958 research outputs found
Floating Phase in 1D Transverse ANNNI Model
To study the ground state of ANNNI chain under transverse field as a function
of frustration parameter and field strength , we present here
two different perturbative analyses. In one, we consider the (known) ground
state at and as the unperturbed state and treat an
increase of the field from 0 to coupled with an increase of
from 0.5 to as perturbation. The first order perturbation
correction to eigenvalue can be calculated exactly and we could conclude that
there are only two phase transition lines emanating from the point
, . In the second perturbation scheme, we consider the
number of domains of length 1 as the perturbation and obtain the zero-th order
eigenfunction for the perturbed ground state. From the longitudinal spin-spin
correlation, we conclude that floating phase exists for small values of
transverse field over the entire region intermediate between the ferromagnetic
phase and antiphase.Comment: 11 pages, 11 figure
Building latent class growth trees
Researchers use latent class growth (LCG) analysis to detect meaningful subpopulations that display different growth curves. However, especially when the number of classes required to obtain a good fit is large, interpretation of the encountered class-specific curves might not be straightforward. To overcome this problem, we propose an alternative way of performing LCG analysis, which we call LCG tree (LCGT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: Classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCGT approach compared to the standard LCG approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. The practical use of the approach is illustrated using applications on drug use during adolescence and mood regulation during the day
Latent class trees with the three-step approach
Latent class (LC) analysis is widely used in the social and behavioral sciences to find meaningful clusters based on a set of categorical variables. To deal with the common problem that a standard LC analysis may yield a large number classes and thus a solution that is difficult to interpret, recently an alternative approach has been proposed, called Latent Class Tree (LCT) analysis. It involves starting with a solution with a small number of "basic" classes, which may subsequently be split into subclasses at the next stages of an analysis. However, in most LC analysis applications, we not only wish to identify the relevant classes, but also want to see how they relate to external variables (covariates or distal outcomes). For this purpose, researchers nowadays prefer using the bias-adjusted three-step method. Here, we show how this bias-adjusted three-step procedure can be applied in the context of LCT modeling. More specifically, an R-package is presented that performs a three-step LCT analysis: it builds a LCT and allows checking how splits are related to the relevant external variables. The new tool is illustrated using a cross-sectional application with multiple indicators on social capital and demographics as external variables and with a longitudinal application with a mood variable measured multiple times during the day and personality traits as external variables
Excited Baryons in Large N_c QCD Revisited: The Resonance Picture Versus Single-Quark Excitations
We analyze excited baryon properties via a 1/N_c expansion from two
perspectives: as resonances in meson-nucleon scattering, and as single-quark
excitations in the context of a simple quark model. For both types of analysis
one can derive novel patterns of degeneracy that emerge as N_c --> \infty, and
that are shown to be compatible with one another. This helps justify the
single-quark excitation picture and may give some insight into its successes.
We also find that in the large N_c limit one of the S_{11} baryons does not
couple to the pi-N channel but couples to the eta-N channel. This is
empirically observed in the N(1535), which couples very weakly to the pi-N
channel and quite strongly to the eta-N channel. The comparatively strong
coupling of the N(1650) to the pi-N channel and weak coupling to eta-N channel
is also predicted. In the context of the simple quark model picture we
reproduce expressions for mixing angles that are accurate up to O(1/N_c)
corrections and are in good agreement with mixing angles extracted
phenomenologically.Comment: 13 pages, ReVTeX
A Mean Field Analysis of One Dimensional Quantum Liquid with Long Range Interaction
Bi-local mean field theory is applied to one dimensional quantum liquid with
long range interaction, which has exact ground state wave function. We
obtain a mean field solution and an effective action which expresses a long
range dynamics. Based on them the ground state energy and correlation functions
are computed. The ground state energy agrees fairly well with the exact value
and exponents have weaker coupling constant dependence than that of partly
known exact value.Comment: EPHOU-93-002, 10 pages (LaTeX), 3 figures available upon request as
hard cop
Quasi-one-dimensional scattering in a discrete model
We study quasi-one-dimensional scattering of one and two particles with
