936 research outputs found
Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices
We present an analytic description of the finite-temperature phase diagram of
the Bose-Hubbard model, successfully describing the physics of cold bosonic
atoms trapped in optical lattices and superlattices. Based on a standard
statistical mechanics approach, we provide the exact expression for the
boundary between the superfluid and the normal fluid by solving the
self-consistency equations involved in the mean-field approximation to the
Bose-Hubbard model. The zero-temperature limit of such result supplies an
analytic expression for the Mott lobes of superlattices, characterized by a
critical fractional filling.Comment: 8 pages, 6 figures, submitted to Phys. Rev.
Attractive ultracold bosons in a necklace optical potential
We study the ground state properties of the Bose-Hubbard model with
attractive interactions on a M-site one-dimensional periodic -- necklace-like
-- lattice, whose experimental realization in terms of ultracold atoms is
promised by a recently proposed optical trapping scheme, as well as by the
control over the atomic interactions and tunneling amplitudes granted by
well-established optical techniques. We compare the properties of the quantum
model to a semiclassical picture based on a number-conserving su(M) coherent
state, which results into a set of modified discrete nonlinear Schroedinger
equations. We show that, owing to the presence of a correction factor ensuing
from number conservation, the ground-state solution to these equations provides
a remarkably satisfactory description of its quantum counterpart not only -- as
expected -- in the weak-interaction, superfluid regime, but even in the deeply
quantum regime of large interactions and possibly small populations. In
particular, we show that in this regime, the delocalized, Schroedinger-cat-like
quantum ground state can be seen as a coherent quantum superposition of the
localized, symmetry-breaking ground-state of the variational approach. We also
show that, depending on the hopping to interaction ratio, three regimes can be
recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear
in Phys. Rev.
Percolation on the average and spontaneous magnetization for q-states Potts model on graph
We prove that the q-states Potts model on graph is spontaneously magnetized
at finite temperature if and only if the graph presents percolation on the
average. Percolation on the average is a combinatorial problem defined by
averaging over all the sites of the graph the probability of belonging to a
cluster of a given size. In the paper we obtain an inequality between this
average probability and the average magnetization, which is a typical extensive
function describing the thermodynamic behaviour of the model
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Shot, scene and keyframe ordering for interactive video re-use
This paper presents a complete system for shot and scene detection in broadcast videos, as well as a method to select the best representative key-frames, which could be used in new interactive interfaces for accessing large collections of edited videos. The final goal is to enable an improved access to video footage and the re-use of video content with the direct management of user-selected video-clips
Microscopic energy flows in disordered Ising spin systems
An efficient microcanonical dynamics has been recently introduced for Ising
spin models embedded in a generic connected graph even in the presence of
disorder i.e. with the spin couplings chosen from a random distribution. Such a
dynamics allows a coherent definition of local temperatures also when open
boundaries are coupled to thermostats, imposing an energy flow. Within this
framework, here we introduce a consistent definition for local energy currents
and we study their dependence on the disorder. In the linear response regime,
when the global gradient between thermostats is small, we also define local
conductivities following a Fourier dicretized picture. Then, we work out a
linearized "mean-field approximation", where local conductivities are supposed
to depend on local couplings and temperatures only. We compare the approximated
currents with the exact results of the nonlinear system, showing the
reliability range of the mean-field approach, which proves very good at high
temperatures and not so efficient in the critical region. In the numerical
studies we focus on the disordered cylinder but our results could be extended
to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure
Propagation of Discrete Solitons in Inhomogeneous Networks
In many physical applications solitons propagate on supports whose
topological properties may induce new and interesting effects. In this paper,
we investigate the propagation of solitons on chains with a topological
inhomogeneity generated by the insertion of a finite discrete network on the
chain. For networks connected by a link to a single site of the chain, we
derive a general criterion yielding the momenta for perfect reflection and
transmission of traveling solitons and we discuss solitonic motion on chains
with topological inhomogeneities
Bose-Einstein condensation in inhomogeneous Josephson arrays
We show that spatial Bose-Einstein condensation of non-interacting bosons
occurs in dimension d < 2 over discrete structures with inhomogeneous topology
and with no need of external confining potentials. Josephson junction arrays
provide a physical realization of this mechanism. The topological origin of the
phenomenon may open the way to the engineering of quantum devices based on
Bose-Einstein condensation. The comb array, which embodies all the relevant
features of this effect, is studied in detail.Comment: 4 pages, 5 figure
Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks
Topological inhomogeneity gives rise to spectral anomalies that can induce
Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies
consist in energy regions composed of an infinite number of states with
vanishing weight in the thermodynamic limit (hidden states). Here we present a
rigorous result giving the most general conditions for BEC on complex networks.
We prove that the presence of hidden states in the lowest region of the
spectrum is the necessary and sufficient condition for condensation in low
dimension (spectral dimension ), while it is shown that BEC
always occurs for .Comment: 4 pages, 10 figure
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