2,032 research outputs found
Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates
We calculate the in-plane modes of the vortex lattice in a rotating Bose
condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The
Tkachenko mode frequency goes from linear in the wavevector, , for lattice
rotational velocities, , much smaller than the lowest sound wave
frequency in a finite system, to quadratic in in the opposite limit. The
system also supports an inertial mode of frequency . The
calculated frequencies are in good agreement with recent observations of
Tkachenko modes at JILA, and provide evidence for the decrease in the shear
modulus of the vortex lattice at rapid rotation.Comment: 4 pages, 2 figure
Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates
We establish the general equations of motion for the modes of a vortex
lattice in a rapidly rotating Bose-Einstein condensate in three dimensions,
taking into account the elastic energy of the lattice and the vortex line
bending energy. As in two dimensions, the vortex lattice supports Tkachenko and
gapped sound modes. In contrast, in three dimensions the Tkachenko mode
frequency at long wavelengths becomes linear in the wavevector for any
propagation direction out of the transverse plane. We compute the correlation
functions of the vortex displacements and the superfluid order parameter for a
homogeneous Bose gas of bounded extent in the axial direction. At zero
temperature the vortex displacement correlations are convergent at large
separation, but at finite temperatures, they grow with separation. The growth
of the vortex displacements should lead to observable melting of vortex
lattices at higher temperatures and somewhat lower particle number and faster
rotation than in current experiments. At zero temperature a system of large
extent in the axial direction maintains long range order-parameter correlations
for large separation, but at finite temperatures the correlations decay with
separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle
density - vortex density coupling and the correct value of the shear modulu
Tkachenko modes as sources of quasiperiodic pulsar spin variations
We study the long wavelength shear modes (Tkachenko waves) of triangular
lattices of singly quantized vortices in neutron star interiors taking into
account the mutual friction between the superfluid and the normal fluid and the
shear viscosity of the normal fluid. The set of Tkachenko modes that propagate
in the plane orthogonal to the spin vector are weakly damped if the coupling
between the superfluid and normal fluid is small. In strong coupling, their
oscillation frequencies are lower and are undamped for small and moderate shear
viscosities. The periods of these modes are consistent with the observed
~100-1000 day variations in spin of PSR 1828-11.Comment: 7 pages, 3 figures, uses RevTex, v2: added discussion/references,
matches published versio
Dislocation-Mediated Melting in Superfluid Vortex Lattices
We describe thermal melting of the two-dimensional vortex lattice in a
rotating superfluid by generalizing the Halperin and Nelson theory of
dislocation-mediated melting. and derive a melting temperature proportional to
the renormalized shear modulus of the vortex lattice. The rigid-body rotation
of the superfluid attenuates the effects of lattice compression on the energy
of dislocations and hence the melting temperature, while not affecting the
shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous
rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the
temperature -- rotation rate plane, and infer that the thermal melting
temperature should lie below the Bose-Einstein transition temperature.Comment: 9 pages, 2 figure
State and problems of green tourism managers' training in Sumy region
Nowadays Ukraine and Sumy region, in particular, have extremely high potential in the development of green or «rural» tourism. However, despite this fact, the Sumy area is not a «place of pilgrimage» for international tourists. Our manors are the most popular only among national guests. One of the reasons of such situation is insufficient vocational training of owners and managers, working in Ukraine’s hospitality industry. That is why training of highly qualified specialists, who can compete both in national and international tourism service market, is one of the most important aspects of the formation and development of green tourism in Ukraine
Robust propagation direction of stresses in a minimal granular packing
By employing the adaptive network simulation method, we demonstrate that the
ensemble-averaged stress caused by a local force for packings of frictionless
rigid beads is concentrated along rays whose slope is consistent with unity:
forces propagate along lines at 45 degrees to the horizontal or vertical. This
slope is shown to be independent of polydispersity or the degree to which the
system is sheared. Further confirmation of this result comes from fitting the
components of the stress tensor to the null stress constitutive equation. The
magnitude of the response is also shown to fall off with the -1/2 power of
distance. We argue that our findings are a natural consequence of a system that
preserves its volume under small perturbations.Comment: 8 pages, 6 figures. Some extra clarification and minor improvements.
To appear in EPJ-
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