Vector Field Induced Chaos in Multi-dimensional Homogeneous Cosmologies

We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists for any number of spatial dimensions and for all homogeneous models. We derive the Poincar\'e return map associated to the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a 4-dimensional space time, the oscillatory regime here constructed overlap the usual Belinski-Khalatnikov-Liftshitz one.Comment: 3 pages, proceedings of the XI Marcel Grossmann meeting on Relativistic Astrophysics, July 23-29, 2006, Berli

Geometric phase around exceptional points

A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\pi$ for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels.Comment: 4 pages, 1 figure, with revisions in the introduction and conclusio

SETTING UP A DIGITAL LEARNING ENVIRONMENT IN A PEDAGOGICAL UNIVERSITY

This article is aimed at discovering the development particularities of the digital Russian university management system in Russia in the context of universal digitalisation, and identifying the opportunities for the development of university digital learning environment elements. The leading research method of the issue is a comparative analysis of the level of digital competences of students of professional education in Russia and the European Union member states. The authors of the article discovered the particularities of modern education transformational processes, revealed the main role of the development of information and communication technologies, determined the place of Russia in the world learning space and analysed the dynamics of the position of Russian higher educational institutions in the world university rating.Este artículo tiene como objetivo descubrir las particularidades de desarrollo del sistema digital de gestión de la universidad rusa en Rusia en el contexto de la digitalización universal, e identificar las oportunidades para el desarrollo de elementos del entorno de aprendizaje digital universitario. El principal método de investigación del tema es un análisis comparativo del nivel de competencias digitales de los estudiantes de educación profesional en Rusia y los estados miembros de la Unión Europea. Los autores del artículo descubrieron las particularidades de los procesos de transformación de la educación moderna, revelaron el papel principal del desarrollo de las tecnologías de información y comunicación, determinaron el lugar de Rusia en el espacio de aprendizaje mundial y analizaron la dinámica de la posición de las instituciones de educación superior rusas en La calificación de la universidad mundial.Este artigo tem como objetivo descobrir as particularidades de desenvolvimento do sistema de gerenciamento de universidades digitais da Rússia na Rússia no contexto da digitalização universal e identificar as oportunidades para o desenvolvimento de elementos do ambiente de aprendizado digital das universidades. O principal método de pesquisa da questão é uma análise comparativa do nível de competências digitais de estudantes de educação profissional na Rússia e nos estados membros da União Europeia. Os autores do artigo descobriram as particularidades dos processos transformacionais da educação moderna, revelaram o papel principal do desenvolvimento das tecnologias da informação e da comunicação, determinaram o lugar da Rússia no espaço de aprendizado mundial e analisaram a dinâmica da posição das instituições de ensino superior russas no país. a classificação mundial da universidade

Separation of variables for the quantum SL(2,R) spin chain

We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure defining the scalar product in the SoV representation and demonstrate that the language of Feynman diagrams is extremely useful in establishing various properties of the model. The kernel of the unitary transformation to the SoV representation is described by the same "pyramid diagram" as appeared before in the SoV representation for the SL(2,C) spin magnet. We argue that this kernel is given by the product of the Baxter Q-operators projected onto a special reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor stylistic changes, version to be publishe