628 research outputs found
Internalizing Change Capacity in Secondary Schools Through Organizational Change
In this article we focus on understanding the meaning of change capacity in secondary schools. Our definition of change capacity focuses on organizational dimensions. We review evidence from a longitudinal study of change in nine secondary schools in a single district to argue that change capacity consists of three attributes: liberation from structures that inhibit innovation (in our case breaking the mold of subject department organizational structures), honoring dissonance, and forging new relationships. We identify the conditions that contribute to the development of change capacity in secondary schools by examining the contributors to the emergence of each element.Dans cet article, les auteurs se penchent sur le sens de la capacité pour le changement dans les écoles secondaires. La définition qu'ils en donnent s'appuie sur des dimensions organisationnelles. Ils évoquent les résultats d'une étude longitudinale de neuf écoles secondaires situées dans un seul district comme preuve que la capacité pour le changement consiste en trois éléments: le fait d'outrepasser les structures qui limitent l'innovation (dans le présent cas, il s'agissait de passer au-delà des contraintes organisationnelles imposées par la structure départementale basée sur les matières-sujets), le respect de la dissonance et l'établissement de nouveaux rapports. En étudiant les facteurs qui contribuent à la naissance de chacun de ces éléments, les auteurs expliquent par le fait même les conditions qui encouragent le développement de la capacité pour le changement dans les écoles secondaires
Real roots of Random Polynomials: Universality close to accumulation points
We identify the scaling region of a width O(n^{-1}) in the vicinity of the
accumulation points of the real roots of a random Kac-like polynomial
of large degree n. We argue that the density of the real roots in this region
tends to a universal form shared by all polynomials with independent,
identically distributed coefficients c_i, as long as the second moment
\sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to
the previously reported abrupt) and quite nontrivial suppression of the number
of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled
as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been
removed. 10 pages, 12 eps figures. This version contains all updates, clearer
pictures and some more thorough explanation
Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane
The shrunk loop theorem presented here is an integral identity which
facilitates the calculation of the relative probability (or probability
amplitude) of any given topology that a free, closed Brownian or Feynman path
of a given 'duration' might have on the twice punctured plane (the plane with
two marked points). The result is expressed as a scattering series of integrals
of increasing dimensionality based on the maximally shrunk version of the path.
Physically, this applies in different contexts: (i) the topology probability of
a closed ideal polymer chain on a plane with two impassable points, (ii) the
trace of the Schroedinger Green function, and thence spectral information, in
the presence of two Aharonov-Bohm fluxes, (iii) the same with two branch points
of a Riemann surface instead of fluxes. Our theorem starts with the Stovicek
expansion for the Green function in the presence of two Aharonov-Bohm flux
lines, which itself is based on the famous Sommerfeld one puncture point
solution of 1896 (the one puncture case has much easier topology, just one
winding number). Stovicek's expansion itself can supply the results at the
expense of choosing a base point on the loop and then integrating it away. The
shrunk loop theorem eliminates this extra two dimensional integration,
distilling the topology from the geometry.Comment: 29 pages, 5 figures (accepted by J. Phys. A: Math. Gen.
The Frobenius formalism in Galois quantum systems
Quantum systems in which the position and momentum take values in the ring
and which are described with -dimensional Hilbert space, are
considered. When is the power of a prime, the position and momentum take
values in the Galois field , the position-momentum phase space is
a finite geometry and the corresponding `Galois quantum systems' have stronger
properties. The study of these systems uses ideas from the subject of field
extension in the context of quantum mechanics. The Frobenius automorphism in
Galois fields leads to Frobenius subspaces and Frobenius transformations in
Galois quantum systems. Links between the Frobenius formalism and Riemann
surfaces, are discussed
Notes on Conformal Invisibility Devices
As a consequence of the wave nature of light, invisibility devices based on
isotropic media cannot be perfect. The principal distortions of invisibility
are due to reflections and time delays. Reflections can be made exponentially
small for devices that are large in comparison with the wavelength of light.
Time delays are unavoidable and will result in wave-front dislocations. This
paper considers invisibility devices based on optical conformal mapping. The
paper shows that the time delays do not depend on the directions and impact
parameters of incident light rays, although the refractive-index profile of any
conformal invisibility device is necessarily asymmetric. The distortions of
images are thus uniform, which reduces the risk of detection. The paper also
shows how the ideas of invisibility devices are connected to the transmutation
of force, the stereographic projection and Escheresque tilings of the plane
The three-body problem and the Hannay angle
The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit
The geometric phase and the dynamics of quantum phase transition induced by a linear quench
We have analysed here the role of the geometric phase in dynamical mechanism
of quantum phase transition in the transverse Ising model. We have investigated
the system when it is driven at a fixed rate characterized by a quench time
across the critical point from a paramagnetic to ferromagnetic phase.
Our argument is based on the fact that the spin fluctuation occurring during
the critical slowing down causes random fluctuation in the ground state
geometric phase at the critical regime. The correlation function of the random
geometric phase determines the excitation probability of the quasiparticles,
which are excited during the transition from the inital paramagnetic to the
ferromagnetic phase. This helps us to evaluate the number density of the kinks
formed during the transition, which is found to scale as
. In addition, we have also estimated the spin-spin
correlation at criticality.Comment: 10 pages, accepted in J. Phys. A: Math and Theor. (Special issue on
Quantum Phases
Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices
We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma
On the semiclassical theory for universal transmission fluctuations in chaotic systems: the importance of unitarity
The standard semiclassical calculation of transmission correlation functions
for chaotic systems is severely influenced by unitarity problems. We show that
unitarity alone imposes a set of relationships between cross sections
correlation functions which go beyond the diagonal approximation. When these
relationships are properly used to supplement the semiclassical scheme we
obtain transmission correlation functions in full agreement with the exact
statistical theory and the experiment. Our approach also provides a novel
prediction for the transmission correlations in the case where time reversal
symmetry is present
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