Fisher zeros in the Kallen–Lehmann approach to 3D Ising model

The distribution of the Fisher zeros in the Kallen–Lehmann approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen–Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α   and of the universal amplitude ratio Δ=A₊/A₋$\Delta =A_{+}/A_{-}$, within the 3.5% and 7% of the Monte Carlo predictions, respectively.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.     

High-temperature atomic superfluidity in lattice Bose-Fermi mixtures

We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via s-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.     

Strongly correlated superconductivity and pseudogap phase near a multiband Mott insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated s-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.     

Determination of continuous variable entanglement by purity measurements

We classify the entanglement of two-mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.     

Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane–air and iso-octane–air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.     

Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula: