Plethora of Fluctuation-Induced Forces (FIF)

red ball  The general ingredients are:

yellow ball Long-range correlated fluctuations in ambient medium (Quantum, thermal, active?)

yellow ball Disturbance of fluctuations by inclusions in the medium (boundary constraints or otherwise).

red ball Long range correlation also arise due to continous broken symmetry (Goldstone) modes,

leading to suggestions of FIF in several correlated fluids in soft matter: 

Liquid Crystals, polyelectrolyte solutions, polymers, membranes, ...

yellow ball Such forces are difficult to observe as  FIF << (direct elastic forces)

yellow ball Contributions of FIF due to superfluid Phonons and Capillary modes have been observed.

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: