2,074 research outputs found
Gravity in Non-Commutative Geometry
We study general relativity in the framework of non-commutative differential
geometry. In particular, we introduce a gravity action for a space-time which
is the product of a four dimensional manifold by a two-point space. In the
simplest situation, where the Riemannian metric is taken to be the same on the
two copies of the manifold, one obtains a model of a scalar field coupled to
Einstein gravity. This field is geometrically interpreted as describing the
distance between the two points in the internal space.Comment: ZU-TH-30/1992 and ETH/TH/92/44, 11 pages. (The earlier version of
this paper was the incomplete and unedited file which accidently replaced the
corrected file
Equation of state and Beginning of Thermalization After Preheating
We study the out-of-equilibrium nonlinear dynamics of fields after
post-inflationary preheating. During preheating, the energy in the homogeneous
inflaton is exponentially rapidly transfered into highly occupied
out-of-equilibrium inhomogeneous modes, which subsequently evolve towards
equilibrium. The infrared modes excited during preheating evolve towards a
saturated distribution long before thermalization completes. We compute the
equation of state during and immediately after preheating. It rapidly evolves
towards radiation domination long before the actual thermal equilibrium is
established. The exact time of this transition is a non-monotonic function of
the coupling between the inflaton and the decay products, and it varies only
very weakly (around 10^(-35) s) as this coupling changes over several orders of
magnitude. This result is applied to refine the relation between the number of
efoldings N and the physical wavelength of perturbations generated during
inflation. We also discuss the implications for the theory of modulated
perturbations from preheating. We finally argue that many questions of the
thermal history of the universe should be addressed in terms of
pre-thermalization, illustrating this point with a calculation of perturbative
production of gravitinos immediately after chaotic inflation. We also highlight
the effects of three-legs inflaton interactions on the dynamics of preheating
and thermalization in an expanding universe.Comment: 15 pages, 13 figure
A Survey of Learning Styles of Engineering Students
This study examined the learning styles of engineering students using the Index of Learning Styles (ILS) developed by Soloman and Felder (Soloman & Felder, 2002), the Cognitive Styles Analysis (CSA) developed by Riding (Riding, 1991), and the Learning Style Inventory (LSI) developed by Kolb (Kolb, 1993). Thirty-five graduate and thirty-six undergraduate engineering students took each of the assessments. There was a strong preference for the visual category on the ILS, but an even split for the imagery/verbal dimension on the CSA. Scores were also evenly split on the active/reflective and sequential/global dimensions on the ILS. Another strong preference was seen for the analytic category on the CSA. On the LSI, most students' scores indicated a preference for the convergent category and no student scores were in the divergent category. An overview of each of the instruments as well as a summary of student learning needs for each of the dimensions is presented.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline
Elliptic dynamical quantum groups and equivariant elliptic cohomology
We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on weight functions and shuffle products. We construct an action of the dynamical elliptic quantum group associated with on the equivariant elliptic cohomology of the union of cotangent bundles of Grassmannians. The generators of the elliptic quantum groups act as difference operators on sections of admissible bundles, a notion introduced in this paper
Dynamics of Symmetry Breaking and Tachyonic Preheating
We reconsider the old problem of the dynamics of spontaneous symmetry
breaking using 3d lattice simulations, and develop a theory of tachyonic
preheating, which occurs due to the spinodal instability of the scalar field.
Tachyonic preheating is so efficient that symmetry breaking typically completes
within a single oscillation of the field distribution as it rolls towards the
minimum of its effective potential. As an application of this theory we
consider preheating in the hybrid inflation scenario, including SUSY-motivated
F-term and D-term inflationary models. We show that preheating in hybrid
inflation is typically tachyonic and the stage of oscillations of a homogeneous
component of the scalar fields driving inflation ends after a single
oscillation. Our results may also be relevant for the theory of the formation
of disoriented chiral condensates in heavy ion collisions.Comment: 7 pages, 6 figures. Higher quality figures and computer generated
movies in gif format illustrating our results can be found at
http://physics.stanford.edu/gfelder/hybri
2D Conformal Field Theories and Holography
It is known that the chiral part of any 2d conformal field theory defines a
3d topological quantum field theory: quantum states of this TQFT are the CFT
conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT
relation exists also for the full CFT. The 3d topological theory that arises is
a certain ``square'' of the chiral TQFT. Such topological theories were studied
by Turaev and Viro; they are related to 3d gravity. We establish an
operator/state correspondence in which operators in the chiral TQFT correspond
to states in the Turaev-Viro theory. We use this correspondence to interpret
CFT correlation functions as particular quantum states of the Turaev-Viro
theory. We compute the components of these states in the basis in the
Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we
obtain is a generalization of the Verlinde formula. The later is obtained from
our expression for a zero colored graph. Our results give an interesting
``holographic'' perspective on conformal field theories in 2 dimensions.Comment: 29+1 pages, many figure
The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra
Using a contraction procedure, we construct a twist operator that satisfies a
shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2))
algebra. The corresponding universal matrix obeys a
Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a
class of representations, the dynamical Yang-Baxter equation may be expressed
as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure
Trace checking of Metric Temporal Logic with Aggregating Modalities using MapReduce
Modern complex software systems produce a large amount of execution data,
often stored in logs. These logs can be analyzed using trace checking
techniques to check whether the system complies with its requirements
specifications. Often these specifications express quantitative properties of
the system, which include timing constraints as well as higher-level
constraints on the occurrences of significant events, expressed using aggregate
operators. In this paper we present an algorithm that exploits the MapReduce
programming model to check specifications expressed in a metric temporal logic
with aggregating modalities, over large execution traces. The algorithm
exploits the structure of the formula to parallelize the evaluation, with a
significant gain in time. We report on the assessment of the implementation -
based on the Hadoop framework - of the proposed algorithm and comment on its
scalability.Comment: 16 pages, 6 figures, Extended version of the SEFM 2014 pape
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