5,705 research outputs found
Dimensional reduction and localization of a Bose-Einstein condensate in a quasi-1D bichromatic optical lattice
We analyze the localization of a Bose-Einstein condensate (BEC) in a
one-dimensional bichromatic quasi-periodic optical-lattice potential by
numerically solving the 1D Gross-Pitaevskii equation (1D GPE). We first derive
the 1D GPE from the dimensional reduction of the 3D quantum field theory of
interacting bosons obtaining two coupled differential equations (for axial
wavefuction and space-time dependent transverse width) which reduce to the 1D
GPE under strict conditions. Then, by using the 1D GPE we report the
suppression of localization in the interacting BEC when the repulsive
scattering length between bosonic atoms is sufficiently large.Comment: 10 pages, 2 figures, presented at the 7th Workshop on Quantum Chaos
and Localisation Phenomena, May 29-31, 2015 - Warsaw, Poland; to be published
in a special issue of Acta Physica Polonica
Quantum scattering in one dimension
A self-contained discussion of nonrelativistic quantum scattering is
presented in the case of central potentials in one space dimension, which will
facilitate the understanding of the more complex scattering theory in two and
three dimensions. The present discussion illustrates in a simple way the
concept of partial-wave decomposition, phase shift, optical theorem and
effective-range expansion.Comment: 8 page
Dynamics of gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice
We suggest and study the stable disk- and cigar-shaped gap solitons of a
dipolar Bose-Einstein condensate of Cr atoms localized in the lowest
band gap by three optical-lattice (OL) potentials along orthogonal directions.
The one-dimensional version of these solitons of experimental interest confined
by an OL along the dipole moment direction and harmonic traps in transverse
directions is also considered. Important dynamics of (i) breathing oscillation
of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a
moving lattice along axial direction demonstrates the stability of gap
solitons. A movie clip of dragging of three-dimensional gap soliton is
included.Comment: To see the dragging movie clip please download sourc
Large-scale anomalies in the cosmic microwave background as signatures of non-Gaussianity
We derive a general expression for the probability of observing deviations
from statistical isotropy in the cosmic microwave background (CMB) if the
primordial fluctuations are non-Gaussian and extend to superhorizon scales. The
primary motivation is to properly characterize the monopole and dipole
modulations of the primordial power spectrum that are generated by the coupling
between superhorizon and subhorizon perturbations. Unlike previous proposals
for generating the hemispherical power asymmetry, we do not assume that the
power asymmetry results from a single large superhorizon mode. Instead, we
extrapolate the observed power spectrum to superhorizon scales and compute the
power asymmetry that would result from a specific realization of non-Gaussian
perturbations on scales larger than the observable universe. Our study
encompasses many of the scenarios that have been put forward as possible
explanations for the CMB hemispherical power asymmetry. We confirm our analytic
predictions for the probability of a given power asymmetry by comparing them to
numerical realizations of CMB maps. We find that non-local models of
non-Gaussianity and scale-dependent local non-Gaussianity produce
scale-dependent modulations of the power spectrum, thereby potentially
producing both a monopolar and a dipolar power modulation on large scales. We
then provide simple examples of finding the posterior distributions for the
parameters of the bispectrum from the observed monopole and dipole modulations.Comment: 21 pages, 11 figures; v2: minor changes to match the PRD accepted
versio
Using data network metrics, graphics, and topology to explore network characteristics
Yehuda Vardi introduced the term network tomography and was the first to
propose and study how statistical inverse methods could be adapted to attack
important network problems (Vardi, 1996). More recently, in one of his final
papers, Vardi proposed notions of metrics on networks to define and measure
distances between a network's links, its paths, and also between different
networks (Vardi, 2004). In this paper, we apply Vardi's general approach for
network metrics to a real data network by using data obtained from special data
network tools and testing procedures presented here. We illustrate how the
metrics help explicate interesting features of the traffic characteristics on
the network. We also adapt the metrics in order to condition on traffic passing
through a portion of the network, such as a router or pair of routers, and show
further how this approach helps to discover and explain interesting network
characteristics.Comment: Published at http://dx.doi.org/10.1214/074921707000000058 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Effective Nonlinear Schr\"odinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
In the case of tight transverse confinement (cigar-shaped trap) the
three-dimensional (3D) nonlinear Schr\"odinger equation, describing superfluid
Fermi atoms at unitarity (infinite scattering length ), is
reduced to an effective one-dimensional form by averaging over the transverse
coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger
equation, which produces results in good agreement with the original 3D one. In
the limit of small and large fermion number the nonlinearity is of simple
power-law type. A similar reduction of the 3D theory to a two-dimensional form
is also performed for a tight axial confinement (disk-shaped trap). The
resultant effective 2D nonpolynomial equation also produces results in
agreement with the original 3D equation and has simple power-law nonlinearity
for small and large . For both cigar- and disk-shaped superfluids our
nonpolynomial Schr\"odinger equations are quite attractive for phenomenological
application.Comment: 22 pages, 5 figure
Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate
We discuss a computational mechanism for the generation of a stationary dark
soliton, or black soliton, in a trapped Bose-Einstein condensate using the
Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction.
It is demonstrated that the black soliton with a "notch" in the probability
density with a zero at the minimum is a stationary eigenstate of the GP
equation and can be efficiently generated numerically as a nonlinear
continuation of the first vibrational excitation of the GP equation in both
attractive and repulsive cases in one and three dimensions for pure harmonic as
well as harmonic plus optical-lattice traps. We also demonstrate the stability
of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy
Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity
We establish universal behavior in temperature dependencies of some
observables in -wave BCS superconductivity in the presence of a weak
wave. There also could appear a second second-order phase transition. As
temperature is lowered past the usual critical temperature , a less
ordered superconducting phase is created in wave, which changes to a more
ordered phase in wave at (). The presence of two phase
transitions manifest in two jumps in specific heat at and . The
temperature dependencies of susceptibility, penetration depth, and thermal
conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures
Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice
By numerical simulation of the time-dependent Gross-Pitaevskii equation we
show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC)
vortex can be localized in a three-dimensional bichromatic quasi-periodic
optical-lattice (OL) potential generated by the superposition of two
standing-wave polarized laser beams with incommensurate wavelengths. This is a
generalization of the localization of a BEC in a one-dimensional bichromatic OL
as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We
demonstrate the stability of the localized state by considering its time
evolution in the form of a stable breathing oscillation in a slightly altered
potential for a large period of time. {Finally, we consider the localization of
a BEC in a random 1D potential in the form of several identical repulsive
spikes arbitrarily distributed in space
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