151,640 research outputs found
The Hall Triple Systems of Small Class
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
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
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
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
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
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
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
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)
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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