582 research outputs found
Collisionless Dynamics in Two-Dimensional Bosonic Gases
We study the dynamics of dilute and ultracold bosonic gases in a quasi
two-dimensional (2D) configuration and in the collisionless regime. We adopt
the 2D Landau-Vlasov equation to describe a three-dimensional gas under very
strong harmonic confinement along one direction. We use this effective equation
to investigate the speed of sound in quasi 2D bosonic gases, i.e. the sound
propagation around a Bose-Einstein distribution in collisionless 2D gases. We
derive coupled algebraic equations for the real and imaginary parts of the
sound velocity, which are then solved taking also into account the equation of
state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless
critical temperature we find that there is rapid growth of the imaginary
component of the sound velocity which implies a strong Landau damping. Quite
remarkably, our theoretical results are in good agreement with very recent
experimental data obtained with a uniform 2D Bose gas of Rb atoms.Comment: 5 pages, 2 figures, improved introduction and conclusions, accepted
for publication in Physical Review
Superfluidity, Sound Velocity and Quasi Condensation in the 2D BCS-BEC Crossover
We study finite-temperature properties of a two-dimensional superfluid made
of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the
region below the critical temperature of the
Berezinskii-Kosterlitz-Thouless phase transition, where there is
quasi-condensation, by analyzing the effects of phase and amplitude
fluctuations of the order parameter. In particular, we calculate the superfluid
fraction, the sound velocity and the quasi-condensate fraction as a function of
the temperature and of the binding energy of fermionic pairs.Comment: 7 pages, 4 figures, improved version to be published in Phys. Rev.
Emulation of lossless exciton-polariton condensates by dual-core optical waveguides: Stability, collective modes, and dark solitons
We propose a possibility to simulate the exciton-polariton (EP) system in the
lossless limit, which is not currently available in semiconductor
microcavities, by means of a simple optical dual-core waveguide, with one core
carrying the nonlinearity and operating close to the
zero-group-velocity-dispersion (GVD) point, and the other core being linear and
dispersive. Both 2D and 1D EP systems may be emulated by means of this optical
setting. In the framework of this system, we find that, while the uniform state
corresponding to the lower branch of the nonlinear dispersion relation is
stable against small perturbations, the upper branch is always subject to the
modulational instability (MI). The stability and instability are verified by
direct simulations too. We analyze collective excitations on top of the stable
lower-branch state, which include a Bogoliubov-like gapless mode and a gapped
one. Analytical results are obtained for the corresponding sound velocity and
energy gap. The effect of a uniform phase gradient (superflow) on the stability
is considered too, with a conclusion that the lower-branch state becomes
unstable above a critical wavenumber of the flux. Finally, we demonstrate that
the stable 1D state may carry robust dark solitons.Comment: 11 pages, 9 figures, to appear in Phys. Rev.
Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
It is well known that the category of super Lie groups (SLG) is equivalent to
the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we
define the category of unitary representations (UR's) of a super Lie group. We
give an extension of the classical inducing construction and Mackey
imprimitivity theorem to this setting. We use our results to classify the
irreducible unitary representations of semidirect products of super translation
groups by classical Lie groups, in particular of the super Poincar\'e groups in
arbitrary dimension. Finally we compare our results with those in the physical
literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre
Delign
Beliaev damping of the Goldstone mode in atomic Fermi superfluids
Beliaev damping in a superfluid is the decay of a collective excitation into
two lower frequency collective excitations; it represents the only decay mode
for a bosonic collective excitation in a superfluid at T = 0. The standard
treatment for this decay assumes a linear spectrum, which in turn implies that
the final state momenta must be collinear to the initial state. We extend this
treatment, showing that the inclusion of a gradient term in the Hamiltonian
yields a realistic spectrum for the bosonic excitations; we then derive a
formula for the decay rate of such excitations, and show that even moderate
nonlinearities in the spectrum can yield substantial deviations from the
standard result. We apply our result to an attractive Fermi gas in the BCS-BEC
crossover: here the low-energy bosonic collective excitations are density
oscillations driven by the phase of the pairing order field. These collective
excitations, which are gapless modes as a consequence of the Goldstone
mechanism, have a spectrum which is well established both theoretically and
experimentally, and whose linewidth, we show, is determined at low temperatures
by the Beliaev decay mechanism.Comment: 8 pages, 3 figure
Positive operator valued measures covariant with respect to an irreducible representation
Given an irreducible representation of a group G, we show that all the
covariant positive operator valued measures based on G/Z, where Z is a central
subgroup, are described by trace class, trace one positive operators.Comment: 9 pages, Latex2
Competition between symmetry breaking and onset of collapse in weakly coupled atomic condensates
We analyze the symmetry breaking of matter-wave solitons in a pair of
cigar-shaped traps coupled by tunneling of atoms. The model is based on a
system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs).
Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in
coupled cubic equations, in the present model the SSB competes with the onset
of collapse in this system. Stability regions of symmetric and asymmetric
solitons, as well as the collapse region, are identified in the parameter space
of the system.Comment: Physical Review A, in pres
Normal completely positive maps on the space of quantum operations
Quantum supermaps are higher-order maps transforming quantum operations into
quantum operations. Here we extend the theory of quantum supermaps, originally
formulated in the finite dimensional setting, to the case of higher-order maps
transforming quantum operations with input in a separable von Neumann algebra
and output in the algebra of the bounded operators on a given separable Hilbert
space. In this setting we prove two dilation theorems for quantum supermaps
that are the analogues of the Stinespring and Radon-Nikodym theorems for
quantum operations. Finally, we consider the case of quantum superinstruments,
namely measures with values in the set of quantum supermaps, and derive a
dilation theorem for them that is analogue to Ozawa's theorem for quantum
instruments. The three dilation theorems presented here show that all the
supermaps defined in this paper can be implemented by connecting devices in
quantum circuits.Comment: 47 pages (in one-column format), including new results about quantum
operations on separable von Neumann algebra
On the morphology and botanical affinities of Lundbladispora balme 1963 in the permian of the Paraná basin, Brazil
Morphological variations observed in specimens so far identifield as Lundbladispora braziliensis (PANT & SRIVASTAVA) MARQUES-TOIGO & PONS 1974, have led to the identification of one more species for the genus: Lundbladispora riobonitensis sp. nov. Both species constitute frequent and characteristic forms in the southern Brazilian Gondwana coals. Possible affinities of these miospores with the Selaginellales are also discussedVariações morfológicas observadas em espécimens até então identificadas como Lundbladispora braziliensis (PANT & SRIVASTAVA) MARQUES-TOIGO & PONS 1974, levaram a identificação de mais uma espécie para o gênero: Lundbladispora riobonitensis sp. nov. As espécies constituem formas freqüentes e características nos carvões Gondwânicos Sul-brasileiros. Também são discutidas possíveis afinidades desses miosporos com Selaginellale
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