Three-fermion problems in optical lattices

We present exact results for the spectra of three fermionic atoms in a single well of an optical lattice. For the three lowest hyperfine states of Li6 atoms, we find a Borromean state across the region of the distinct pairwise Feshbach resonances. For K40 atoms, nearby Feshbach resonances are known for two of the pairs, and a bound three-body state develops towards the positive scattering-length side. In addition, we study the sensitivity of our results to atomic details. The predicted few-body phenomena can be realized in optical lattices in the limit of low tunneling.Comment: 4 pages, 4 figures, minor changes, to appear in Phys. Rev. Let

Limiting Case of Modified Electroweak Model for Contracted Gauge Group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction, clarified motivatio

Higgsless Electroweak Model and Contraction of Gauge Group

A modified formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The {\it free} Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same experimentally verified fields with the same masses as the Standard Electroweak Model. The vector bosons masses are automatically generated, so there is no need in special mechanism of spontaneous symmetry breaking. The limiting case of the modified Higgsless Electroweak Model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson, electromagnetic and electron fields are interpreted as an external ones with respect to W-bosons and neutrino fields. The W-bosons and neutrino fields do not effect on these external fields. The masses of all particles remain the same, but the field interactions in contracted model are more simple as compared with the standard Electroweak Model due to nullification of some terms.Comment: Talk at the International Workshop "`Supersymmetries and Quantum Symmetries"' (SQS-09), Dubna, Russia, July 29 -- August 3, 2009, 11

Survey of the world practice of implementing energy-efficient technologies in terms of mining enterprises

Purpose is the analysis of world practice of applying the best available techniques to increase energy saving and energy efficiency of mining enterprises being the important factor of the economic development. Methods. The research methodology is based on the scientific approaches: historical-evolutionary, interdisciplinary, integration, process, and situational. Methods of retrospective, categorical, and system analysis as well as modeling have been applied. The analysis was performed on the basis of both initial information sources (original texts of legislative documents, strategies) and material of the international analytical organizations (International Energy Agency, World Bank) as well as the data of official statistical records. Findings. For the first time, different variants of the best available techniques in Japan, the USA, and the EU have been analyzed as well as the role of a state in applying institutional measures of energy efficiency support, including mining complex, and prospects of its use in the Russian Federation. It has been determined that energy efficiency is the effective and economically feasible tool in reaching sustainable development of the national economy. It has been demonstrated that energy saving and increased energy efficiency may reduce the needs in investment, raise industrial competitiveness and consumer welfare as well as improve environmental protection owing to the reduced greenhouse gas emissions and decreased air pollution. Energy efficiency growth has direct effect upon the industrial competitiveness; it can be achieved by means of innovations. Originality. Emphasis has been put on the key scientific and technical aspects and approaches stimulating increased energy efficiency in the developed countries under the effect of strong, coordinated, and consistent national policy in different sectors of economy. Practical implications. The carried-out analysis is useful in terms of the innovative and technological development of different industries of the Russian Federation in the context of its complicated cooperation with European countries and the USA, dependence on foreign technologies, and limited access to them.Мета. Аналіз світового досвіду використання найкращих доступних технологій для підвищення енергозбереження та енергетичної ефективності гірничодобувних підприємств, які є важливими факторами інноваційного розвитку і економіки. Методика. В основі методології дослідження застосовані наукові підходи: історико-еволюційний, міждисциплінарний, інтеграційний, процесний і ситуаційний. Використано методики ретроспективного, категоріального, системного аналізу, моделювання. Аналіз виконувався на основі як первинних інформаційних джерел (оригінальні тексти законодавства, стратегій), так і на основі матеріалів міжнародних аналітичних організацій (Міжнародного енергетичного агентства, Світового банку), а також даних офіційного статистичного обліку. Результати. Вперше проаналізовані різні варіанти найкращих доступних технологій в Японії, США, ЄС, роль держави у застосуванні інституційних заходів підтримки енергоефективності, в тому числі у гірничодобувному комплексі, а також перспективи їх використання у Російській Федерації. Визначено, що енергоефективність є дієвим і рентабельним інструментом досягнення сталого розвитку економіки країни в цілому. Показано, що енергозбереження та підвищення енергоефективності може знижувати потребу в інвестиціях, збільшити конкурентоспроможність промисловості й добробут споживача, а також покращувати охорону навколишнього середовища, завдяки зниженню викидів парникових газів та зменшенню забруднення повітря. Підвищення енергоефективності безпосередньо впливає на конкурентоспроможність промисловості та може бути досягнуто за рахунок інновацій. Наукова новизна. Виділено ключові науково-технічні асп екти й підходи, що стимулюють підвищення енергоефективності в розвинених зарубіжних країнах під впливом сильної, скоординованої та послідовної політики держави у різних секторах економіки. Практична значимість. Проведений аналіз корисний у побудові інноваційного та технологічного розвитку різних галузей Російської Федерації в умовах її непростої взаємодії з країнами Європи і США, залежно від зарубіжних технологій та обмеженого доступу до них.Цель. Анализ мирового опыта использования наилучших доступных технологий для повышения энергосбережения и повышение энергетической эффективности горнодобывающих предприятий, которые являются важными факторами развития экономики. Методика. В основе методологии исследования применены научные подходы: историко-эволюционный, междисциплинарный, интеграционный, процессный и ситуационный. Использованы методики ретроспективного, категориального, системного анализа, моделирования. Анализ выполнялся на основе как первичных информационных источников (оригинальные тексты законодательства, стратегий), так и на основе материалов международных аналитических организаций (Международного энергетического агентства, Всемирного банка), а также данных официального статистического учета. Результаты. Впервые проанализированы различные варианты наилучших доступных технологий в Японии, США, ЕС, а также роль государства в применении институциональных мер поддержки энергоэффективности, в том числе в горнодобывающем комплексе, перспективы его использования в Российской Федерации. Определено, что энергоэффективность является действенным и рентабельным инструментом достижения устойчивого развития экономики страны в целом. Показано, что энергосбережение и повышение энергоэффективности может снижать потребность в инвестициях, увеличить конкурентоспособность промышленности и благосостояние потребителя, а также улучшать охрану окружающей среды, благодаря снижению выбросов парниковых газов и уменьшению загрязнения воздуха. Повышение энергоэффективности напрямую влияет на конкурентоспособность промышленности и может быть достигнуто за счет инноваций. Научная новизна. Выделены ключевые научно-технические аспекты и подходы, стимулирующие повышение энергоэффективности в развитых зарубежных странах под влиянием сильной, скоординированной и последовательной политики государства в различных секторах экономики. Практическая значимость. Проведенный анализ полезен в построении инновационного и технологического развития различных отраслей Российской Федерации в условиях ее непростого взаимодействия со странами Европы и США, зависимости от зарубежных технологий и ограниченного доступа к ним.This article was prepared as a part of the project section of the government contract as requested by the Ministry of Science and Higher Education of the Russian Federation on the subject formulated as “Development of Methodological Principles and Organizational Economic Mechanism of Strategic Management of Economic Security in Russia” (Assignment No. 26.3913.2017/4.6)

