527 research outputs found
Anderson localization in optical lattices with speckle disorder
We study the localization properties of non-interacting waves propagating in
a speckle-like potential superposed on a one-dimensional lattice. Using a
decimation/renormalization procedure, we estimate the localization length for a
tight-binding Hamiltonian where site-energies are square-sinc-correlated random
variables. By decreasing the width of the correlation function, the disorder
patterns approaches a -correlated disorder, and the localization length
becomes almost energy-independent in the strong disorder limit. We show that
this regime can be reached for a size of the speckle grains of the order of
(lower than) four lattice steps.Comment: 4 pages, 1 figur
Structure and stability of quasi-two-dimensional boson-fermion mixtures with vortex-antivortex superposed states
We investigate the equilibrium properties of a quasi-two-dimensional
degenerate boson-fermion mixture (DBFM) with a bosonic vortex-antivortex
superposed state (VAVSS) using a quantum-hydrodynamic model. We show that,
depending on the choice of parameters, the DBFM with a VAVSS can exhibit rich
phase structures. For repulsive boson-fermion (BF) interaction, the
Bose-Einstein condensate (BEC) may constitute a petal-shaped "core" inside the
honeycomb-like fermionic component, or a ring-shaped joint "shell" around the
onion-like fermionic cloud, or multiple segregated "islands" embedded in the
disc-shaped Fermi gas. For attractive BF interaction just below the threshold
for collapse, an almost complete mixing between the bosonic and fermionic
components is formed, where the fermionic component tends to mimic a bosonic
VAVSS. The influence of an anharmonic trap on the density distributions of the
DBFM with a bosonic VAVSS is discussed. In addition, a stability region for
different cases of DBFM (without vortex, with a bosonic vortex, and with a
bosonic VAVSS) with specific parameters is given.Comment: 8 pages,5 figure
Transmittivity of a Bose-Einstein condensate on a lattice: interference from period doubling and the effect of disorder
We evaluate the particle current flowing in steady state through a
Bose-Einstein condensate subject to a constant force in a quasi-onedimensional
lattice and to attractive interactions from fermionic atoms that are localized
in various configurations inside the lattice wells. The system is treated
within a Bose-Hubbard tight binding model by an out-of-equilibrium Green's
function approach. A new band gap opens up when the lattice period is doubled
by locating the fermions in alternate wells and yields an interference pattern
in the transmittivity on varying the intensity of the driving force. The
positions of the transmittivity minima are determined by matching the period of
Bloch oscillations and the time for tunnelling across the band gap. Massive
disorder in the distribution of the fermions will wash out the interference
pattern, but the same period doubling of the lattice can be experimentally
realized in a four-beam set-up. We report illustrative numerical results for a
mixture of 87Rb and 40K atoms in an optical lattice created by laser beams with
a wavelength of 763 nm.Comment: 13 pages, 5 figure
Demixing in mesoscopic boson-fermion clouds inside cylindrical harmonic traps: quantum phase diagram and role of temperature
We use a semiclassical three-fluid thermodynamic model to evaluate the
phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic
atoms at high dilution under harmonic confinement, assuming repulsive
boson-boson and boson-fermion interactions and including account of a bosonic
thermal cloud at finite temperature T. The finite system size allows three
different regimes for the equilibrium density profiles at T=0: a fully mixed
state, a partially mixed state in which the overlap between the boson and
fermion clouds is decreasing, and a fully demixed state where the two clouds
have zero overlap. We propose simple analytical rules for the two cross-overs
between the three regimes as functions of the physical system parameters and
support these rules by extensive numerical calculations. A universal ``phase
diagram'' expressed in terms of simple scaling parameters is shown to be valid
for the transition to the regime of full demixing, inside which we identify
several exotic configurations for the two phase-separated clouds in addition to
simple ones consisting of a core of bosons enveloped by fermions and "vice
versa". With increasing temperature the main role of the growing thermal cloud
of bosons is to transform some exotic configurations into more symmetric ones,
until demixing is ultimately lost. For very high values of boson-fermion
repulsive coupling we also report demixing between the fermions and the
thermally excited bosons.Comment: 11 pages, 8 figure
Collective excitations in trapped boson-fermion mixtures: from demixing to collapse
We calculate the spectrum of low-lying collective excitations in a gaseous
cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over
a range of the boson-fermion coupling strength extending from strongly
repulsive to strongly attractive. Increasing boson-fermion repulsions drive the
system towards spatial separation of its components (``demixing''), whereas
boson-fermion attractions drive it towards implosion (``collapse''). The
