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

Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending decreases when curvature increases, i.e. bending manifests itself as a trap for excitations. Moreover, the potential of this trap is double-well, thus leading to a symmetry breaking phenomenon: a symmetric stationary state may become unstable and transform into an energetically favorable asymmetric stationary state. The essentials of symmetry breaking are examined analytically for a simplified model. We also demonstrate a threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving nonlinear excitation passing through the bending.Comment: 13 pages (LaTeX) with 10 figures (EPS

Nonequilibrium electrons in tunnel structures under high-voltage injection

We investigate electronic distributions in nonequilibrium tunnel junctions subject to a high voltage bias $V$ under competing electron-electron and electron-phonon relaxation processes. We derive conditions for reaching quasi-equilibrium and show that, though the distribution can still be thermal for low energies where the rate of the electron-electron relaxation exceeds significantly the electron-phonon relaxation rate, it develops a power-law tail at energies of order of $eV$. In a general case of comparable electron-electron and electron-phonon relaxation rates, this tail leads to emission of high-energy phonons which carry away most of the energy pumped in by the injected current.Comment: Revised versio

On the vibron dressing in the α\alpha--helicoidal macromolecular chains

We present a study of the physical properties of the vibrational excitation in $\alpha$--helicoidal macromolecular chains, caused by the interaction with acoustical and optical phonon modes. The influence of the temperature and the basic system parameters on the vibron dressing has been analyzed by employing the simple mean--field approach based on the variational extension of the Lang--Firsov unitary transformation. Applied approach predicts a region in system parameter space where one takes place an abrupt transition from partially dressed (light and mobile) to fully dressed (immobile) vibron states. We found that the boundary of this region depends on system temperature and type of bond among structural elements in the macromolecular chain.Comment: 22 pages, 12 figures, title changed, the interaction with optical phonon modes jointly with acoustical ones added, consideration significantly enlarged, references added, the paper develops the results of arxiv:1210.3918, accepted for publication in Chinese Physics

AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics

We consider the relationship between the tight-binding Hamiltonian of the two-dimensional honeycomb lattice of carbon atoms with nearest neighbor hopping only and the 2+1 dimensional Hamiltonian of quantum electrodynamics which follows in the continuum limit. We pay particular attention to the symmetries of the free Dirac fermions including spatial inversion, time reversal, charge conjugation and chirality. We illustrate the power of such a mapping by considering the effect of the possible symmetry breaking which corresponds to the creation of a finite Dirac mass, on various optical properties. In particular, we consider the diagonal AC conductivity with emphasis on how the finite Dirac mass might manifest itself in experiment. The optical sum rules for the diagonal and Hall conductivities are discussed.Comment: 46 pages, ws-ijmpb, 7 EPS figures; final version published in IJMP

Hall-like effect induced by spin-orbit interaction

The effect of spin-orbit interaction on electron transport properties of a cross-junction structure is studied. It is shown that it results in spin polarization of left and right outgoing electron waves. Consequently, incoming electron wave of a proper polarization induces voltage drop perpendicularly to the direct current flow between source and drain of the considered four-terminal cross-structure. The resulting Hall-like resistance is estimated to be of the order of 10^-3 - 10^-2 h/e^2 for technologically available structures. The effect becomes more pronounced in the vicinity of resonances where Hall-like resistance changes its sign as function of the Fermi energy.Comment: 4 pages (RevTeX), 4 figures, will appear in Phys. Rev. Let