Atom-Dimer Scattering in a Three-Component Fermi Gas

Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12>+|3> -> |23>+|1>. Such a suppression is caused by interference between different decay paths and demonstrates the possiblity to use Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.Comment: 5 pages, 3 figure

Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups

Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $GL_q(1|2)$ and corresponding quantum superspace $C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $C_h(1|2;\iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of Physic

An Infinite Number of Closed FLRW Universes for Any Value of the Spatial Curvature

The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly mentioned.Comment: 4 pages. Contribution to the 5th International Workshop on Astronomy and Relativistic Astrophysics (Joao Pessoa, PB, Brazil, October 10-12, 2011) and to the 1o. Simposio Jayme Tiomno (Brasilia, DF, Brazil, October 27-28, 2011). In version 2: a few minor corrections; two new references added. In this version: title correction in Ref. 3; dedication paragraph at the en

Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the Hylleraas-Undheim method, we construct rigorous upper bounds to the collective frequencies for the radial and the axial breathing mode of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The bounds are compared to experimental data for trapped vapors of Li6 atoms.Comment: 11 pages, 2 figure

BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses

We determine the energetically lowest lying states in the BEC-BCS crossover regime of s-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schrodinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with N=4 fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to N=20 fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the s-wave scattering length a_s for N=2-20 fermions and different mass ratios \kappa of the two species. On the BEC and BCS sides, our energies agree with analytically-determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to \kappa = 20. Our energies for the strongly-interacting trapped system in the unitarity regime show no shell structure, and are well described by a simple expression, whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter \xi for the trapped system for various \kappa is determined, and comparisons with results for the homogeneous system are presented.Comment: 11 pages, 6 figures, extended versio