Cubic spline prewavelets on the four-directional mesh

In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L^2(\RR^2). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree

Quantum coherence and carriers mobility in organic semiconductors

We present a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier. Thermal intermolecular phonons and librations tend to localize pure coherent states and to assist the motion of less coherent ones. Decoherence is thus the primary mechanism by which conduction occurs. It is driven by the coupling of the carrier to the molecular lattice through polarization and transfer integral fluctuations as described by the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent regime are modeled via the Anderson hamiltonian with correlated diagonal and non-diagonal disorder leading to the determination of the carrier localization length. This length defines the coherent extension of the ground state and determines, in turn, the diffusion range in the incoherent regime and thus the mobility. The transfer integral disorder of Troisi and Orlandi can also be incorporated. This model, based on the idea of decoherence, allowed us to predict the value and temperature dependence of the carrier mobility in prototypical organic semiconductors that are in qualitative accord with experiments

Lattice dynamics and a magnetic-structural phase transition in the nickel orthoborate Ni3(BO3)2Ni_{3}(BO_{3})_{2}

Nickel orthoborate $Ni_{3}(BO_{3})_{2}$ having a complex orthorhombic structure $P_{nnm}$ (#58, Z=2) of the kotoite type is known for quite a long time as an antiferromagnetic material below $T_{N}$ = 46 K, but up to now its physical properties including the lattice dynamics have not been explored. Six magnetic nickel $Ni^{2+}$ ions (S=1) in the unit cell are distributed over the 2a and 4f positions in the centers of distorted $[O_{6}]$ octahedra. The $[NiO_{6}]$ units are linked via rigid $[BO_{3}]$ groups and these structural particularities impose restrictions on the lattice dynamics and spin-phonon interactions. We performed the symmetry analysis of the phonon modes at the center of the Brillouin zone. The structural parameters and phonon modes were calculated using Dmol3 program. We report and analyze results of infrared and Raman studies of phonon spectra measured in all required polarizations. Most of the even and odd phonons predicted on the basis of the symmetry analysis and theoretical calculations were reliably identified in the measured spectra. Absorption measurements in the infrared region showed emergence of several very narrow and weak phonons at the magnetic ordering temperature $T_{N}$. This observation proves the existence of a structural phase transition not reported before which is evidently coupled intrinsically with the magnetic dynamics of $Ni_{3}(BO_{3})_{2}$. A clear evidence of spin-phonon interaction was observed for some particular phonons below $T_{N}$.Comment: New version: 29 pages, 10 figures, 73 reference

Calculation of the energy spectrum of a two-electron spherical quantum dot

We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate ground-state Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.Comment: 18 pages, LaTeX, 2 figures-ep

Nanodiamonds carrying quantum emitters with almost lifetime-limited linewidths

Nanodiamonds (NDs) hosting optically active defects are an important technical material for applications in quantum sensing, biological imaging, and quantum optics. The negatively charged silicon vacancy (SiV) defect is known to fluoresce in molecular sized NDs (1 to 6 nm) and its spectral properties depend on the quality of the surrounding host lattice. This defect is therefore a good probe to investigate the material properties of small NDs. Here we report unprecedented narrow optical transitions for SiV colour centers hosted in nanodiamonds produced using a novel high-pressure high-temperature (HPHT) technique. The SiV zero-phonon lines were measured to have an inhomogeneous distribution of 1.05 nm at 5 K across a sample of numerous NDs. Individual spectral lines as narrow as 354 MHz were measured for SiV centres in nanodiamonds smaller than 200 nm, which is four times narrower than the best SiV line previously reported for nanodiamonds. Correcting for apparent spectral diffusion yielded a homogeneous linewith of about 200 MHz, which is close to the width limit imposed by the radiative lifetime. These results demonstrate that the direct HPHT synthesis technique is capable of producing nanodiamonds with high crystal lattice quality, which are therefore a valuable technical material

Anomalous Thermal Stability of Metastable C_20 Fullerene

The results of computer simulation of the dynamics of fullerene C_20 at different temperatures are presented. It is shown that, although it is metastable, this isomer is very stable with respect to the transition to a lower energy configuration and retains its chemical structure under heating to very high temperatures, T ~ 3000 K. Its decay activation energy is found to be E_a ~ 7 eV. Possible decay channels are studied, and the height of the minimum potential barrier to decay is determined to be U = 5.0 eV. The results obtained make it possible to understand the reasons for the anomalous stability of fullerene C_20 under normal conditions.Comment: Slightly corrected version of the paper submitted to Phys. Solid Stat