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

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 $\bar{d}\leq 2$), while it is shown that BEC always occurs for $\bar{d}>2$.Comment: 4 pages, 10 figure