12 research outputs found
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 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 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
. The electric field
and oscillations of the density become ``coupled,'' since the density gradient
causes a spontaneous polarization , and the electric force
contains the term . The analysis shows that
the field changes the velocities of first and second sounds,
propagating along , by the formula (where ; is the velocity of the -th sound for
, and is a constant). We have found that the field
jointly with a wave of the first (second) sound
should create in He II hybrid acousto-electric (thermo-electric) density waves
, where . The
amplitudes of acousto-electric waves and the quantity are
negligibly small, but they should increase in the resonance way at definite
and . 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: . 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