On the Possibility of "Dry" Friction in Superfluid He-4

We propose a possible microscopic explanation of the exhaustion of \rho_s of helium-II on the wall at T>T_{c} = 0.5 - 1 K and predict a possibility of the existence in He-II of the "dry" friction at T < T_{c}. Both of the effects connect with that the energy of the 2D-rotons is 2K less then the energy of 3D-rotons, so the wall is a potential well for the last ones.Comment: 3 pages, 1 figur

Quasimomentum of an elementary excitation for a system of point bosons under zero boundary conditions

As is known, an elementary excitation of a many-particle system with boundaries is not characterized by a definite momentum. We obtain the formula for the quasimomentum of an elementary excitation for a one-dimensional system of $N$ spinless point bosons under zero boundary conditions (BCs). In this case, we use the Gaudin's solutions obtained with the help of the Bethe ansatz. We have also found the dispersion laws of the particle-like and hole-like excitations under zero BCs. They coincide with the known dispersion laws obtained for periodic BCs.Comment: 7 pages, 1 figure, v5: accepted versio

Microstructure of He II in the presence of boundaries

We have studied the microstructure of a system of interacting Bose particles under zero boundary conditions and have found two possible orderings. One ordering is traditional and is characterized by the Bogolyubov dispersion law E^2 = (h^2 k^2/2m)^{2} + qn\nu(k)[h^2 k^2/m] (with q=1) at a weak interaction. The second one is new and is characterized by the same dispersion law, but with q=2^{-f}, where $f$ is the number of noncyclic coordinates. At a weak interaction, the ground-state energy is less for the new solution. The boundaries affect the bulk microstructure due to the difference of the topologies of closed and open systems.Comment: 17 pages, 2 figures, v5: explanations are revised; v6: journal versio

Acoustic modes in He I and He II in the presence of an alternating electric field

By solving the equations of ordinary and two-fluid hydrodynamics, we study the oscillatory modes in isotropic nonpolar dielectrics He I and He II in the presence of an alternating electric field $\textbf{E}=E_{0}\textbf{i}_{z}\sin{(k_{0}z-\omega_{0} t)}$. The electric field and oscillations of the density become ``coupled,'' since the density gradient causes a spontaneous polarization $\textbf{P}_{s}$, and the electric force contains the term $(\textbf{P}_{s}\nabla)\textbf{E}$. The analysis shows that the field $\textbf{E}$ changes the velocities of first and second sounds, propagating along $\textbf{E}$, by the formula $u_{j}\approx c_{j}+\chi_{j} E_{0}^{2}$ (where $j=1, 2$; $c_{j}$ is the velocity of the $j$-th sound for $E_{0}=0$, and $\chi_{j}$ is a constant). We have found that the field $\textbf{E}$ jointly with a wave of the first (second) sound $(\omega,k)$ should create in He II hybrid acousto-electric (thermo-electric) density waves $(\omega + l \omega_{0},k + lk_{0})$, where $l=\pm 1, \pm 2, \ldots$. The amplitudes of acousto-electric waves and the quantity $|u_{1}-c_{1}|$ are negligibly small, but they should increase in the resonance way at definite $\omega$ and $\omega_{0}$. Apparently, the first resonance corresponds to the decay of a photon into two phonons with the transfer of a momentum to the whole liquid. Therefore, the spectrum of an electromagnetic signal should contain a narrow absorption line like that in the M\"{o}ssbauer effect.Comment: 23 pages, 1 figure; v3: accepted versio

Symmetry properties of the ground state of the system of interacting spinless bosons

We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: $\rho(\textbf{r})=const$. Moreover, under the perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density.Comment: 21 pages, no figures; v2: sections are rearranged; a discussion of fractional statistics is added in section

On the mutual polarization of two He-4 atoms

We propose a simple method based on the standard quantum-mechanical perturbation theory to calculate the mutual polarization of two atoms He^4.Comment: 9 pages, 1 table; the article is revised and the calculation is essentially refined; v4: final version, the Introduction is delete

Theory of a Narrow roton Absorption Line in the Spectrum of a Disk-Shaped SHF Resonator

We calculate the probability of the birth of a circular phonon (c-phonon) in He II by a c-photon of the resonator. It is shown that this probability has sharp maxima at frequencies, where the effective group velocity of the c-phonon is equal to zero; the density of states of c-phonons strongly grows at such frequencies. For He II, these frequencies correspond to a roton and a maxon. From the probability of the c-roton birth, we calculate the roto line width which is found to approximately agree with the experimental one. We conclude that the roton line observed in the super-high-frequency (SHF) absorption spectrum of helium is related to the birth of c-rotons. A possible interpretation of the Stark effect observed for the roton line is also proposed.Comment: 13 pages, 1 figure, v2: journal variant, several minor correction