Thermal Fluctuations


Finite Size Scaling at Criticality

Correlation lengths diverge at a critical point:

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

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

The parameter c is a universal constant, related (in 2d) to the central charge in conformal field theory.

H.W.J. Blote, J.L. Cardy, and M.P. Nightingale, Phys. Rev. Lett. 56, 742 (1986)


Superfluid Helium

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

.

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

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


Wetting by a Superfluid Film

Garcia 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)

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

The film is thinner at the transition, and in the superfluid phase


Surface Undulations

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

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

R. Zandi, J. Rudnick, and M. Kardar, Phys. Rev. Lett. 93, 155302 (2004)

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

Undulations 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

There is a corresponding force:

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

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

Recent results (May 2006) confirm collapse of scaled curves on less rough substrates.