225 research outputs found
Vortex structures of rotating Bose-Einstein condensates in anisotropic harmonic potential
We found an analytical solution for the vortex structure in a rapidly
rotating trapped Bose-Einstein condensate in the lowest Landau level
approximation. This solution is exact in the limit of a large number of
vortices and is obtained for the case of anisotropic harmonic potential. For
the case of symmetric harmonic trap when the rotation frequency is equal to the
trapping frequency, the solution coincides with the Abrikosov triangle vortex
lattice in type-II superconductors.
In a general case the coarse grained density is found to be close to the
Thomas-Fermi profile, except the vicinity of edges of a condensate cloud.Comment: 7 pages, 3 figure
Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model
We study finite size effects for the gap of the quasiparticle excitation
spectrum in the weakly interacting regime one-dimensional Hubbard model with
on-site attraction. Two type of corrections to the result of the thermodynamic
limit are obtained. Aside from a power law (conformal) correction due to
gapless excitations which behaves as , where is the number of
lattice sites, we obtain corrections related to the existence of gapped
excitations. First of all, there is an exponential correction which in the
weakly interacting regime () behaves as in the extreme limit of ,
where is the hopping amplitude, is the on-site energy, and
is the gap in the thermodynamic limit. Second, in a finite
size system a spin-flip producing unpaired fermions leads to the appearance of
solitons with non-zero momenta, which provides an extra (non-exponential)
contribution . For moderate but still large values of
, these corrections significantly increase and may
become comparable with the conformal correction. Moreover, in the case
of weak interactions where , the exponential correction
exceeds higher order power law corrections in a wide range of parameters,
namely for , and so does
even in a wider range of . For sufficiently small number of particles,
which can be of the order of thousands in the weakly interacting regime, the
gap is fully dominated by finite size effects.Comment: 17 pages, 5 figure
Zero sound in a two-dimensional dipolar Fermi gas
We study zero sound in a weakly interacting 2D gas of single-component
fermionic dipoles (polar molecules or atoms with a large magnetic moment)
tilted with respect to the plane of their translational motion. It is shown
that the propagation of zero sound is provided by both mean field and many-body
(beyond mean field) effects, and the anisotropy of the sound velocity is the
same as the one of the Fermi velocity. The damping of zero sound modes can be
much slower than that of quasiparticle excitations of the same energy. One thus
has wide possibilities for the observation of zero sound modes in experiments
with 2D fermionic dipoles, although the zero sound peak in the structure
function is very close to the particle-hole continuum.Comment: 15 pages, 2 figure
One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction
We consider a one-dimensional (1D) two-component atomic Fermi gas with
contact interaction in the even-wave channel (Yang-Gaudin model) and study the
effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within
one of the components. Starting from the microscopic Hamiltonian, we derive an
effective field theory for the spin degrees of freedom using the bosonization
technique. It is shown that at a critical value of the odd-wave interaction
there is a first-order phase transition from a phase with zero total spin and
zero magnetization to the spin-segregated phase where the magnetization locally
differs from zero.Comment: 18 pages, 3 fugures; references adde
Stripe phase: analytical results for weakly coupled repulsive Hubbard model
Motivated by the stripe developments in cuprates, we review some analytical
results of our studies of the charge- and spin density modulations (CDW and
SDW) in a weakly coupled one dimensional repulsive electron system on a
lattice. It is shown that close to half filling, in the high temperature regime
above the mean field transition temperature, short range repulsions favor
charge density fluctuations with wave vectors bearing special relations with
those of the spin density fluctuations. In the low temperature regime, not only
the wave vectors, but also the mutual phases of the CDW and SDW become coupled
due to a quantum interference phenomenon, leading to the stripe phase
instability in a quasi one-dimensional repulsive electron system. It is shown
that away from half filling periodic lattice potential causes cooperative
condensation of the spin and charge superlattices. "Switching off" this
potential causes vanishing of the stripe order. The leading spin-charge
coupling term in the effective Landau functional is derived microscopically.
Results of the 1D renormalization group (parquet) analysis away from half
filling are also presented, which indicate transient-scale correlations
resembling the mean-field pattern. Farther, the self-consistent solution for
the spin-charge solitonic superstructure in a quasi-one-dimensional electron
system is obtained in the framework of the Hubbard model as a function of hole
doping and temperature. Possible relationship with the stripe phase
correlations observed in high T_c cuprates is discussed.Comment: 29 pages,10 figures, Late
Vortex structures in rotating Bose-Einstein condensates
We present an analytical solution for the vortex lattice in a rapidly
rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and
discuss deviations from the Thomas-Fermi density profile. This solution is
exact in the limit of a large number of vortices and is obtained for the cases
of circularly symmetric and narrow channel geometries. The latter is realized
when the trapping frequencies in the plane perpendicular to the rotation axis
are different from each other and the rotation frequency is equal to the
smallest of them. This leads to the cancelation of the trapping potential in
the direction of the weaker confinement and makes the system infinitely
elongated in this direction. For this case we calculate the phase diagram as a
function of the interaction strength and rotation frequency and identify the
order of quantum phase transitions between the states with a different number
of vortex rows.Comment: 17 pages, 12 figures, with addition
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