3,529 research outputs found
Tachyons in de Sitter space and analytical continuation from dS/CFT to AdS/CFT
We discuss analytic continuation from d-dimensional Lorentzian de Sitter
(dS) to d-dimensional Lorentzian anti-de Sitter (AdS) spacetime. We
show that AdS, with opposite signature of the metric, can be obtained as
analytic continuation of a portion of dS. This implies that the dynamics of
(positive square-mass) scalar particles in AdS can be obtained from the
dynamics of tachyons in dS. We discuss this correspondence both at the
level of the solution of the field equations and of the Green functions. The
AdS/CFT duality is obtained as analytic continuation of the dS/CFT duality.Comment: 17 pages, 1 figure, JHEP styl
Wigner-Dyson Statistics from the Replica Method
We compute the correlation functions of the eigenvalues in the Gaussian
unitary ensemble using the fermionic replica method. We show that non--trivial
saddle points, which break replica symmetry, must be included in the
calculation in order to reproduce correctly the exact results for the
correlation functions at large distance.Comment: 13 pages, added reference
The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum
We calculate the probability to find exactly eigenvalues in a spectral
interval of a large random matrix when this interval contains eigenvalues on average. The calculations exploit an analogy to the
problem of finding a two-dimensional charge distribution on the interface of a
semiconductor heterostructure under the influence of a split gate.Comment: 4 pages, postscrip
Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
We determine the asymptotic level spacing distribution for the Laguerre
Ensemble in a single scaled interval, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, found by Tracy and Widom, are reproduced without the use of the
Bessel kernel and the associated Painlev\'e transcendent. In the same
approximation, the next leading term, due to a ``finite temperature''
perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe
Action research in physical education: focusing beyond myself through cooperative learning
This paper reports on the pedagogical changes that I experienced as a teacher engaged in an action research project in which I designed and implemented an indirect, developmentally appropriate and childâcentred approach to my teaching. There have been repeated calls to expunge â or at least rationalise â the use of traditional, teacherâled practice in physical education. Yet despite the advocacy of many leading academics there is little evidence that such a change of approach is occurring. In my role as teacherâasâresearcher I sought to implement a new pedagogical approach, in the form of cooperative learning, and bring about a positive change in the form of enhanced pupil learning. Data collection included a reflective journal, postâteaching reflective analysis, pupil questionnaires, student interviews, document analysis, and nonâparticipant observations. The research team analysed the data using inductive analysis and constant comparison. Six themes emerged from the data: teaching and learning, reflections on cooperation, performance, time, teacher change, and social interaction. The paper argues that cooperative learning allowed me to place social and academic learning goals on an even footing, which in turn placed a focus on pupilsâ understanding and improvement of skills in athletics alongside their interpersonal development
Fluctuation properties of strength functions associated with giant resonances
We performed fluctuation analysis by means of the local scaling dimension for
the strength function of the isoscalar (IS) and the isovector (IV) giant
quadrupole resonances (GQR) in Ca, where the strength functions are
obtained by the shell model calculation within up to the 2p2h configurations.
It is found that at small energy scale, fluctuation of the strength function
almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit.
On the other hand, we found a deviation from the GOE limit at the intermediate
energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results
imply that different types of fluctuations coexist at different energy scales.
Detailed analysis strongly suggests that GOE fluctuation at small energy scale
is due to the complicated nature of 2p2h states and that fluctuation at the
intermediate energy scale is associated with the spreading width of the
Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure
Statistical Analysis of Magnetic Field Spectra
We have calculated and statistically analyzed the magnetic-field spectrum
(the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems
with classically chaotic shape. This is a new problem which arises naturally in
transport measurements where the incoming electron has a fixed energy while one
tunes the magnetic field to obtain resonance conductance patterns. The
``B-spectrum'', defined as the collection of values at which
conductance takes extremal values, is determined by a quadratic
eigenvalue equation, in distinct difference to the usual linear eigenvalue
problem satisfied by the energy levels. We found that the lower part of the
``B-spectrum'' satisfies the distribution belonging to Gaussian Unitary
Ensemble, while the higher part obeys a Poisson-like behavior. We also found
that the ``B-spectrum'' fluctuations of the chaotic system are consistent with
the results we obtained from random matrices
Triple-horizon spherically symmetric spacetime and holographic principle
We present a family of spherically symmetric spacetimes, specified by the
density profile of a vacuum dark energy, which have the same global structure
as the de Sitter spacetime but the reduced symmetry which leads to a
time-evolving and spatially inhomogeneous cosmological term. It connects
smoothly two de Sitter vacua with different values of cosmological constant and
corresponds to anisotropic vacuum dark fluid defined by symmetry of its
stress-energy tensor which is invariant under the radial boosts. This family
contains a special class distinguished by dynamics of evaporation of a
cosmological horizon which evolves to the triple horizon with the finite
entropy, zero temperature, zero curvature, infinite positive specific heat, and
infinite scrambling time. Non-zero value of the cosmological constant in the
triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of
the cosmological horizon.Comment: Honorable Mentioned Essay - Gravity Research Foundation 2012;
submitted to Int. J. Mod. Phys.
Spectral Statistics Beyond Random Matrix Theory
Using a nonperturbative approach we examine the large frequency asymptotics
of the two-point level density correlator in weakly disordered metallic grains.
This allows us to study the behavior of the two-level structure factor close to
the Heisenberg time. We find that the singularities (present for random matrix
ensembles) are washed out in a grain with a finite conductance. The results are
nonuniversal (they depend on the shape of the grain and on its conductance),
though they suggest a generalization for any system with finite Heisenberg
time.Comment: Uuencoded file with two eps figures, 10 pages
On frequencies of small oscillations of some dynamical systems associated with root systems
In the paper by F. Calogero and author [Commun. Math. Phys. 59 (1978)
109-116] the formula for frequencies of small oscillations of the Sutherland
system ( case) was found. In present note the generalization of this
formula for the case of arbitrary root system is given.Comment: arxiv version is already officia
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