Phase separation in the bosonic Hubbard model with ring exchange

We show that soft core bosons in two dimensions with a ring exchange term exhibit a tendency for phase separation. This observation suggests that the thermodynamic stability of normal bose liquid phases driven by ring exchange should be carefully examined.Comment: 4 pages, 6 figure

Modelling of the radiative properties of an opaque porous ceramic layer

Solid Oxide Fuel Cells (SOFCs) operate at temperatures above 1,100 K where radiation effects can be significant. Therefore, an accurate thermal model of an SOFC requires the inclusion of the contribution of thermal radiation. This implies that the thermal radiative properties of the oxide ceramics used in the design of SOFCs must be known. However, little information can be found in the literature concerning their operating temperatures. On the other hand, several types of ceramics with different chemical compositions and microstructures for designing efficient cells are now being tested. This is a situation where the use of a numerical tool making possible the prediction of the thermal radiative properties of SOFC materials, whatever their chemical composition and microstructure are, may be a decisive help. Using this method, first attempts to predict the radiative properties of a lanthanum nickelate porous layer deposited onto an yttria stabilized zirconium substrate can be reported

Asymptotic Properties of Approximate Bayesian Computation

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, its limiting shape, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including supplementary materia

State diagrams for harmonically trapped bosons in optical lattices

We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the density and a local compressibility to identify the phases present in the inhomogeneous density profiles. We emphasize the use of the "characteristic density" to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low (T<t/2), temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.Comment: 10 pages, 11 figures, published versio

Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice

We study the dipole oscillations of strongly correlated 1D bosons, in the hard-core limit, on a lattice, by an exact numerical approach. We show that far from the regime where a Mott insulator appears in the system, damping is always present and increases for larger initial displacements of the trap, causing dramatic changes in the momentum distribution, $n_k$. When a Mott insulator sets in the middle of the trap, the center of mass barely moves after an initial displacement, and $n_k$ remains very similar to the one in the ground state. We also study changes introduced by the damping in the natural orbital occupations, and the revival of the center of mass oscillations after long times.Comment: 4 pages, 5 figures, published versio

Ring Exchange and Phase Separation in the Two-dimensional Boson Hubbard model

We present Quantum Monte Carlo simulations of the soft-core bosonic Hubbard model with a ring exchange term K. For values of K which exceed roughly half the on-site repulsion U, the density is a non-monotonic function of the chemical potential, indicating that the system has a tendency to phase separate. This behavior is confirmed by an examination of the density-density structure factor and real space images of the boson configurations. Adding a near-neighbor repulsion can compete with phase separation, but still does not give rise to a stable normal Bose liquid.Comment: 12 pages, 23 figure

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}