7,598 research outputs found
Group gradings on finitary simple Lie algebras
We classify, up to isomorphism, all gradings by an arbitrary abelian group on
simple finitary Lie algebras of linear transformations (special linear,
orthogonal and symplectic) on infinite-dimensional vector spaces over an
algebraically closed field of characteristic different from 2.Comment: Several typographical errors have been correcte
Algebraic Approach to Interacting Quantum Systems
We present an algebraic framework for interacting extended quantum systems to
study complex phenomena characterized by the coexistence and competition of
different states of matter. We start by showing how to connect different
(spin-particle-gauge) {\it languages} by means of exact mappings (isomorphisms)
that we name {\it dictionaries} and prove a fundamental theorem establishing
when two arbitrary languages can be connected. These mappings serve to unravel
symmetries which are hidden in one representation but become manifest in
another. In addition, we establish a formal link between seemingly unrelated
physical phenomena by changing the language of our model description. This link
leads to the idea of {\it universality} or equivalence. Moreover, we introduce
the novel concept of {\it emergent symmetry} as another symmetry guiding
principle. By introducing the notion of {\it hierarchical languages}, we
determine the quantum phase diagram of lattice models (previously unsolved) and
unveil hidden order parameters to explore new states of matter. Hierarchical
languages also constitute an essential tool to provide a unified description of
phases which compete and coexist. Overall, our framework provides a simple and
systematic methodology to predict and discover new kinds of orders. Another
aspect exploited by the present formalism is the relation between condensed
matter and lattice gauge theories through quantum link models. We conclude
discussing applications of these dictionaries to the area of quantum
information and computation with emphasis in building new models of computation
and quantum programming languages.Comment: 44 pages, 14 psfigures. Advances in Physics 53, 1 (2004
Black holes admitting a Freudenthal dual
The quantised charges x of four dimensional stringy black holes may be
assigned to elements of an integral Freudenthal triple system whose
automorphism group is the corresponding U-duality and whose U-invariant quartic
norm Delta(x) determines the lowest order entropy. Here we introduce a
Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although
distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the
requirement that \tilde{x} be integer restricts us to the subset of black holes
for which Delta(x) is necessarily a perfect square. The issue of higher-order
corrections remains open as some, but not all, of the discrete U-duality
invariants are Freudenthal invariant. Similarly, the quantised charges A of
five dimensional black holes and strings may be assigned to elements of an
integral Jordan algebra, whose cubic norm N(A) determines the lowest order
entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a
perfect cube, for which A**=A and which leaves N(A) invariant. The two
dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde
Small Orbits
We study both the "large" and "small" U-duality charge orbits of extremal
black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories
with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan
algebras and their associated Freudenthal triple systems, in order to derive
the minimal charge representatives, their stabilizers and the associated
"moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2
and N = 4 theories coupled to an arbitrary number of vector multiplets, as well
as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered
as part of the general N = 2 sequence, albeit with an additional triality
symmetry, the ST^2 and T^3 models demand a separate treatment, since their
representative Jordan algebras are Euclidean or only admit non-zero elements of
rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter
coupled N = 3, and "pure" N = 5 theories.Comment: 40 pages, 9 tables. References added. Expanded comments added to
sections III. C. 1. and III. F.
Nonassociative differential extensions of characteristic p
Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Amitsur and Jacobson. We construct families of nonassociative division algebras which can be viewed as generalizations of associative cyclic extensions of a purely inseparable field extension of exponent one or a central division algebra. Division algebras which are nonassociative cyclic extensions of a purely inseparable field extension of exponent one are particularly easy to obtain
Validity of the Generalized Second Law of Thermodynamics of the Universe Bounded by the Event Horizon in Brane Scenario
In this paper, we examine the validity of the generalized second law of
thermodynamics (GSLT) of the universe bounded by the event horizon in
brane-world gravity. Here we consider homogeneous and isotropic model of the
universe filled with perfect fluid in one case and in another case holographic
dark energy model of the universe has been considered. The conclusions are
presented point wise.Comment: 8 pages, the paper has been accepted in EPJC for publication.
Conclusion has been modified an some references have been adde
Systems development methods and usability in Norway: An industrial perspective
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2007 Springer Berlin HeidelbergThis paper investigates the relationship between traditional systems development methodologies and usability, through a survey of 78 Norwegian IT companies. Building on previous research we proposed two hypotheses; (1) that software companies will generally pay lip service to usability, but do not prioritize it in industrial projects, and (2) that systems development methods and usability are perceived as not being integrated. We find support for both hypotheses. Thus, the use of systems development methods is fairly stable, confirming earlier research. Most companies do not use a formal method, and of those who do, the majority use their own method. Generally, the use of methods is rather pragmatic: Companies that do not use formal methods report that they use elements from such methods. Further, companies that use their own method import elements from standardised methods into their own
Model of black hole evolution
From the postulate that a black hole can be replaced by a boundary on the
apparent horizon with suitable boundary conditions, an unconventional scenario
for the evolution emerges. Only an insignificant fraction of energy of order
is radiated out. The outgoing wave carries a very small part of the
quantum mechanical information of the collapsed body, the bulk of the
information remaining in the final stable black hole geometry.Comment: 9 pages, harvmac, 3 figures, minor addition
Generic bounds on dipolar gravitational radiation from inspiralling compact binaries
Various alternative theories of gravity predict dipolar gravitational
radiation in addition to quadrupolar radiation. We show that gravitational wave
(GW) observations of inspiralling compact binaries can put interesting
constraints on the strengths of the dipole modes of GW polarizations. We put
forward a physically motivated gravitational waveform for dipole modes, in the
Fourier domain, in terms of two parameters: one which captures the relative
amplitude of the dipole mode with respect to the quadrupole mode () and
the other a dipole term in the phase (). We then use this two parameter
representation to discuss typical bounds on their values using GW measurements.
We obtain the expected bounds on the amplitude parameter and the phase
parameter for Advanced LIGO (AdvLIGO) and Einstein Telescope (ET) noise
power spectral densities using Fisher information matrix. AdvLIGO and ET may at
best bound to an accuracy of and and
to an accuracy of and respectively.Comment: Matches with the published versio
Model of black hole evolution
From the postulate that a black hole can be replaced by a boundary on the
apparent horizon with suitable boundary conditions, an unconventional scenario
for the evolution emerges. Only an insignificant fraction of energy of order
is radiated out. The outgoing wave carries a very small part of the
quantum mechanical information of the collapsed body, the bulk of the
information remaining in the final stable black hole geometry.Comment: 9 pages, harvmac, 3 figures, minor addition
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