Phase Transitions in Isolated Vortex Chains

In very anisotropic layered superconductors (e.g. Bi$_2$Sr$_2$CaCu$_2$O$_x$) a tilted magnetic field can penetrate as two co-existing lattices of vortices parallel and perpendicular to the layers. At low out-of-plane fields the perpendicular vortices form a set of isolated vortex chains, which have recently been observed in detail with scanning Hall-probe measurements. We present calculations that show a very delicate stability of this isolated-chain state. As the vortex density increases along the chain there is a first-order transition to a buckled chain, and then the chain will expel vortices in a continuous transition to a composite-chain state. At low densities there is an instability towards clustering, due to a long-range attraction between the vortices on the chain, and at very low densities it becomes energetically favorable to form a tilted chain, which may explain the sudden disappearance of vortices along the chains seen in recent experiments.Comment: 9 pages, 10 figure

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z_n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig

Problems of digitalization of Russian economy

In the article, the authors set a goal to analyze the prospects for digitalization of the Russian economy. Despite the adoption of the state program "Digital Economy of the Russian Federation" and the active work of the Government in this area, the introduction of digital technologies is not fast enough. According to the authors, the main reasons for the current situation are underdeveloped ecosystem, lack of personnel and financial resources, conservative thinking. The success of digitalization is possible only with active government support. © 2019 Ivanovo State University of Chemistry and Technology. All rights reserved

Room-temperature lasing in microring cavities with an InAs/InGaAs quantum-dot active region

Microring cavities (diameter D = 2.7-7 μm) with an active region based on InAs/InGaAs quantum dots are fabricated and their characteristics are studied by the microphotoluminescence method and near-field optical microscopy. A value of 22 000 is obtained for the Q factor of a microring cavity with the diameter D = 6 μm. Lasing up to room temperature is obtained in an optically pumped ring microlaser with a diameter of D = 2.7 μm. © 2013 Pleiades Publishing, Ltd