173 research outputs found
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
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
Detection of Optical Flares on the Selected G-M Dwarfs from Long-term Photometric Series
We have carried out a search for flares from the analysis of light curves for
12 active G, K, and M dwarfs. As sources of data we used ground-based
observations in 2000-2020 from the photometric databases ASAS, SuperWASP, KWS.
Events of low-amplitude brightening (Delta V < 0.25 mag), which possibly could
be flares, were revealed for 11 stars. A large number of such increases in
brightness were found on K dwarfs. Events of increasing in V-magnitudes to 0.5
mag or more were detected on light curves of one G star, BE Cet, and two M
dwarfs. For three flares we could follow their development with time. We have
estimated the duration of these flares; they lasted more than an hour, but less
than 3 hours. In most cases we could not determine a lifetime of the suggested
flares, but we believe that most of the probable flares on the investigated
cool dwarfs are short-lived, on the order of several minutes.Comment: 6 pages, 3 figures, 2 table
Thermodynamics of a trapped interacting Bose gas and the renormalization group
We apply perturbative renormalization group theory to the symmetric phase of
a dilute interacting Bose gas which is trapped in a three-dimensional harmonic
potential. Using Wilsonian energy-shell renormalization and the
epsilon-expansion, we derive the flow equations for the system. We relate these
equations to the flow for the homogeneous Bose gas. In the thermodynamic limit,
we apply our results to study the transition temperature as a function of the
scattering length. Our results compare well to previous studies of the problem.Comment: 14 pages, 5 figure
Phase-fluctuating 3D condensates in elongated traps
We find that in very elongated 3D trapped Bose gases, even at temperatures
far below the BEC transition temperature Tc, the equilibrium state will be a 3D
condensate with fluctuating phase (quasicondensate). At sufficiently low
temperatures the phase fluctuations are suppressed and the quasicondensate
turns into a true condensate. The presence of the phase fluctuations allows for
extending thermometry of Bose-condensed gases well below those established in
current experiments.Comment: 5 pages REVTeX, 3 figures, misprints correcte
Anderson localization in Bose-Einstein condensates
The understanding of disordered quantum systems is still far from being
complete, despite many decades of research on a variety of physical systems. In
this review we discuss how Bose-Einstein condensates of ultracold atoms in
disordered potentials have opened a new window for studying fundamental
phenomena related to disorder. In particular, we point our attention to recent
experimental studies on Anderson localization and on the interplay of disorder
and weak interactions. These realize a very promising starting point for a
deeper understanding of the complex behaviour of interacting, disordered
systems.Comment: 15 pages review, to appear in Reports on Progress in Physic
Excitation-assisted inelastic processes in trapped Bose-Einstein condensates
We find that inelastic collisional processes in Bose-Einstein condensates
induce local variations of the mean-field interparticle interaction and are
accompanied by the creation/annihilation of elementary excitation. The physical
picture is demonstrated for the case of three body recombination in a trapped
condensate. For a high trap barrier the production of high energy trapped
single particle excitations results in a strong increase of the loss rate of
atoms from the condensate.Comment: 4 pages, no figure
Hydrodynamic behavior in expanding thermal clouds of Rb-87
We study hydrodynamic behavior in expanding thermal clouds of Rb-87 released
from an elongated trap. At our highest densities the mean free path is smaller
than the radial size of the cloud. After release the clouds expand
anisotropically. The cloud temperature drops by as much as 30%. This is
attributed to isentropic cooling during the early stages of the expansion. We
present an analytical model to describe the expansion and to estimate the
cooling. Important consequences for time-of-flight thermometry are discussed.Comment: 7 pages with 2 figure
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