271 research outputs found
The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
The LIT method has allowed ab initio calculations of electroweak cross
sections in light nuclear systems. This review presents a description of the
method from both a general and a more technical point of view, as well as a
summary of the results obtained by its application. The remarkable features of
the LIT approach, which make it particularly efficient in dealing with a
general reaction involving continuum states, are underlined. Emphasis is given
on the results obtained for electroweak cross sections of few--nucleon systems.
Their implications for the present understanding of microscopic nuclear
dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo
Glueballs from 1+1 Dimensional Gauge Theories with Transverse Degrees of Freedom
We study -dimensional gauge theories with adjoint scalar matter
representations, based on a dimensional truncation of and
-dimensional pure QCD, which approximate the dynamics of transversely
polarized gluons. The glueballs are investigated non-perturbatively using
light-front quantisation, detailed spectra and wavefunctions being obtained for
the large- limit. In general there is some qualitative agreement of the
spectra with lattice Monte Carlo data from the higher dimensional QCD. From the
light-front wavefunctions we calculate (polarized) structure functions and
interpret the gluon and spin content of glueballs. We discuss the phase
structure of the reduced theories in relation to matrix models for relativistic
non-critical strings.Comment: To appear in Nucl. Phys. B; some small clarifications and 3
references adde
Electromagnetic Sum Rules and Response Functions from the Symmetry-Adapted No-Core Shell Model
Recent developments in ab initio nuclear structure have provided us with a variety of many-body methods capable of describing nuclei into the medium-mass region of the chart of nuclides. One of these, the symmetry-adapted no-core shell model (SA-NCSM), capitalizes on inherent symmetries of the nucleus and is uniquely suited to examine the underlying physics of dynamical quantities, such as the response function.
We examine the applicability of the SA-NCSM to calculations of these quantities and assess the quality of its inputs by calculating electromagnetic sum rules and response functions with the Lanczos sum rule method and Lanczos response function method, respectively. Our systematic analysis of 4He shows good agreement in the sum rules between the SA-NCSM and hyperspherical harmonics, an exact method. We also detail a novel use of a projection technique to remove spurious center-of-mass contributions to our sum rules. Our calculations for the response functions of 4He, 16O, and 20Ne reveal the advantages of the SA-NCSM when examining giant resonances and we detail a straightforward procedure to calculate the compressibility of nuclear matter from only the microscopic calculations of these response functions.
The results of this work illustrate the ability of the SA-NCSM to reliably and accurately calculate electromagnetic sum rules, as well as its usefulness in providing physically-informed interpretations of electromagnetic response functions. This suggests future work with the SA-NCSM could provide valuable insights, particularly for open-shell nuclei beyond the reach of other methods
Topological Phases: An Expedition off Lattice
Motivated by the goal to give the simplest possible microscopic foundation
for a broad class of topological phases, we study quantum mechanical lattice
models where the topology of the lattice is one of the dynamical variables.
However, a fluctuating geometry can remove the separation between the system
size and the range of local interactions, which is important for topological
protection and ultimately the stability of a topological phase. In particular,
it can open the door to a pathology, which has been studied in the context of
quantum gravity and goes by the name of `baby universe', Here we discuss three
distinct approaches to suppressing these pathological fluctuations. We
complement this discussion by applying Cheeger's theory relating the geometry
of manifolds to their vibrational modes to study the spectra of Hamiltonians.
In particular, we present a detailed study of the statistical properties of
loop gas and string net models on fluctuating lattices, both analytically and
numerically.Comment: 38 pages, 22 figure
Colour-Dielectric Gauge Theory on a Transverse Lattice
We investigate in some detail consequences of the effective colour-dielectric
formulation of lattice gauge theory using the light-cone Hamiltonian formalism
with a transverse lattice. As a quantitative test of this approach, we have
performed extensive analytic and numerical calculations for 2+1-dimensional
pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one
effectively studies a 1+1-dimensional gauge theory coupled to matter in the
adjoint representation. We study the structure of coupling constant space for
our effective potential by comparing with the physical results available from
conventional Euclidean lattice Monte Carlo simulations of this system. In
particular, we calculate and measure the scaling behaviour of the entire
low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic
density of states, and deconfining temperature. We employ a new hybrid
DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian
matrix elements, along with extrapolation in Tamm-Dancoff truncation,
significantly reducing numerical errors. Finally we discuss, in light of our
results, what further measurements and calculations could be made in order to
systematically remove lattice spacing dependence from our effective potential a
priori.Comment: 48 pages, Latex, uses macro boxedeps.tex, minor errors corrected in
revised versio
Matrices, moments and rational quadrature
15 pages, no figures.-- MSC2000 code: 65D15.MR#: MR2456794 (2009h:65035)Zbl#: Zbl pre05362059^aMany problems in science and engineering require the evaluation of functionals of the form F_u(A)=u^\ssf Tf(A)u , where A is a large symmetric matrix, u a vector, and f a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to A with initial vector u, and then evaluating pairs of Gauss and Gauss–Radau quadrature rules associated with the tridiagonal matrix determined by the Lanczos procedure. The present paper extends this approach to allow the use of rational Gauss quadrature rules.Publicad
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