dynamics of the system is treated in the experimentally relevant collisionless
regime by means of a Random-Phase approximation and the behavior of a
mesoscopic cloud under isotropic harmonic confinement is contrasted with that
of a macroscopic mixture at given average particle densities. In the latter
case the locations of both the demixing and the collapse phase transitions are
sharply defined by the same stability condition, which is determined by the
softening of an eigenmode of either fermionic or bosonic origin. In contrast,
the transitions to either demixing or collapse in a mesoscopic cloud at fixed
confinement and particle numbers are spread out over a range of boson-fermion
coupling strength, and some initial decrease of the frequencies of a set of
collective modes is followed by hardening as evidenced by blue shifts of most
eigenmodes. The spectral hardening can serve as a signal of the impending
transition and is most evident when the number of bosons in the cloud is
relatively large. We propose physical interpretations for these dynamical
behaviors with the help of suitably defined partial compressibilities for the
gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex
Two-dimensional gravitation and Sine-Gordon-Solitons
Some aspects of two-dimensional gravity coupled to matter fields, especially
to the Sine-Gordon-model are examined. General properties and boundary
conditions of possible soliton-solutions are considered. Analytic
soliton-solutions are discovered and the structure of the induced space-time
geometry is discussed. These solutions have interesting features and may serve
as a starting point for further investigations.Comment: 23 pages, latex, references added, to appear in Phys.Rev.
Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap
Using an asymptotic phase representation of the particle density operator
in the one-dimensional harmonic trap, the part which describes the Friedel oscillations is extracted. The
expectation value with respect to the interacting
ground state requires the calculation of the mean square average of a properly
defined phase operator. This calculation is performed analytically for the
Tomonaga-Luttinger model with harmonic confinement. It is found that the
envelope of the Friedel oscillations at zero temperature decays with the
boundary exponent away from the classical boundaries. This
value differs from that known for open boundary conditions or strong pinning
impurities. The soft boundary in the present case thus modifies the decay of
Friedel oscillations. The case of two components is also discussed.Comment: Revised version to appear in Journal of Physics B: Atomic, Molecular
and Optical Physic
Back Reaction of Strings in Self-Consistent String Cosmology
We compute the string energy-momentum tensor and {\bf derive} the string
equation of state from exact string dynamics in cosmological spacetimes.
and -dimensional universes are treated for any expansion factor
. Strings obey the perfect fluid relation with
three different behaviours: (i) {\it Unstable} for with
growing energy density , {\bf negative} pressure, and ; (ii){\it Dual} for , with , {\bf positive} pressure and (as radiation); (iii) {\it
Stable} for with , {\bf vanishing}
pressure and (as cold matter). We find the back reaction effect
of these strings on the spacetime and we take into account the quantum string
decay through string splitting. This is achieved by considering {\bf
self-consistently} the strings as matter sources for the Einstein equations, as
well as for the complete effective string equations. String splitting
exponentially suppress the density of unstable strings for large . The
self-consistent solution to the Einstein equations for string dominated
universes exhibits the realistic matter dominated behaviour for large times and the radiation dominated behaviour for early times. De Sitter universe does not emerge as
solution of the effective string equations. The effective string action
(whatever be the dilaton, its potential and the central charge term) is not the
appropriate framework in which to address the question of string driven
inflation.Comment: 29 pages, revtex, LPTHE-94-2
Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions
We investigate the particle and kinetic energy densities of harmonically
trapped fermion gases at zero temperature in arbitrary dimensions. We derive
analytically a differential equation connecting these densities, which so far
have been proven only in one or two dimensions, and give other interesting
relations involving several densities or the particle density alone. We show
that in the asymptotic limit of large particle numbers, the densities go over
into the semi-classical Thomas-Fermi (TF) densities. Hereby the Fermi energy to
be used in the TF densities is identified uniquely. We derive an analytical
expansion for the remaining oscillating parts and obtain very simple closed
forms for the leading-order oscillating densities. Finally, we show that the
simple TF functional relation between kinetic and particle
density is fulfilled also for the asymptotic quantum densities and
including their leading-order oscillating terms.Comment: LaTeX, 22 pages with 6 figures (*.eps), to be submitted to J. Phys.
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