Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications

We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series Z = \log(\e^X \e^Y) in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when $X$ and $Y$ are real or complex matrices.Comment: 30 page

Mesoscopic phase separation in La2CuO4.02 - a 139La NQR study

In crystals of La2CuO4.02 oxygen diffusion can be limited to such small length scales, that the resulting phase separation is invisible for neutrons. Decomposition of the 139La NQR spectra shows the existence of three different regions, of which one orders antiferromagnetically below 17K concomitantly with the onset of a weak superconductivity in the crystal. These regions are compared to the macroscopic phases seen previously in the title compound and the cluster-glass and striped phases reported for the underdoped Sr-doped cuprates.Comment: 4 pages, RevTeX, 5 figures, to be published in PR

Resonant electron transfer between quantum dots

An interaction of electromagnetic field with a nanostructure composed of two quantum dots is studied theoretically. An effect of a resonant electron transfer between the localized low-lying states of quantum dots is predicted. A necessary condition for such an effect is the existence of an excited bound state whose energy lies close to the top of the barrier separating the quantum dots. This effect may be used to realize the reversible quantum logic gate NOT if the superposition of electron states in different quantum dots is viewed as the superposition of bits 0 and 1.Comment: 8 pages, 1 EPS-figure, submitted to Phys. Rev.

Magneto-Gyrotropic Photogalvanic Effects in Semiconductor Quantum Wells

We show that free-carrier (Drude) absorption of both polarized and unpolarized terahertz radiation in quantum well (QW) structures causes an electric photocurrent in the presence of an in-plane magnetic field. Experimental and theoretical analysis evidences that the observed photocurrents are spin-dependent and related to the gyrotropy of the QWs. Microscopic models for the photogalvanic effects in QWs based on asymmetry of photoexcitation and relaxation processes are proposed. In most of the investigated structures the observed magneto-induced photocurrents are caused by spin-dependent relaxation of non-equilibrium carriers

Катализатор восстановления оксида азота оксидом углерода

The catalyst for NO reduction by carbon monoxide containing copper chromite, chromium, copper and iron oxides on y-Al2O3, has been developed. NO conversion over the catalyst in the reaction mixture containing 10 vol.% of oxygen is up to 83 % (200 °C, 12 000 h-1). Carbon monoxide oxidation proceeds at the expense of catalyst lattice oxygen, and the resultant reduced sites are oxidized by nitrous oxide or oxygen from gaseous phase.Разработан катализатор восстановления NO оксидом углерода, содержащий хромит меди, оксиды хрома, меди и железа на y-Al2O3. Конверсия NO в его присутствии достигает ~83 % при 10 об.% кислорода в газовой смеси (200оС, 12000 ч-1). Окисление СО идет за счет решеточного кислорода катализатора, а образующиеся восстановленные центры катализатора окисляются оксидом азота или газообразным кислородом

Каталитическая дезоксигенация воды на волокнистых ионитах, модифицированных гидроксидами железа и марганца

Catalysts based on iron and manganese hydroxide modified fibrous ion exchangers FIBAN K-4 and FIBAN X-1 have been synthesized and tested for hydrogenation of oxygen dissolved in water. It has been found that polyampholyte FIBAN X-1 samples containing ferric hydroxide are the most active in water deoxygenation: the residual oxygen content under the best process conditions does not exceed 20 g/1, which corresponds to the industry standards. It has been shown that the formation of iron - amino group nitrogen complex in the ion exchanger matrix occurs due to introduction of Fe3+ cations in FIBAN X-1 (pH 2-2.2). It has also been shown that iron and manganese hydroxide modified FIBAN X-1 is a highly active catalyst for H2O2 decomposition.На основе волокнистых ионитов ФИБАН К-4 и ФИБАН Х-1, модифицированных гидроксидами железа и марганца, синтезированы катализаторы и испытаны в реакции гидрирования растворенного в воде кислорода. Установлено, что наиболее активными в процессе дезоксигенации воды являются образцы полиамфолита ФИБАН Х-1, содержащие гидроксид железа в качестве активного компонента: остаточное содержание кислорода в воде в оптимальных условиях процесса не превышает 20 мкг/л, что соответствует отраслевому нормативу объектов теплоэнергетики по данному показателю. Показано, что при ионообменном введении катионов Fe3+ в ФИБАН Х-1 (рН 2-2,2) происходит образование комплексов железа с участием азота аминогрупп матрицы ионита. ФИБАН Х-1, модифицированный гидроксидами железа и марганца, обладает высокой каталитической активностью в разложении Н2О2

"Pair" Fermi contour and repulsion-induced superconductivity in cuprates

The pairing of charge carriers with large pair momentum is considered in connection with high-temperature superconductivity of cuprate compounds. The possibility of pairing arises due to some essential features of quasi-two-dimensional electronic structure of cuprates: (i) The Fermi contour with strong nesting features; (ii) The presence of extended saddle point near the Fermi level; (iii) The existence of some ordered state (for example, antiferromagnetic) close to the superconducting one as a reason for an appearing of "pair" Fermi contour resulting from carrier redistribution in momentum space. In an extended vicinity of the saddle point, momentum space has hyperbolic (pseudoeuclidean) metrics, therefore, the principal values of two-dimensional reciprocal reduced effective mass tensor have unlike signs. Rearrangement of holes in momentum space results in a rise of "pair" Fermi contour which may be defined as zero-energy line for relative motion of the pair. The superconducting gap arises just on this line. Pair Fermi contour formation inside the region of momentum space with hyperbolic metrics results in not only superconducting pairing but in a rise of quasi-stationary state in the relative motion of the pair. Such a state has rather small decay and may be related to the pseudogap regime of underdoped cuprates. It is concluded that the pairing in cuprates may be due to screened Coulomb repulsion. In this case, the superconducting energy gap in hole-doped cuprates exists in the region of hole concentration which is bounded both above and below. The superconducting state with positive condensation energy exists in more narrow range of doping level inside this region. Such hole concentration dependence correlates with typical phase diagram of cuprates.Comment: 23 pages, 11 figures. Submitted to Phys. Rev.

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem