Робоча програма і методичні вказівки до самостійного вивчення дисципліни "Основи теорії транспорту"

Гірничовидобувна промисловість України набуває розвитку на базі без- перервного використання досягнень науково-технічного прогресу, застосування комплексної механізації та автоматизації всіх процесів виробництва, поліпшен- ня якісних показників підприємств, підвищення продуктивності й безпеки пра- ці.Гірничовидобувна промисловість України набуває розвитку на базі без- перервного використання досягнень науково-технічного прогресу, застосування комплексної механізації та автоматизації всіх процесів виробництва, поліпшен- ня якісних показників підприємств, підвищення продуктивності й безпеки пра- ці

Field-induced level crossings in spin clusters: Thermodynamics and magneto-elastic instability

Quantum spin clusters with dominant antiferromagnetic Heisenberg exchange interactions typically exhibit a sequence of field-induced level crossings in the ground state as function of magnetic field. For fields near a level crossing, the cluster can be approximated by a two-level Hamiltonian at low temperatures. Perturbations, such as magnetic anisotropy or spin-phonon coupling, sensitively affect the behavior at the level-crossing points. The general two-level Hamiltonian of the spin system is derived in first-order perturbation theory, and the thermodynamic functions magnetization, magnetic torque, and magnetic specific heat are calculated. Then a magneto-elastic coupling is introduced and the effective two-level Hamilitonian for the spin-lattice system derived in the adiabatic approximation of the phonons. At the level crossings the system becomes unconditionally unstable against lattice distortions due to the effects of magnetic anisotropy. The resultant magneto-elastic instabilities at the level crossings are discussed, as well as the magnetic behavior.Comment: 13 pages, 8 figures, REVTEX

Thomson and Compton scattering with an intense laser pulse

Our paper concerns the scattering of intense laser radiation on free electrons and it is focused on the relation between nonlinear Compton and nonlinear Thomson scattering. The analysis is performed for a laser field modeled by an ideal pulse with a finite duration, a fixed direction of propagation and indefinitely extended in the plane perpendicular to it. We derive the classical limit of the quantum spectral and angular distribution of the emitted radiation, for an arbitrary polarization of the laser pulse. We also rederive our result directly, in the framework of classical electrodynamics, obtaining, at the same time, the distribution for the emitted radiation with a well defined polarization. The results reduce to those established by Krafft et al. [Phys. Rev. E 72, 056502 (2005)] in the particular case of linear polarization of the pulse, orthogonal to the initial electron momentum. Conditions in which the differences between classical and quantum results are visible are discussed and illustrated by graphs

Simple proof of gauge invariance for the S-matrix element of strong-field photoionization

The relationship between the length gauge (LG) and the velocity gauge (VG) exact forms of the photoionization probability amplitude is considered. Our motivation for this paper comes from applications of the Keldysh-Faisal-Reiss (KFR) theory, which describes atoms (or ions) in a strong laser field (in the nonrelativistic approach, in the dipole approximation). On the faith of a certain widely-accepted assumption, we present a simple proof that the well-known LG form of the exact photoionization (or photodetachment) probability amplitude is indeed the gauge-invariant result. In contrast, to obtain the VG form of this probability amplitude, one has to either (i) neglect the well-known Goeppert-Mayer exponential factor (which assures gauge invariance) during all the time evolution of the ionized electron or (ii) put some conditions on the vector potential of the laser field.Comment: The paper was initially submitted (in a previous version) on 16 October 2006 to J. Phys. A and rejected. This is the extended version (with 2 figures), which is identical to the paper published online on 12 December 2007 in Physica Script

The investigation of dangerous geological processes resulting in land subsidence while designing the main gas pipeline in South Yakutia

The number of gas main accidents has increased recently due to dangerous geological processes in underdeveloped areas located in difficult geological conditions. The paper analyses land subsidence caused by karst and thermokarst processes in the right of way, reveals the assessment criteria for geological hazards and creates zoning schemes considering the levels of karst and thermorkarst hazards

Vacuum-stimulated cooling of single atoms in three dimensions

Taming quantum dynamical processes is the key to novel applications of quantum physics, e.g. in quantum information science. The control of light-matter interactions at the single-atom and single-photon level can be achieved in cavity quantum electrodynamics, in particular in the regime of strong coupling where atom and cavity form a single entity. In the optical domain, this requires permanent trapping and cooling of an atom in a micro-cavity. We have now realized three-dimensional cavity cooling and trapping for an orthogonal arrangement of cooling laser, trap laser and cavity vacuum. This leads to average single-atom trapping times exceeding 15 seconds, unprecedented for a strongly coupled atom under permanent observation.Comment: 4 pages, 4 figure

The Straw Tube Trackers of the PANDA Experiment

The PANDA experiment will be built at the FAIR facility at Darmstadt (Germany) to perform accurate tests of the strong interaction through bar pp and bar pA annihilation's studies. To track charged particles, two systems consisting of a set of planar, closed-packed, self-supporting straw tube layers are under construction. The PANDA straw tubes will have also unique characteristics in term of material budget and performance. They consist of very thin mylar-aluminized cathodes which are made self-supporting by means of the operation gas-mixture over-pressure. This solution allows to reduce at maximum the weight of the mechanical support frame and hence the detector material budget. The PANDA straw tube central tracker will not only reconstruct charged particle trajectories, but also will help in low momentum (< 1 GeV) particle identification via dE/dx measurements. This is a quite new approach that PANDA tracking group has first tested with detailed Monte Carlo simulations, and then with experimental tests of detector prototypes. This paper addresses the design issues of the PANDA straw tube trackers and the performance obtained in prototype tests.Comment: 7 pages,16 figure

Spherical averages in the space of marked lattices

A marked lattice is a $d$-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on ${\mathbb Z}^d$. We prove that, if the field is strongly mixing with a faster-than-logarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a non-trivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the Boltzmann-Grad limit