Mappings preserving spectrum and commutativity on Hermitian matrices

The general form of a continuous mapping φ acting on the real vector space of all n × n complex Hermitian or real symmetric matrices, and preserving spectrum and commutativity, is derived. It turns out that φ is either linear or its image forms a commutative set.     

Preparation of an ion-selective electrode by chemical treatment of copper wire for the measurement of copper(II) and iodide by batch and flow-injection potentiometry

The preparation of an ion-selective electrode by chemical treatment of copper wire and its application for the measurements of copper (II) and iodide ions is described. The proposed reaction mechanism at the sensing surface, which explains the response of the electrode to Cu²⁺ and iodide ions, is discussed. The prepared electrode was suitable for direct potentiometric measurements of iodide and copper (II) in batch experiments down to concentrations of 1 × 10^–5 mol L^–1. A tubular electrode, prepared in the same way, may be used as a potentiometric sensor in a flow-injection analysis for Cu (II) and/or iodide determinations.     

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.     

Fundamental properties of lead and tin nanocrystals in a dielectric matrix

A careful inspection of the temperature evolution of Pb and Sn nanoparticles encased in a SiO_x(x, 1) matrix was carried out by means of optical reflectivity and dark field electron microscopy measurements. A strong decrease of the melting temperature with size and the presence of an hysteresis cycle, which clearly separates melting and solidification temperatures, are evidenced. It is shown that an appreciable tailoring of the properties of the effective medium can be obtained.     

Effects of configuration-dependent hybridization on core-level photoemission spectra

The Ni2p X-ray photoemission spectrum (XPS) for NiCl₂ is reanalyzed on the basis of a NiCl₆⁴⁻ cluster model. By taking into account the electron configuration dependence of the hybridization strengths between Ni3d and Cl3p orbitals, we show that the model can consistently reproduce the experimental 2p-XPS and the energy gap of the system.     

Lithium aluminate-doped lithium orthosilicate: Sol-gel ceramics and lithium dynamics

Dense ceramics (Li_4+xSi_1−xAl_xO₄ with 0 ≤ x ≤ 0.3) are obtained by sintering at 700–900°C, without prior calcination, of sol-gel powders prepared by an alkoxide-hydroxide route. In comparison with the pure lithium orthosilicate (3 × 10⁻⁴ S · cm⁻¹ at 350°C), only a slight enhancement of the ionic conductivity is noted for monophase ceramics with Li₄SiO₄-type structure (5 × 10⁻⁴ S · cm⁻¹ at 350°C for x = 0.3). Higher conductivity (2 × 10⁻² S · cm⁻¹ at 350°C) is observed for an heterogeneous material formed of a lithium silicoaluminate phase (x = 0.2) with the Li₄SiO₄-type structure coexisting with lithium hydroxide. In this two-phase material, ac conductivity and ⁷Li spin-lattice relaxation data are consistent with the formation of a new kinetic path, via a thin layer along the interface, which enhances the lithium mobility.     

Inertial ranges for turbulent solutions of complex Ginzburg-Landau equations

We consider the spatially periodic, complex Ginzburg-Landau (CGL) equation in regimes close to that of a critical or supercritical focusing non-linear Schrödinger (NLS) equation, which is known to have solutions that exhibit self-similar blow-up. We use the NLS blow-up solutions as a template to develop a theory of how nearly self-similar intermittent burst events can create a power-law inertial range in the time-averaged wave-number spectrum of CGL solutions. Numerical experiments in one dimension with a quintic (critical) and septant (supercritical) non-linearity show a that power-law inertial range emerges which differs from that predicted by the theory. However, as one approaches the NLS limit in the supercritical case, a second power-law inertial range is seen to emerge that agrees with the theory.