2,072 research outputs found
Tkachenko modes in a superfluid Fermi gas at unitarity
We calculate the frequencies of the Tkachenko oscillations of a vortex
lattice in a harmonically trapped superfluid Fermi gas. We use the
elasto-hydrodynamic theory by properly accounting for the elastic constants,
the Thomas-Fermi density profile of the atomic cloud, and the boundary
conditions. Thanks to the Fermi pressure, which is responsible for larger cloud
radii with respect to the case of dilute Bose-Einstein condensed gases, large
vortex lattices are achievable in the unitary limit of infinite scattering
length, even at relatively small angular velocities. This opens the possibility
of experimentally observing vortex oscillations in the regime where the
dispersion relation approaches the Tkachenko law for incompressible fluids and
the mode frequency is almost comparable to the trapping frequencies.Comment: 5 pages, 1 figure; minor changes, now published as Phys. Rev. A 77,
021602(R) (2008
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
Dissipationless Phonon Hall Viscosity
We study the acoustic phonon response of crystals hosting a gapped
time-reversal symmetry breaking electronic state. The phonon effective action
can in general acquire a dissipationless "Hall" viscosity, which is determined
by the adiabatic Berry curvature of the electron wave function. This Hall
viscosity endows the system with a characteristic frequency, \omega_v; for
acoustic phonons of frequency \omega, it shifts the phonon spectrum by an
amount of order (\omega/\omega_v)^2 and it mixes the longitudinal and
transverse acoustic phonons with a relative amplitude ratio of \omega/\omega_v
and with a phase shift of +/- \pi/2, to lowest order in \omega/\omega_v. We
study several examples, including the integer quantum Hall states, the quantum
anomalous Hall state in Hg_{1-y}Mn_{y}Te quantum wells, and a mean-field model
for p_x + i p_y superconductors. We discuss situations in which the acoustic
phonon response is directly related to the gravitational response, for which
striking predictions have been made. When the electron-phonon system is viewed
as a whole, this provides an example where measurements of Goldstone modes may
serve as a probe of adiabatic curvature of the wave function of the gapped
sector of a system.Comment: 14 page
Vortex Lattice Inhomogeneity in Spatially Inhomogeneous Superfluids
A trapped degenerate Bose gas exhibits superfluidity with spatially
nonuniform superfluid density. We show that the vortex distribution in such a
highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The
inhomogeneity in vortex density, which diminishes in the rapid-rotation limit,
is driven by the discrete way vortices impart angular momentum to the
superfluid. This effect favors highest vortex density in regions where the
superfluid density is most uniform (e.g., the center of a harmonically trapped
gas). A striking consequence of this is that the boson velocity deviates from a
rigid-body form exhibiting a radial-shear flow past the vortex lattice.Comment: 5 RevTeX pgs,2 figures, published versio
Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions
After delineating the physical regimes which vortex lattices encounter in
rotating Bose-Einstein condensates as the rotation rate, , increases,
we derive the normal modes of the vortex lattice in two dimensions at zero
temperature. Taking into account effects of the finite compressibility, we find
an inertial mode of frequency , and a primarily transverse
Tkachenko mode, whose frequency goes from being linear in the wave vector in
the slowly rotating regime, where is small compared with the lowest
compressional mode frequency, to quadratic in the wave vector in the opposite
limit. We calculate the correlation functions of vortex displacements and
phase, density and superfluid velocities, and find that the zero-point
excitations of the soft quadratic Tkachenko modes lead in a large system to a
loss of long range phase correlations, growing logarithmically with distance,
and hence lead to a fragmented state at zero temperature. The vortex positional
ordering is preserved at zero temperature, but the thermally excited Tkachenko
modes cause the relative positional fluctuations to grow logarithmically with
separation at finite temperature. The superfluid density, defined in terms of
the transverse velocity autocorrelation function, vanishes at all temperatures.
Finally we construct the long wavelength single particle Green's function in
the rotating system and calculate the condensate depletion as a function of
temperature.Comment: 11 pages Latex, no figure
Theory of vortex-lattice melting in a one-dimensional optical lattice
We investigate quantum and temperature fluctuations of a vortex lattice in a
one-dimensional optical lattice. We discuss in particular the Bloch bands of
the Tkachenko modes and calculate the correlation function of the vortex
positions along the direction of the optical lattice. Because of the small
number of particles in the pancake Bose-Einstein condensates at every site of
the optical lattice, finite-size effects become very important. Moreover, the
fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous
density. As a result, the melting of the lattice occurs from the outside
inwards. However, tunneling between neighboring pancakes substantially reduces
the inhomogeneity as well as the size of the fluctuations. On the other hand,
nonzero temperatures increase the size of the fluctuations dramatically. We
calculate the crossover temperature from quantum melting to classical melting.
We also investigate melting in the presence of a quartic radial potential,
where a liquid can form in the center instead of at the outer edge of the
pancake Bose-Einstein condensates.Comment: 17 pages, 17 figures, submitted to Phys. Rev. A, references update
Yorke and Wright 3/2-stability theorems from a unified point of view
We consider a family of scalar delay differential equations ,
with a nonlinearity satisfying a negative feedback condition combined with
a boundedness condition. We present a global stability criterion for this
family, which in particular unifies the celebrated 3/2-conditions given for the
Yorke and the Wright type equations. We illustrate our results with some
applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS,
devoted to the fourth international conference on Dynamical Systems and
Differential Equations, held at UNC at Wilmington, May 2002. Minor changes
from the previous versio
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