentials at the wall

independent of the dynamics of the particles (momentum integrations)

yellow ball For a dilute gas:      (non-universal corrections)s


red ball Radiation:  Photon density is temperature dependent:

Stefan-Boltzmann law of black-body pressure:


red ballCasimir Force: 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 Since 1995 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)

Long-range correlations lead to long-range fluctuation-induced forces. (Universal?)



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)