Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

Derivation of the particle dynamics from kinetic equations

We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversible. Also, we construct the so called approximate microscopic solutions. These solutions are continuously differentiable and they are reversible on bounded time intervals. This analysis suggests a way to reconcile the time-irreversible kinetic equations with the time-reversible particle dynamics. Usually one tries to derive the kinetic equations from the particle dynamics. On the contrary, we postulate the Boltzmann-Enskog equation or another kinetic equation and treat their microscopic solutions as the particle dynamics. So, instead of the derivation of the kinetic equations from the microdynamics we suggest a kind of derivation of the microdynamics from the kinetic equations.Comment: 18 pages; some misprints have been corrected, some references have been adde

Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential

Novel Nonreciprocal Acoustic Effects in Antiferromagnets

The possible occurrence of nonreciprocal acoustic effects in antiferromagnets in the absence of an external magnetic field is investigated using both (i) a microscopic formulation of the magnetoelastic interaction between spins and phonons and (ii) symmetry arguments. We predict for certain antiferromagnets the existence of two new nonreciprocal (non-time invariant) effects: A boundary-condition induced nonreciprocal effect and the occurrence of transversal phonon modes propagating in opposite directions having different velocities. Estimates are given and possible materials for these effects to be observed are suggested.Comment: Euro. Phys. Lett. (in press

Faraday rotation, stochastic magnetic fields and CMB maps

The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $\Lambda$CDM paradigm (m$\Lambda$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal m$\Lambda$CDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite.Comment: 53 pages, 15 included figure

Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation

We consider the quintic one dimensional nonlinear Schr\"odinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.Comment: 14 pages, 17 figure

Investigation of oxidation process of mechanically activated ultrafine iron powders

The oxidation of mechanically activated ultrafine iron powders was studied using X-ray powder diffraction and thermogravimetric analyzes. The powders with average particles size of 100 nm were made by the electric explosion of wire, and were subjected to mechanical activation in planetary ball mill for 15 and 40 minutes. It was shown that a certain amount of FeO phase is formed during mechanical activation of ultrafine iron powders. According to thermogravimetric analysis, the oxidation process of non-milled ultrafine iron powders is a complex process and occurs in three stages. The preliminary mechanical activation of powders considerably changes the nature of the iron powders oxidation, leads to increasing in the temperature of oxidation onset and shifts the reaction to higher temperatures. For the milled powders, the oxidation is more simple process and occurs in a single step