Thermal Casimir Force


yellow ball Finite-size contribution of long-wavelength fluctuations at criticality:

yellow ball The thermal analog of the Casimir effect should lead to observable effects in wetting phenomena near critical points:

M.P. Nightingale and J.O. Indekeu, Phys. Rev. Lett. 54, 1824 (1985)

Wetting by a Superfluid Film

red ballGarcia and Chan monitored thickness of a wetting film of helium near the superfluid transition.

"Critical Fluctuation-Induced Thinning of He Films near the Superfluid Transition,"

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

yellow ballThickness of the film (denoted by d) is obtained by minimizing its energy, as

yellow ballThe film is thinner at the transition, and in the superfluid phase

Phonons in the superfluid

red ballThe superfluid phase of helium supports phonons ("mass-less" Goldstone modes)


yellow ballThe interaction resulting from (thermal) fluctuations of these modes is:

H. Li . Kardar, Phys. Rev. Lett. 67, 3275 (1991); Phys. Rev. A 46, 6490 (1992) 

Surface Undulations

red ballCan surface fluctuations account for the (additional) thinning of the superfluid film?

"Casimir Forces, Surface Fluctuations, and Thinning of Superfluid Films,"

Zandi, Rudnick, & Kardar, Phys. Rev. Lett. 93, 155302 (2004)

yellow ballThe normal fluid is clamped due to viscosity, while the superfluid has a velocity

yellow ballUndulations of the surface set up a superfluid velocity field that extends through the film, and vanishes at the substrate. The corresponding Hamiltonian, and free energy, give

yellow ballThere is a corresponding force:

[Dzyaloshinskii, Lifshitz, Pitaevskii (1961); Mahale and Cole (1986)]

yellow ballThe net effect of phonons and surface undulations appear to account for the thinning of superfluid films: