25,289 research outputs found
Thermodynamic properties of a dipolar Fermi gas
Based on the semi-classical theory, we investigate the thermodynamic
properties of a dipolar Fermi gas. Through a self-consistent procedure, we
numerically obtain the phase space distribution function at finite temperature.
We show that the deformations in both momentum and real space becomes smaller
and smaller as one increases the temperature. For homogeneous case, we also
calculate pressure, entropy, and heat capacity. In particular, at low
temperature limit and in weak interaction regime, we obtain an analytic
expression for the entropy, which agrees qualitatively with our numerical
result. The stability of a trapped gas at finite temperature is also explored
Dynamical properties of a trapped dipolar Fermi gas at finite temperature
We investigate the dynamical properties of a trapped finite-temperature
normal Fermi gas with dipole-dipole interaction. For the free expansion
dynamics, we show that the expanded gas always becomes stretched along the
direction of the dipole moment. In addition, we present the temperature and
interaction dependences of the asymptotical aspect ratio. We further study the
collapse dynamics of the system by suddenly increasing the dipolar interaction
strength. We show that, in contrast to the anisotropic collapse of a dipolar
Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically
when the system becomes globally unstable. We also explore the interaction and
temperature dependences for the frequencies of the low-lying collective
excitations.Comment: 11 pages, 7 figure
Making vortices in dipolar spinor condensates via rapid adiabatic passage
We propose to the create vortices in spin-1 condensates via magnetic
dipole-dipole interaction. Starting with a polarized condensate prepared under
large axial magnetic field, we show that by gradually inverting the field,
population transfer among different spin states can be realized in a controlled
manner. Under optimal condition, we generate a doubly quantized vortex state
containing nearly all atoms in the condensate. The resulting vortex state is a
direct manifestation of the dipole-dipole interaction and spin textures in
spinor condensates. We also point out that the whole process can be
qualitatively described by a simple rapid adiabatic passage model.Comment: 4 pages, 4 figure
The two-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves
Two atoms in an optical lattice may be made to interact strongly at higher
partial waves near a Feshbach resonance. These atoms, under appropriate
constraints, could be bosonic or fermionic. The universal energy spectrum
for such a system, with a caveat, is presented in this paper, and checked with
the spectrum obtained by direct numerical integration of the Schr\"odinger
equation. The results reported here extend those of Yip for p-wave resonance
(Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a
universal expression for the spectrum for the higher partial waves.Comment: To be published in Physical Review
Conjecture on the Avoidance of the Big Crunch
KKLT give a mechanism to generate de Sitter vacua in string theory. And
recently, the scenario, {\em landscape}, is suggested to explain the problem of
the cosmological constant. In this scenario, the cosmological constant is a de
Sitter vacuum. The vacuum is metastable and would decay into an anti-de Sitter
vacuum finally. Then the catastrophe of the big crunch appears. In this paper
by conjecturing the physics at the Planck scale, we modify the definition of
the Hawking temperature. Hinted by this modification, we modify the Friedmann
equation. we find that this avoid the singularity and gives a bouncing
cosmological model.Comment: 6 page
Singlet and triplet BCS pairs in a gas of two-species fermionic polar molecules
We investigate the BCS pairing in a mixture of fermionic polar molecules with
two different hyperfine states. We derive a set of coupled gap equations and
find that this system supports both spin-singlet and -triplet BCS pairs. We
also calculate the critical temperatures and the angular dependence of order
parameters. In addition, by tuning short-range interaction between
inter-species molecules, the transition between singlet and triplet paired
states may be realized.Comment: 5 pages, 4 figure
Locality of not-so-weak coloring
Many graph problems are locally checkable: a solution is globally feasible if
it looks valid in all constant-radius neighborhoods. This idea is formalized in
the concept of locally checkable labelings (LCLs), introduced by Naor and
Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree
graphs, every LCL problem belongs to one of the following classes:
- "Easy": solvable in rounds with both deterministic and
randomized distributed algorithms.
- "Hard": requires at least rounds with deterministic and
rounds with randomized distributed algorithms.
Hence for any parameterized LCL problem, when we move from local problems
towards global problems, there is some point at which complexity suddenly jumps
from easy to hard. For example, for vertex coloring in -regular graphs it is
now known that this jump is at precisely colors: coloring with colors
is easy, while coloring with colors is hard.
However, it is currently poorly understood where this jump takes place when
one looks at defective colorings. To study this question, we define -partial
-coloring as follows: nodes are labeled with numbers between and ,
and every node is incident to at least properly colored edges.
It is known that -partial -coloring (a.k.a. weak -coloring) is easy
for any . As our main result, we show that -partial -coloring
becomes hard as soon as , no matter how large a we have.
We also show that this is fundamentally different from -partial
-coloring: no matter which we choose, the problem is always hard
for but it becomes easy when . The same was known previously
for partial -coloring with , but the case of was open
Structural phase transitions of vortex matter in an optical lattice
We consider the vortex structure of a rapidly rotating trapped atomic
Bose-Einstein condensate in the presence of a co-rotating periodic optical
lattice potential. We observe a rich variety of structural phases which reflect
the interplay of the vortex-vortex and vortex-lattice interactions. The lattice
structure is very sensitive to the ratio of vortices to pinning sites and we
observe structural phase transitions and domain formation as this ratio is
varied.Comment: 4 pages, 3 figure
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