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We present an analytical solution of the Ginzburgs $Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point, and we revisit the corresponding experiments in light of our findings. We find reasonably good agreement between the $Psi$-theory predictions and the experimental data. Our calculated force is attractive, and the largest absolute value of the scaling function is $1.848$, while experiment yields $1.30$. The position of the extremum is predicted to be at $x=(L/xi_0)(T/T_lambda-1)^{1/ u}=pi$, while experiment is consistent with $x=3.8$. Here $L$ is the thickness of the film, $T_lambda$ is the bulk critical temperature and $xi_0$ is the correlation length amplitude of the system for $T>T_lambda$.
We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburgs $Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider thr
Recent experimental data for the complete wetting behavior of pure 4He and of 3He-4He mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda-transition an
We develop an analytic theory of strong anisotropy of the energy spectra in the thermally-driven turbulent counterflow of superfluid He-4. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy f
The second layer of $^4$He films adsorbed on a graphite substrate is an excellent experimental platform to study the interplay between superfluid and structural orders. Here, we report a rigid two-frequency torsional oscillator study on the second la
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic detail