151,640 research outputs found

    The Hall Triple Systems of Small Class

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    A Hall triple system (HTS) is a Steiner triple system in which any three non-collinear points generate an affine plane AG(2, 3). Let k be the central nilpotency class of the corresponding Moufang loop. When k = 2 or 3, and when k â©Ÿ 4 we determine the, possible values of the order with respect to the dimension. Moreover we prove that there are only four HTSs of order 36. Recall that Marshall Hall Jr. (resp. Kepka and the author independently) had proved that there are only two HTSs of order 34 (resp. 35). As a consequence one may give now the complete list of centreless Fischer groups in which the number of order 2 elements is at most 36

    A noncommutative framework for topological insulators

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    We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In particular we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realised as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the sample's (possibly noncommutative) Brillouin zone.Comment: 32 pages, final versio

    Charge Deficiency, Charge Transport and Comparison of Dimensions

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    We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure

    Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems

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    The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc. (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.Comment: 44 pages, 4 figures. v2: typos corrected and references updated. v3: Minor changes, to appear in J. Phys. A (Mathematical and Theoretical

    Multiplicity in Early Stellar Evolution

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    Observations from optical to centimeter wavelengths have demonstrated that multiple systems of two or more bodies is the norm at all stellar evolutionary stages. Multiple systems are widely agreed to result from the collapse and fragmentation of cloud cores, despite the inhibiting influence of magnetic fields. Surveys of Class 0 protostars with mm interferometers have revealed a very high multiplicity frequency of about 2/3, even though there are observational difficulties in resolving close protobinaries, thus supporting the possibility that all stars could be born in multiple systems. Near-infrared adaptive optics observations of Class I protostars show a lower binary frequency relative to the Class 0 phase, a declining trend that continues through the Class II/III stages to the field population. This loss of companions is a natural consequence of dynamical interplay in small multiple systems, leading to ejection of members. We discuss observational consequences of this dynamical evolution, and its influence on circumstellar disks, and we review the evolution of circumbinary disks and their role in defining binary mass ratios. Special attention is paid to eclipsing PMS binaries, which allow for observational tests of evolutionary models of early stellar evolution. Many stars are born in clusters and small groups, and we discuss how interactions in dense stellar environments can significantly alter the distribution of binary separations through dissolution of wider binaries. The binaries and multiples we find in the field are the survivors of these internal and external destructive processes, and we provide a detailed overview of the multiplicity statistics of the field, which form a boundary condition for all models of binary evolution. Finally we discuss various formation mechanisms for massive binaries, and the properties of massive trapezia.Comment: Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin

    Can a teaching university be an entrepreneurial university? Civic entrepreneurship and the formation of a cultural cluster in Ashland, Oregon

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    There has been debate over whether a teaching university can be an entrepreneurial university (Clark, 1998). In a traditional conception of academic entrepreneurship focused on achieving commercial profit, a research base may be a pre-requisite to creating spin-offs. However, if we expand entrepreneurship into a broader conception to map its different forms such as commercial, social, cultural and civic entrepreneurship, it is clear that the answer is positive. In this study, we focus on the Oregon Shakespeare Festival (OSF), which has transformed a small town based on resource extraction, a market center and a rail-hub into a theatre arts and cultural cluster. The convergence of entrepreneurship, triple helix model, cluster and regional innovation theories, exemplified by the Ashland case, has provided a model as instructive as Silicon Valley, to seekers of a general theory and practice of regional innovation and entrepreneurship. The role of Southern Oregon University (SOU) in the inception of a cultural cluster gives rise to a model for education-focused universities to play a significant role in local economic development through civic entrepreneurship

    The Formation of Brown Dwarfs as Ejected Stellar Embryos

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    We conjecture that brown dwarfs are substellar objects because they have been ejected from small newborn multiple systems which have decayed in dynamical interactions. In this view, brown dwarfs are stellar embryos for which the star formation process was aborted before the hydrostatic cores could build up enough mass to eventually start hydrogen burning. The disintegration of a small multiple system is a stochastic process, which can be described only in terms of the half-life of the decay. A stellar embryo competes with its siblings in order to accrete infalling matter, and the one that grows slowest is most likely to be ejected. With better luck, a brown dwarf would therefore have become a normal star. This interpretation of brown dwarfs readily explains the rarity of brown dwarfs as companions to normal stars (aka the ``brown dwarf desert''), the absence of wide brown dwarf binaries, and the flattening of the low mass end of the initial mass function. Possible observational tests of this scenario include statistics of brown dwarfs near Class 0 sources, and the kinematics of brown dwarfs in star forming regions while they still retain a kinematic signature of their expulsion. Because the ejection process limits the amount of gas brought along in a disk, it is predicted that substellar equivalents to the classical T Tauri stars should be very rare.Comment: 8 pages, 1 figure, Accepted by the Astronomical Journa

    The AEI 10 m prototype interferometer

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    A 10 m prototype interferometer facility is currently being set up at the AEI in Hannover, Germany. The prototype interferometer will be housed inside a 100 m^3 ultra-high vacuum envelope. Seismically isolated optical tables inside the vacuum system will be interferometrically interconnected via a suspension platform interferometer. Advanced isolation techniques will be used, such as inverted pendulums and geometrical anti-spring filters in combination with multiple-cascaded pendulum suspensions, containing an all-silica monolithic last stage. The light source is a 35 W Nd:YAG laser, geometrically filtered by passing it through a photonic crystal fibre and a rigid pre-modecleaner cavity. Laser frequency stabilisation will be achieved with the aid of a high finesse suspended reference cavity in conjunction with a molecular iodine reference. Coating thermal noise will be reduced by the use of Khalili cavities as compound end mirrors. Data acquisition and control of the experiments is based on the AdvLIGO digital control and data system. The aim of the project is to test advanced techniques for GEO 600 as well as to conduct experiments in macroscopic quantum mechanics. Reaching standard quantum-limit sensitivity for an interferometer with 100 g mirrors and subsequently breaching this limit, features most prominently among these experiments. In this paper we present the layout and current status of the AEI 10 m Prototype Interferometer project

    Jacobson generators, Fock representations and statistics of sl(n+1)

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    The properties of A-statistics, related to the class of simple Lie algebras sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are further investigated. The description of each sl(n+1) is carried out via generators and their relations, first introduced by Jacobson. The related Fock spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The Pauli principle of the underlying statistics is formulated. In addition the paper contains the following new results: (a) The A-statistics are interpreted as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ..., B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is proved that in an appropriate topology the limit of B(p)_i^\pm for p going to infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation operators; (c) It is shown that the local statistics of the degenerated hard-core Bose models and of the related Heisenberg spin models is p=1 A-statistics.Comment: LaTeX-file, 33 page
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