16,405 research outputs found
Noncommutative Dynamics of Random Operators
We continue our program of unifying general relativity and quantum mechanics
in terms of a noncommutative algebra on a transformation groupoid
where is the total space of a principal fibre bundle
over spacetime, and a suitable group acting on . We show that
every defines a random operator, and we study the dynamics of
such operators. In the noncommutative regime, there is no usual time but, on
the strength of the Tomita-Takesaki theorem, there exists a one-parameter group
of automorphisms of the algebra which can be used to define a state
dependent dynamics; i.e., the pair , where is a state
on , is a ``dynamic object''. Only if certain additional conditions
are satisfied, the Connes-Nikodym-Radon theorem can be applied and the
dependence on disappears. In these cases, the usual unitary quantum
mechanical evolution is recovered. We also notice that the same pair defines the so-called free probability calculus, as developed by
Voiculescu and others, with the state playing the role of the
noncommutative probability measure. This shows that in the noncommutative
regime dynamics and probability are unified. This also explains probabilistic
properties of the usual quantum mechanics.Comment: 13 pages, LaTe
QCD Thermodynamics from the Lattice
We review the current methods and results of lattice simulations of quantum
chromodynamics at nonzero temperatures and densities. The review is intended to
introduce the subject to interested nonspecialists and beginners. It includes a
brief overview of lattice gauge theory, a discussion of the determination of
the crossover temperature, the QCD phase diagram at zero and nonzero densities,
the equation of state, some in-medium properties of hadrons including
charmonium, and some plasma transport coefficients.Comment: 74 pp. 31 figs. To appear in the European Physical Journal A and
Advances in Physics of Particles and Nuclei. Added references, corrected
typos, and updated the discussion of the thermal heavy quark/antiquark
potential. Added and updated references. Final versio
Conceptual Unification of Gravity and Quanta
We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition
of generalized Einstein's field equation
Anatomy of Malicious Singularities
As well known, the b-boundaries of the closed Friedman world model and of
Schwarzschild solution consist of a single point. We study this phenomenon in a
broader context of differential and structured spaces. We show that it is an
equivalence relation , defined on the Cauchy completed total space
of the frame bundle over a given space-time, that is responsible for
this pathology. A singularity is called malicious if the equivalence class
related to the singularity remains in close contact with all other
equivalence classes, i.e., if for every . We
formulate conditions for which such a situation occurs. The differential
structure of any space-time with malicious singularities consists only of
constant functions which means that, from the topological point of view,
everything collapses to a single point. It was noncommutative geometry that was
especially devised to deal with such situations. A noncommutative algebra on
, which turns out to be a von Neumann algebra of random operators,
allows us to study probabilistic properties (in a generalized sense) of
malicious singularities. Our main result is that, in the noncommutative regime,
even the strongest singularities are probabilistically irrelevant.Comment: 16 pages in LaTe
Space probe/satellite ejection apparatus for spacecraft
An ejection apparatus for spinning and propelling objects for ejection from a spacecraft at a desired velocity and rotational speed is discussed. The apparatus includes a launch cradle on which the space object to be ejected rests. The cradle is rotatably supported by a central hub secured to the upper end of the pneumatic cylinder piston shaft. Release mechanisms consisting of a retractable pin and locking lug is utilized to hold the cradle and object to be ejected. The release mechanism has a fixed barrier member which holds the retractable pin in engagement with the locking lug until release by upward movement of the launch cradle beyond the barrier height
Entanglement, Holography and Causal Diamonds
We argue that the degrees of freedom in a d-dimensional CFT can be
re-organized in an insightful way by studying observables on the moduli space
of causal diamonds (or equivalently, the space of pairs of timelike separated
points). This 2d-dimensional space naturally captures some of the fundamental
nonlocality and causal structure inherent in the entanglement of CFT states.
For any primary CFT operator, we construct an observable on this space, which
is defined by smearing the associated one-point function over causal diamonds.
Known examples of such quantities are the entanglement entropy of vacuum
excitations and its higher spin generalizations. We show that in holographic
CFTs, these observables are given by suitably defined integrals of dual bulk
fields over the corresponding Ryu-Takayanagi minimal surfaces. Furthermore, we
explain connections to the operator product expansion and the first law of
entanglement entropy from this unifying point of view. We demonstrate that for
small perturbations of the vacuum, our observables obey linear two-derivative
equations of motion on the space of causal diamonds. In two dimensions, the
latter is given by a product of two copies of a two-dimensional de Sitter
space. For a class of universal states, we show that the entanglement entropy
and its spin-three generalization obey nonlinear equations of motion with local
interactions on this moduli space, which can be identified with Liouville and
Toda equations, respectively. This suggests the possibility of extending the
definition of our new observables beyond the linear level more generally and in
such a way that they give rise to new dynamically interacting theories on the
moduli space of causal diamonds. Various challenges one has to face in order to
implement this idea are discussed.Comment: 84 pages, 12 figures; v2: expanded discussion on constraints in
section 7, matches published versio
Transitioning Rework Shape Optimisation Technology for ADF Airframe Applications
Through-life management of aircraft structural integrity (ASI) is an important program in both civilian and military aviation providing structural safety, improvements in aircraft availability, and reduced cost of ownership. One innovative method for life extension is rework shape optimisation to minimise stresses at crack prone regions in metallic airframe components. This paper covers the collaborative work carried out between ASI-DGTA and AVD-DSTO in developing and transitioning the shape optimisation technology to manage and improve ASI within a regulatory environment. It is shown that numerical methods based on structural mechanics, can be used to develop robust and practical optimised rework shapes. Key lessons learned are discussed, including indicative results for the interaction of some key design parameters on peak stresses and predicted fatigue lives. Finally strategies for the application and transition management of this technology are given
Heavy-light meson decay constants from NRQCD: an analysis of the 1/M corrections
We present {\it preliminary} results for the decay constants of heavy-light
mesons using NRQCD heavy and tadpole improved Clover light quarks. A comparison
is made with data obtained using Wilson light quarks. We present an analysis of
the 1/M corrections to the decay constants in the static limit and compare with
the predictions of HQET.Comment: Contribution to Lattice 95, 4 pages uuencoded compressed postscript
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On the neutrality issue in the Polyakov-loop NJL model
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona
Lasinio (PNJL) model at finite density within the adopted mean field
approximation. Also we point out how usual assumption about the diagonal form
of the Wilson loop may fail in the presence of the diquark condensate on
several grounds.Comment: 8 pages, 1 figure. Introduction enlarged, several comments about the
adopted mean field approximation and the relation with Elitzur's theorem
added. Version to appear on Phys. Rev.
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