Complete latticeability in vector-valued sequence spaces

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of the set of disjoint non-norm null weakly null sequences and of the set of disjoint non-norm null regular-polynomially null sequences in Banach lattices. Then we apply the mother vector technique to prove the complete latticeability of ${\lambda }_{\pi }(E)\setminus {\lambda }_s(E)$, which implies the complete latticeability of $({\ell }_p{\widehat{\otimes }}_{|\pi |}E)\setminus ({\ell }_p{\widehat{\otimes }}_{\pi }E)$, where E is a Banach lattice and .     

Quantum‐optical analogies using photonic structures

Engineered photonic waveguides have provided in the past decade an extremely rich laboratory tool to visualize with optical waves the classic analogues of a wide variety of coherent quantum phenomena encountered in atomic, molecular or condensed‐matter physics. As compared to quantum systems, optics offers the rather unique advantage of a direct mapping of the wave function evolution in coordinate space by simple fluorescence imaging or scanning tunneling optical microscopy techniques. In this contribution recent theoretical and experimental advances in the field of quantum‐optical analogies are reviewed. Special attention is devoted to some relevant optical analogies based on the use of curved photonic structures, including: coherent destruction of tunneling in driven bistable potentials; coherent population transfer and adiabatic passage in laser‐driven multilevel atomic systems; quantum decay control and Zeno dynamics; electronic Bloch oscillations and Zener tunneling, Anderson localization and dynamic localization in crystalline potentials.     

Three-dimensional lattice ground states for Riesz and Lennard-Jones–type energies

The Riesz potential $f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard-Jones–type potentials $f_{n,m}^{\mathrm{LJ}}(r):=a{r}^{-n}-b{r}^{-m}$, $n>m$ that are widely used in molecular simulations. In this paper, we investigate analytically and numerically the minimizers among three-dimensional lattices of Riesz and Lennard-Jones energies. We discuss the minimality of the body-centered-cubic (BCC) lattice, face-centered-cubic (FCC) lattice, simple hexagonal (SH) lattices, and hexagonal close-packing (HCP) structure, globally and at fixed density. In the Riesz case, new evidence of the global minimality at fixed density of the BCC lattice is shown for and the HCP lattice is computed to have higher energy than the FCC (for $s>3/2$) and BCC (for ) lattices. In the Lennard-Jones case with exponents , the ground state among lattices is confirmed to be an FCC lattice whereas an HCP phase occurs once added to the investigated structures. Furthermore, phase transitions of type “FCC-SH” and “FCC-HCP-SH” (when the HCP lattice is added) as the inverse density V increases are observed for a large spectrum of exponents $(n,m)$. In the SH phase, the variation of the ratio Δ between the interlayer distance d and the lattice parameter a is studied as V increases. In the critical region of exponents , the SH phase with an extreme value of the anisotropy parameter Δ dominates. If one limits oneself to rigid lattices, the BCC-FCC-HCP phase diagram is found. For , the BCC lattice is the only energy minimizer. Choosing , the FCC and SH latices become minimizers.     

A New Sodium Thioborate Fast Ion Conductor: Na3B5S9

We report a new sodium fast-ion conductor, Na₃B₅S₉, that exhibits a high Na ion total conductivity of 0.80 mS cm⁻¹ (sintered pellet; cold-pressed pellet=0.21 mS cm⁻¹). The structure consists of corner-sharing B₁₀S₂₀ supertetrahedral clusters, which create a framework that supports 3D Na ion diffusion channels. The Na ions are well-distributed in the channels and form a disordered sublattice spanning five Na crystallographic sites. The combination of structural elucidation via single crystal X-ray diffraction and powder synchrotron X-ray diffraction at variable temperatures, solid-state nuclear magnetic resonance spectra and ab initio molecular dynamics simulations reveal high Na-ion mobility (predicted conductivity: 0.96 mS cm⁻¹) and the nature of the 3D diffusion pathways. Notably, the Na ion sublattice orders at low temperatures, resulting in isolated Na polyhedra and thus much lower ionic conductivity. This highlights the importance of a disordered Na ion sublattice—and existence of well-connected Na ion migration pathways formed via face-sharing polyhedra—in dictating Na ion diffusion.     

Binary Mixtures of n‐C36H74 with Certain Shorter Chain n‐Alkanes: Powder XRD Investigations

Powder XRD investigations on hexatriacontane hydrocarbon, forming binary mixtures with octadecane, hexadecane, decane and decanol were made and the results were interpreted in terms of additive (impurity) effect, phase changes, strength of phases and phase separation. Possibility of the occurrence of super lattices in these systems is considered.