4,460 research outputs found
Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices
We report a multiple-site mean-field analysis of the zero-temperature phase
diagram for ultracold bosons in realistic optical superlattices. The system of
interacting bosons is described by a Bose-Hubbard model whose site-dependent
parameters reflect the nontrivial periodicity of the optical superlattice. An
analytic approach is formulated based on the analysis of the stability of a
fixed-point of the map defined by the self-consistency condition inherent in
the mean-field approximation. The experimentally relevant case of the period-2
one-dimensional superlattice is briefly discussed. In particular, it is shown
that, for a special choice of the superlattice parameters, the half-filling
insulator domain features an unusual loophole shape that the single-site
mean-field approach fails to capture.Comment: 7 pages, 1 figur
Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model
We consider a Bose-Hubbard model with an arbitrary hopping term and provide
the boundary of the insulating phase thereof in terms of third-order strong
coupling perturbative expansions for the ground state energy. In the general
case two previously unreported terms occur, arising from triangular loops and
hopping inhomogeneities, respectively. Quite interestingly the latter involves
the entire spectrum of the hopping matrix rather than its maximal eigenpair,
like the remaining perturbative terms. We also show that hopping
inhomogeneities produce a first order correction in the local density of
bosons. Our results apply to ultracold bosons trapped in confining potentials
with arbitrary topology, including the realistic case of optical superlattices
with uneven hopping amplitudes. Significant examples are provided. Furthermore,
our results can be extented to magnetically tuned transitions in Josephson
junction arrays.Comment: 5 pages, 2 figures,final versio
Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices
Recent advances in random matrix theory have spurred the adoption of
eigenvalue-based detection techniques for cooperative spectrum sensing in
cognitive radio. Most of such techniques use the ratio between the largest and
the smallest eigenvalues of the received signal covariance matrix to infer the
presence or absence of the primary signal. The results derived so far in this
field are based on asymptotical assumptions, due to the difficulties in
characterizing the exact distribution of the eigenvalues ratio. By exploiting a
recent result on the limiting distribution of the smallest eigenvalue in
complex Wishart matrices, in this paper we derive an expression for the
limiting eigenvalue ratio distribution, which turns out to be much more
accurate than the previous approximations also in the non-asymptotical region.
This result is then straightforwardly applied to calculate the decision
threshold as a function of a target probability of false alarm. Numerical
simulations show that the proposed detection rule provides a substantial
performance improvement compared to the other eigenvalue-based algorithms.Comment: 7 pages, 2 figures, submitted to IEEE Communications Letter
On the Structure of the Bose-Einstein Condensate Ground State
We construct a macroscopic wave function that describes the Bose-Einstein
condensate and weakly excited states, using the su(1,1) structure of the
mean-field hamiltonian, and compare this state with the experimental values of
second and third order correlation functions.Comment: 10 pages, 2 figure
Quantum signatures of self-trapping transition in attractive lattice bosons
We consider the Bose-Hubbard model describing attractive bosonic particles
hopping across the sites of a translation-invariant lattice, and compare the
relevant ground-state properties with those of the corresponding
symmetry-breaking semiclassical nonlinear theory. The introduction of a
suitable measure allows us to highlight many correspondences between the
nonlinear theory and the inherently linear quantum theory, characterized by the
well-known self-trapping phenomenon. In particular we demonstrate that the
localization properties and bifurcation pattern of the semiclassical
ground-state can be clearly recognized at the quantum level. Our analysis
highlights a finite-number effect.Comment: 9 pages, 8 figure
Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping
The zero-temperature phase diagram for ultracold Bosons in a random 1D
potential is obtained through a site-decoupling mean-field scheme performed
over a Bose-Hubbard (BH) Hamiltonian whose hopping term is considered as a
random variable. As for the model with random on-site potential, the presence
of disorder leads to the appearance of a Bose-glass phase. The different phases
-i.e. Mott insulator, superfluid, Bose-glass- are characterized in terms of
condensate fraction and superfluid fraction. Furthermore, the boundary of the
Mott lobes are related to an off-diagonal Anderson model featuring the same
disorder distribution as the original BH Hamiltonian.Comment: 7 pages, 6 figures. Submitted to Laser Physic
Strong-field tidal distortions of rotating black holes: III. Embeddings in hyperbolic 3-space
In previous work, we developed tools for quantifying the tidal distortion of
a black hole's event horizon due to an orbiting companion. These tools use
techniques which require large mass ratios (companion mass much smaller
than black hole mass ), but can be used for arbitrary bound orbits, and for
any black hole spin. We also showed how to visualize these distorted black
holes by embedding their horizons in a global Euclidean 3-space,
. Such visualizations illustrate interesting and important
information about horizon dynamics. Unfortunately, we could not visualize black
holes with spin parameter : such holes cannot
be globally embedded into . In this paper, we overcome this
difficulty by showing how to embed the horizons of tidally distorted Kerr black
holes in a hyperbolic 3-space, . We use black hole perturbation
theory to compute the Gaussian curvatures of tidally distorted event horizons,
from which we build a two-dimensional metric of their distorted horizons. We
develop a numerical method for embedding the tidally distorted horizons in
. As an application, we give a sequence of embeddings into
of a tidally interacting black hole with spin . A
small amplitude, high frequency oscillation seen in previous work shows up
particularly clearly in these embeddings.Comment: 10 pages, 6 figure
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