Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

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