Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

No Ending Point in The Bragg-to-Vortex Glass Phase Transition Line at Low Temperatures

We have measured the magnetic hysteresis loops and the magnetic relaxation for $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212) single crystals which exhibit the second magnetization peak effect. Although no second peak effect is observed below 20 K in the measurement with fast field sweeping rate, it is found that the second peak effect will appear again after long time relaxation or in a measurement with very slow field sweeping rate at 16 K. It is anticipated that the peak effect will appear at very low temperatures (approaching zero K) when the relaxation time is long enough. We attribute this phenomenon to the profile of the interior magnetic field and conclude that the phase transition line of Bragg glass to vortex glass has no ending point at low temperatures.Comment: 4 pages, 5 figure

Тактика и техника медиастинальной лимфаденэктомии в легочной онкологии

Fascial cellular mediastinal spaces containing lymphatic nodes allocated regionally to lungs are described.The incidence of different groups with intrathoracic lymphatic nodes involvement depending on the site of tum our origin was investigated.Mediastinal lymphoidectomy approach with the removal of collateral mediastinal and fixed in roots lymphatic nodes is described. The findings in 802 patients treated with the mentioned method are presented (lymph impairments: NO in 290, N1 in 277, N3 in 20). Five year survival rate in monosurgical management of malignant cellular cancer was comprised in 53% (in NO — 70%, in N1 — 54%, in N2 — 33%).Lymphoidectomy technique and approach are discussed.В статье рассматриваются поверхностные клеточные средостенные пространства, содержащие лимфатические узлы, сопряженные регионально с легкими.Исследовался случай различных групп больных с внутриторакальным опухолевым вовлечением лимфатических узлов, зависящим от положения опухолевого начала.Описывается подход к средостенной лимфаденэктомии через удаление коллатеральных медиастинальных и прикорневых лимфатических узлов. Представлены результаты по 802 больным, пролеченных по упомянутой методике (нарушения лимфоциркуляции: N0 у 290, N1 у 277, N3 у 20). Был отмечен пятилетний уровень выживаемости при монохирургическом лечении немелкоклеточного рака у 53% наблюдений (у N0 — 70%, у N1 — 54%, у N2 — 33%).Обсуждаются техника и подходы к лимфаденэктомии

A straightforward method for stereospecific assignment of val and leu prochiral methyl groups by solid-state NMR: Scrambling in the [2-13C]Glucose labeling scheme.

The unambiguous stereospecific assignment of the prochiral methyl groups in Val and Leu plays an important role in the structural investigation of proteins by NMR. Here, we present a straightforward method for their stereospecific solid-state NMR assignment based on [2-13C]Glucose ([2-13C]Glc) as the sole carbon source during protein expression. The approach is fundamentally based on the stereo-selective biosynthetic pathway of Val and Leu, and the co-presence of [2-13C]pyruvate produced mainly by glycolysis and [3-13C]/[1,3-13C]pyruvate most probably formed through scrambling in the pentose phosphate pathway. As a consequence, the isotope spin pairs 13Cβ-13Cγ2 and 13Cα-13Cγ1 in Val, and 13Cγ-13Cδ2 and 13Cβ-13Cδ1 in Leu are obtained. The approach is successfully demonstrated with the stereospecific assignment of the methyl groups of Val and Leu of type 3 secretion system PrgI needles and microcrystalline ubiquitin

Images of very high energy cosmic ray sources in the Galaxy: I. A source towards the Galactic Centre

Recent analyses of the anisotropy of cosmic rays at $10^{18}$ eV (the AGASA and SUGAR data) show significant excesses from regions close to the Galactic Centre and Cygnus. Our aim is to check whether such anisotropies can be caused by single sources of charged particles. We investigate propagation of protons in two models of the Galactic regular magnetic field (with the irregular component included) assuming that the particles are injected by a short lived discrete source lying in the direction of the Galactic Centre. We show that apart from a prompt image of the source, the regular magnetic field may cause delayed images at quite large angular distances from the actual source direction. The image is strongly dependent on the time elapsed after ejection of particles and it is also very sensitive to their energy. For the most favourable conditions for particle acceleration by a young pulsar the predicted fluxes are two to four order of magnitudes higher than that observed. The particular numbers depend strongly on the Galactic magnetic field model adopted but it looks that a single pulsar in the Galactic Centre could be responsible for the observed excess.Comment: 20 pages, 7 figures, accepted to J. Phys.

Effect of electron irradiation on vortex dynamics in YBa_2Cu_3O_{7-x} single crystals

We report on drastic change of vortex dynamics with increase of quenched disorder: for rather weak disorder we found a single vortex creep regime, which we attribute to a Bragg-glass phase, while for enhanced disorder we found an increase of both the depinning current and activation energy with magnetic field, which we attribute to entangled vortex phase. We also found that introduction of additional defects always increases the depinning current, but it increases activation energy only for elastic vortex creep, while it decreases activation energy for plastic vortex creep.Comment: 4 pages, 3 figures, submited to Phys. Rev.

Unified order-disorder vortex phase transition in high-Tc superconductors

The diversity of vortex melting and solid-solid transition lines measured in different high-T$_{c}$ superconductors is explained, postulating a unified order-disorder phase transition driven by both thermally- and disorder-induced fluctuations. The temperature dependence of the transition line and the nature of the disordered phase (solid, liquid, or pinned liquid) are determined by the relative contributions of these fluctuations and by the pinning mechanism. By varying the pinning mechanism and the pinning strength one obtains a spectrum of monotonic and non-monotonic transition lines similar to those measured in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$$, YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, Nd$_{1.85}$Ce$_{0.15}$CuO$$, Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and (La$_{0.937}$Sr$_{0.063}$)$_{2}$CuO$_{4}$Comment: To be published in Phys. Rev. B Rapid Com

Disorder and thermally driven vortex-lattice melting in La{2-x}Sr{x}CuO{4} crystals

Magnetization measurements in La{2-x}Sr{x}CuO{4} crystals indicate vortex order-disorder transition manifested by a sharp kink in the second magnetization peak. The transition field exhibits unique temperature dependence, namely a strong decrease with temperature in the entire measured range. This behavior rules out the conventional interpretation of a disorder-driven transition into an entangled vortex solid phase. It is shown that the transition in La{2-x}Sr{x}CuO{4} is driven by both thermally- and disorder-induced fluctuations, resulting in a pinned liquid state. We conclude that vortex solid-liquid, solid-solid and solid to pinned-liquid transitions are different manifestations of the same thermodynamic order-disorder transition, distinguished by the relative contributions of thermal and disorder-induced fluctuations.Comment: To be published in phys. Rev. B Rapid Com

Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_\lambda(iso_{\omega}(2))$. This family contains the quantum Euclidean, Galilei and Poincar\'e algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and $q$--Casimir equations which play the role of $q$--Schr\"odinger equations.Comment: LaTeX 2e, 20 page