693 research outputs found
School Quality, Educational Attainment and Aggregation Bias
Data from 31 countries participating in the Programme for International Student Assessment (PISA) is used to estimate education production functions for reading literacy.The analysis suggests that the probability of finding statistically significant and correctly signed class size effects increases the higher the level of aggregation used to measure class size.Class size, PISA data, bias
Probing Vortex Unbinding via Dipole Fluctuations
We develop a numerical method for detecting a vortex unbinding transition in
a two-dimensional system by measuring large scale fluctuations in the total
vortex dipole moment of the system. These are characterized by a
quantity which measures the number of configurations in a simulation
for which the either or is half the system size. It is shown that
tends to a non-vanishing constant for large system sizes in the
unbound phase, and vanishes in the bound phase. The method is applied to the XY
model both in the absence and presence of a magnetic field. In the latter case,
the system size dependence of suggests that there exist three distinct
phases, one unbound vortex phase, a logarithmically bound phase, and a linearly
bound phase.Comment: 6 pages, 2 figure
The motif problem
Fix a choice and ordering of four pairwise non-adjacent vertices of a
parallelepiped, and call a motif a sequence of four points in R^3 that coincide
with these vertices for some, possibly degenerate, parallelepiped whose edges
are parallel to the axes. We show that a set of r points can contain at most
r^2 motifs. Generalizing the notion of motif to a sequence of L points in R^p,
we show that the maximum number of motifs that can occur in a point set of a
given size is related to a linear programming problem arising from hypergraph
theory, and discuss some related questions.Comment: 17 pages, 1 figur
Band topology and quantum spin Hall effect in bilayer graphene
We consider bilayer graphene in the presence of spin orbit coupling, to
assess its behavior as a topological insulator. The first Chern number for
the energy bands of single and bilayer graphene is computed and compared. It is
shown that for a given valley and spin, in a bilayer is doubled with
respect to the monolayer. This implies that bilayer graphene will have twice as
many edge states as single layer graphene, which we confirm with numerical
calculations and analytically in the case of an armchair terminated surface.
Bilayer graphene is a weak topological insulator, whose surface spectrum is
susceptible to gap opening under spin-mixing perturbations. We also assess the
stability of the associated topological bulk state of bilayer graphene under
various perturbations. Finally, we consider an intermediate situation in which
only one of the two layers has spin orbit coupling, and find that although
individual valleys have non-trivial Chern numbers, the spectrum as a whole is
not gapped, so that the system is not a topological insulator.Comment: 9 pages. 9 figures include
Collective charge density fluctuations in superconducting layered systems with bilayer unit cells
Collective modes of bilayered superconducting superlattices (e.g., YBCO) are
investigated within the conserving gauge-invariant ladder diagram approximation
including both the nearest interlayer single electron tunneling and the
Josephson-type Cooper pair tunneling. By calculating the density-density
response function including Coulomb and pairing interactions, we examine the
two collective mode branches corresponding to the in-phase and out-of-phase
charge fluctuations between the two layers in the unit cell. The out-of-phase
collective mode develops a long wavelength plasmon gap whose magnitude depends
on the tunneling strength with the mode dispersions being insensitive to the
specific tunneling mechanism (i.e., single electron or Josephson). We also show
that in the presence of tunneling the oscillator strength of the out-of-phase
mode overwhelms that of the in-phase-mode at and finite ,
where and are respectively the mode wave vectors perpendicular
and along the layer. We discuss the possible experimental observability of the
phase fluctuation modes in the context of our theoretical results for the mode
dispersion and spectral weight.Comment: 9 pages, 3 figure
Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field
We develop a method to compute shakeup effects on photoluminescence from a
strong magnetic field induced two-dimensional Wigner crystal. Only localized
holes are considered. Our method treats the lattice electrons and the tunneling
electron on an equal footing, and uses a quantum-mechanical calculation of the
collective modes that does not depend in any way on a harmonic approximation.
We find that shakeup produces a series of sidebands that may be identified with
maxima in the collective mode density of states, and definitively distinguishes
the crystal state from a liquid state in the absence of electron-hole
interaction. In the presence of electron-hole interaction, sidebands also
appear in the liquid state coming from short-range density fluctuations around
the hole. However, the sidebands in the liquid state and the crystal state have
different qualitative behaviors. We also find a shift in the main luminescence
peak, that is associated with lattice relaxation in the vicinity of a vacancy.
The relationship of the shakeup spectrum with previous mean-field calculations
is discussed.Comment: 14 pages, uuencoded postscript file for entire paper, also available
at (click phd14) http://rainbow.uchicago.edu/~ldz/paper/paper.htm
Collective Modes of Quantum Hall Stripes
The collective modes of striped phases in a quantum Hall system are computed
using the time-dependent Hartree-Fock approximation. Uniform stripe phases are
shown to be unstable to the formation of modulations along the stripes, so that
within the Hartree-Fock approximation the groundstate is a stripe crystal. Such
crystalline states are generically gapped at any finite wavevector; however, in
the quantum Hall system the interactions of modulations among different stripes
is found to be remarkably weak, leading to an infinite collection of collective
modes with immeasurably small gaps. The resulting long wavelength behavior is
derivable from an elastic theory for smectic liquid crystals. Collective modes
for the phonon branch are computed throughout the Brillouin zone, as are spin
wave and magnetoplasmon modes. A soft mode in the phonon spectrum is identified
for partial filling factors sufficiently far from 1/2, indicating a second
order phase transition. The modes contain several other signatures that should
be experimentally observable.Comment: 36 pages LaTex with 11 postscript figures. Short animations of the
collective modes can be found at
http://www.physique.usherb.ca/~rcote/stripes/stripes.ht
Dynamics of quantum Hall stripes in double-quantum-well systems
The collective modes of stripes in double layer quantum Hall systems are
computed using the time-dependent Hartree-Fock approximation. It is found that,
when the system possesses spontaneous interlayer coherence, there are two
gapless modes, one a phonon associated with broken translational invariance,
the other a pseudospin-wave associated with a broken U(1) symmetry. For large
layer separations the modes disperse weakly for wavevectors perpendicular to
the stripe orientation, indicating the system becomes akin to an array of
weakly coupled one-dimensional XY systems. At higher wavevectors the collective
modes develop a roton minimum associated with a transition out of the coherent
state with further increasing layer separation. A spin wave model of the system
is developed, and it is shown that the collective modes may be described as
those of a system with helimagnetic ordering.Comment: 16 pages including 7 postscript figure
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