short-range interactions on a discrete lattice model in two dimensions. One of
the directions is tightly confined by an arbitrary trapping potential. We
obtain the collisional properties of these systems both at finite and zero
Bloch quasi- momenta, considering as well finite sizes and transversal traps
that support a continuum of states. This is made straightforward by using the
exact ansatz for the quasi-one-dimensional states from the beginning. In the
more interesting case of genuine two-particle scattering, we find that more
than one confinement-induced resonance appear due to the non-separability of
the center-of-mass and relative coordinates on the lattice. This is done by
solving its corresponding Lippmann- Schwinger-like equation. We characterize
the effective one-dimensional interaction and compare it with a model that
includes only the effect of the dominant, broadest resonance, which amounts to
a single-pole approximation for the interaction coupling constant.Comment: 8 pages, 6 figure
Skyrmion Quantization and the Decay of the Delta
We present the complete solution to the so-called ``Yukawa problem'' of the
Skyrme model. This refers to the perceived difficulty of reproducing---purely
from soliton physics---the usual pseudovector pion-nucleon coupling, echoed by
pion coupling to the higher spin/isospin baryons in a manner fixed by large- group theory. The solution involves
surprisingly elegant interplay between the classical and quantum properties of
a new configuration, the ``new improved skyrmion''. This is the near-hedgehog
obtained by minimizing the usual skyrmion mass functional augmented by an
all-important isorotational kinetic term. The numerics are pleasing: a
decay width within a few MeV of its measured value, and furthermore, the
higher-spin baryons with widths so large ()
that these undesirable large- artifacts effectively drop out of the
spectrum, and pose no phenomenological problem. Beyond these specific results,
we ground the Skyrme model in the Feynman Path Integral, and set up a
transparent collective coordinate formalism that makes maximal use of the
expansion. This approach elucidates the connection between skyrmions on
the one hand, and Feynman diagrams in an effective field theory on the other.Comment: This TeX file inputs the macropackage harvmac.tex . Choose the ``b''
(big) option or equations will overrun
Baryons with Many Colors and Flavors
Using recently-developed diagrammatic techniques, I derive some general
results concerning baryons in the expansion, where is the number of
QCD colors. I show that the spin-flavor relations which hold for baryons in the
large- limit, as well as the form of the corrections to these relations at
higher orders in , hold even if , where is the
number of light quark flavors. I also show that the amplitude for a baryon to
emit mesons is , and that meson loops attached to
baryon lines are unsupressed in the large- limit, independent of . For
, there are ambiguities in the extrapolation away from because
the baryon flavor multiplets for a given spin grow with . I argue that the
expansion is valid for baryons with spin and {\it arbitrary}
flavor quantum numbers, including e.g. baryons with isospin and/or strangeness
. This allows the formulation of a large- expansion in which it is not
necessary to identify the physical baryons with particular large- states.
symmetry can be made manifest to all orders in , yet group
theory factors must be evaluated explicitly only for . To
illustrate this expansion, I consider the non-singlet axial currents, baryon
mass splittings, and matrix elements of \mybar ss and \mybar s \gam_\mu
\gam_5 s in the nucleon.Comment: 19 pages, plain TeX, 4 uuencoded postscrip figures, LBL-35539,
NSF-ITP-94-4
Probing the spin states of three interacting electrons in quantum dots
We observe a low-lying sharp spin mode of three interacting electrons in an
array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic
light scattering. The finding is enabled by a suppression of the inhomogeneous
contribution to the excitation spectra obtained by reducing the number of
optically-probed quantum dots. Supported by configuration-interaction
calculations we argue that the observed spin mode offers a direct probe of
Stoner ferromagnetism in the simplest case of three interacting spin one-half
fermions
Decays of Baryons --- Quark Model versus Large-
We study nonleptonic decays of the orbitally excited, \su6 \rep{70}-plet
baryons in order to test the hypothesis that the successes of the
nonrelativistic quark model have a natural explanation in the large- limit
of QCD. By working in a Hartree approximation, we isolate a specific set of
operators that contribute to the observed s- and d-wave decays in leading order
in . We fit our results to the current experimental decay data, and make
predictions for a number of allowed but unobserved modes. Our tentative
conclusion is that there is more to the nonrelativistic quark model of baryons
than large-.Comment: LaTeX 49pp. (38 pp. landscape), PicTex, PrePicTex, PostPicTex
required for 3 figures, Harvard Preprint HUTP-94/A008. (Two additional
operators are included, but conclusions are unchanged.
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