Morse Theory in Field Theory

We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in TQM can be expressed via intersection numbers of certain submanifolds of the target space with paths of steepest descent between critical points of a Morse function. In the end we conjecture another correspondence between quantum mechanics correlators and integrals of Massey products of certain cohomology classes.Comment: updated versio

Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides

Spintronics is aimed at active controlling and manipulating the spin degrees of freedom in semiconductor devices. A promising way to achieve this goal is to make use of the tunable Rashba effect that relies on the spin-orbit interaction (SOI) in a two-dimensional (2D) electron system immersed in an inversion-asymmetric environment. The SOI induced spin-splitting of the 2D-electron state provides a basis for many theoretically proposed spintronic devices. However, the lack of semiconductors with large Rashba effect hinders realization of these devices in actual practice. Here we report on a giant Rashba-type spin splitting in 2D electron systems which reside at tellurium-terminated surfaces of bismuth tellurohalides. Among these semiconductors, BiTeCl stands out for its isotropic metallic surface-state band with the Gamma-point energy lying deep inside the bulk band gap. The giant spin-splitting of this band ensures a substantial spin asymmetry of the inelastic mean free path of quasiparticles with different spin orientations.Comment: 12 pages, 5 figure

Surface-electronic structure of La(0001) and Lu(0001)

Most spectroscopic methods for studying the electronic structure of metal surfaces have the disadvantage that either only occupied or only unoccupied states can be probed, and the signal is cut at the Fermi edge. This leads to significant uncertainties, when states are very close to the Fermi level. By performing low-temperature scanning tunneling spectroscopy and ab initio calculations, we study the surface-electronic structure of La(0001) and Lu(0001), and demonstrate that in this way detailed information on the surface-electronic structure very close to the Fermi energy can be derived with high accuracy.Comment: 6 pages, 4 figures, 1 table submitted to PR

Future of the Artificial Intelligence: Object of Law or Legal Personality?

Objective: to reveal the problems associated with legal regulation of public relations, in which artificial intelligence systems are used, and to rationally comprehend the possibility of endowing such systems with a legal subject status, which is being discussed by legal scientists.Methods: the methodological basis of the research are the general scientific methods of analysis and synthesis, analogy, abstraction and classification. Among the legal methods primarily applied in the work are formal-legal, comparative-legal and systemic-structural methods, as well as the methods of law interpretation and legal modeling.Results: the authors present a review of the state of artificial intelligence development and its introduction into practice by the time of the research. Legal framework in this sphere is considered; the key current concepts of endowing artificial intelligence with a legal personality (individual, collective and gradient legal personality of artificial intelligence) are reviewed. Each approach is assessed; conclusions are made as to the most preferable amendments in the current legislation, which ceases to correspond to the reality. The growing inconsistency is due to the accelerated development of artificial intelligence and its spreading in various sectors of economy, social sphere, and in the nearest future – in public management. All this testifies to the increased risk of a break between legal matter and the changing social reality.Scientific novelty: scientific approaches are classified which endow artificial intelligence with a legal personality. Within each approach, the key moments are identified, the use of which will allow in the future creating legal constructs based on combinations, avoiding extremes and observing the balance between the interests of all parties. The optimal variant to define the legal status of artificial intelligence might be to include intellectual systems into a list of civil rights objects, but differentiating the legal regulation of artificial intelligence as an object of law and an “electronic agent” as a quasi subject of law. The demarcation line should be drawn depending on the functional differences between intellectual systems, while not only a robot but also a virtual intellectual system can be considered an “electronic agent”.Practical significance: the research materials can be used when preparing proposals for making amendments and additions to the current legislation, as well as when elaborating academic course and writing tutorials on the topics related to regulation of using artificial intelligence

Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: Surfaces of bismuth tellurohalides

Spintronics is aimed at actively controlling and manipulating the spin degrees of freedom in semiconductor devices. A promising way to achieve this goal is to make use of the tunable Rashba effect that relies on the spin-orbit interaction in a two-dimensional electron system immersed in an inversion-asymmetric environment. The spin-orbit-induced spin splitting of the two-dimensional electron state provides a basis for many theoretically proposed spintronic devices. However, the lack of semiconductors with large Rashba effect hinders realization of these devices in actual practice. Here we report on a giant Rashba-type spin splitting in two-dimensional electron systems that reside at tellurium-terminated surfaces of bismuth tellurohalides. Among these semiconductors, BiTeCl stands out for its isotropic metallic surface-state band with the Γ̄-point energy lying deep inside the bulk band gap. The giant spin splitting of this band ensures a substantial spin asymmetry of the inelastic mean free path of quasiparticles with different spin orientations. © 2012 American Physical Society.We acknowledge partial support by the University of the Basque Country (Project No. GV-UPV/EHU, Grant No. IT-366-07) and Ministerio de Ciencia e Inovación (Grant No. FIS2010-19609-C02-00).Peer Reviewe

Unoccupied Topological States on Bismuth Chalcogenides

The unoccupied part of the band structure of topological insulators Bi$_2$Te$_{x}$Se$_{3-x}$ ($x=0,2,3$) is studied by angle-resolved two-photon photoemission and density functional theory. For all surfaces linearly-dispersing surface states are found at the center of the surface Brillouin zone at energies around 1.3 eV above the Fermi level. Theoretical analysis shows that this feature appears in a spin-orbit-interaction induced and inverted local energy gap. This inversion is insensitive to variation of electronic and structural parameters in Bi$_2$Se$_3$ and Bi$_2$Te$_2$Se. In Bi$_2$Te$_3$ small structural variations can change the character of the local energy gap depending on which an unoccupied Dirac state does or does not exist. Circular dichroism measurements confirm the expected spin texture. From these findings we assign the observed state to an unoccupied topological surface state

Вещественный состав метеорита Северный Колчим

New data on the material composition of the Severny Kolchim meteorite, found in the Perm region territory in 1965, is presented. It is established that the cosmic substance is composed of forsterite, enstatite, diopside, plagioclase (oligoclase, bitovnite), glass, chromite, magnetite, ilmenite, rutile, iron and nickel metals (kamasite, taenite and tetrataenite), sulphides (troilite, pentlandite), chlorapatite and merrillite. Some minerals, namely the diopside, tetrataenite, chlorapatite and merrillite, were determined in the Severny Kolchim meteorite first time. The data on the chemical composition of minerals and the trace element composition are given. It was verified that this meteorite is a nonequilibrium stone chondrite and belongs to the petrological type H3.Приведены современные данные о вещественном составе метеорита Северный Колчим, найденного на территории Пермского края в 1965 г. Установлено, что космическое вещество сложено форстеритом, энстатитом, диопсидом, плагиоклазами (олигоклазом, битовнитом), стеклом, хромитом, магнетитом, ильменитом, рутилом, металлами железа и никеля (камаситом, тэнитом и тетратэнитом), сульфидами (троилитом, пентландитом), хлорапатитом и мерриллитом. При этом диопсид, тетратэнит, хлорапатит и мерриллит определены в метеорите Северный Колчим впервые. Приведены данные о химическом составе минералов и микроэлементном составе породы. Сам метеорит является неравновесным каменным хондритом и относится к петрологическому типу H3