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Register a new userExact solution of Ginzburgs $Psi$-theory for the Casimir force in $^4$He superfluid films
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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 $T>T_lambda$.
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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 and the tricritical end point, respectively, which can be attributed to critical Casimir forces f_C. We calculate the scaling functions vartheta of f_C within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of vartheta deduced from the experimental data and predicts the crossover behavior between the tricritical point and the lambda-transition of pure 4He which are connected by a line of critical points. The formation of a soft-mode phase within the wetting films gives rise to a pronounced maximum of f_C below the tricritical point as observed experimentally. Near the tricritical point we find logarithmic corrections ~L^(-3)(ln L)^(1/2) for the leading behavior of vartheta dominating the contributions from the background dispersion forces.
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 flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by the numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiment, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade-dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters. This article is a part of the theme issue Scaling the turbulence edifice.
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 layer as a function of temperature and $^4$He atomic density. We find that the superfluid density is independent of frequency, which can be interpreted as unequivocal evidence of genuine superfluidity. The phase diagram established in this work reveals that a superfluid phase coexists with hexatic density-wave correlation and a registered solid phase. This suggests the second layer as a candidate for hosting two exotic quantum ground states: the spatially modulated superfluid and supersolid phases, resulting from the interplay between superfluid and structural orders.
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 details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.
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