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

The AF structure of non commutative toroidal Z/4Z orbifolds

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

Theory of Photon Blockade by an Optical Cavity with One Trapped Atom

In our recent paper [1], we reported observations of photon blockade by one atom strongly coupled to an optical cavity. In support of these measurements, here we provide an expanded discussion of the general phenomenology of photon blockade as well as of the theoretical model and results that were presented in Ref. [1]. We describe the general condition for photon blockade in terms of the transmission coefficients for photon number states. For the atom-cavity system of Ref. [1], we present the model Hamiltonian and examine the relationship of the eigenvalues to the predicted intensity correlation function. We explore the effect of different driving mechanisms on the photon statistics. We also present additional corrections to the model to describe cavity birefringence and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).Comment: 10 pages, 6 figure

Iron(III) Complexes on a Dendrimeric Basis and Various Amine Core Investigated by Mössbauer Spectroscopy

Dendrimers of various generations were synthesized by the divergent method. Starting from various amine cores (G(0a), G(0b), G(0c)) the generations were built by reaction of the amine with acrylnitrile followed by hydrogenation with DIBAL-H. Treatment with salicylaldehyde creates a fivefold coordination sphere for iron in the molecular periphery. The resulting multinuclear coordination compounds are investigated by Mossbauer spectroscopy

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

Theta Vectors and Quantum Theta Functions

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector in comparison with the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no more meaningful. We explain why Manin's quantum theta function obtained via algebra (quantum tori) valued inner product of the theta vector is a natural choice for quantum version of the classical theta function (kq representation). We then show that this approach holds for a more general theta vector with constant obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in the Manin's construction. We further discuss the properties of the theta vector and of the quantum theta function, both of which have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in the tex

Recent Results on the Periodic Lorentz Gas

The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some appropriate scaling assumption -- known as the Boltzmann-Grad scaling by analogy with the kinetic theory of rarefied gases -- this system can be described in some limit by a linear Boltzmann equation, assuming that the configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185 (1969), 308]). The case of a periodic configuration of obstacles (like atoms in a crystal) leads to a completely different limiting dynamics. These lecture notes review several results on this problem obtained in the past decade as joint work with J. Bourgain, E. Caglioti and B. Wennberg.Comment: 62 pages. Course at the conference "Topics in PDEs and applications 2008" held in Granada, April 7-11 2008; figure 13 and a misprint in Theorem 4.6 corrected in the new versio