2,378 research outputs found
Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
First principle calculation of the QCD spectral functions (SPFs) based on the
lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian
inference theory and the Maximum Entropy Method (MEM), which is a useful tool
to extract SPFs from the imaginary-time correlation functions numerically
obtained by the Monte Carlo method. Three important aspects of MEM are (i) it
does not require a priori assumptions or parametrizations of SPFs, (ii) for
given data, a unique solution is obtained if it exists, and (iii) the
statistical significance of the solution can be quantitatively analyzed.
The ability of MEM is explicitly demonstrated by using mock data as well as
lattice QCD data. When applied to lattice data, MEM correctly reproduces the
low-energy resonances and shows the existence of high-energy continuum in
hadronic correlation functions. This opens up various possibilities for
studying hadronic properties in QCD beyond the conventional way of analyzing
the lattice data. Future problems to be studied by MEM in lattice QCD are also
summarized.Comment: 51 pages, 17 figures, typos corrected, discussions on the boundary
conditions and renormalization constants added. To appear in Progress in
Particle and Nuclear Physics, Vol.4
Spin-dependent Polarizability of Nucleon with Dispersion Relation in the Skyrme Model
We calculate the spin-dependent polarizability of the nucleon in the Skyrme
model. The result is compared with that of a heavy baryon chiral perturbation
theory(HBChPT), and is shown to be the same as that of HBChPT up to the
-pole terms in the narrow width limit of the state and with
the experimental physical constants. The effect of the channel is
rather small and is numerically quite similar to that of the loop in
the HBChPT. The electric and magnetic polarizabilities are recalculated using
the transverse photon and a consistent inclusion of the width.Comment: 11 pages, LaTeX, no figures. misprints correcte
Hadronic Spectral Functions above the QCD Phase Transition
We extract the spectral functions in the scalar, pseudo-scalar, vector, and
axial vector channels above the deconfinement phase transition temperature (Tc)
using the maximum entropy method (MEM). We use anisotropic lattices, 32^3 * 32,
40, 54, 72, 80, and 96 (corresponding to T = 2.3 Tc --> 0.8 Tc), with the
renormalized anisotropy xi = 4.0 to have enough temporal data points to carry
out the MEM analysis. Our result suggests that the spectral functions continue
to possess non-trivial structures even above Tc and in addition that there is a
qualitative change in the state of the deconfined matter between 1.5 Tc and 2
Tc.Comment: 3 pages, 4 figures, Lattice2002(nonzerot
Majorana Fermions and Non-Abelian Statistics in Three Dimensions
We show that three dimensional superconductors, described within a Bogoliubov
de Gennes framework can have zero energy bound states associated with pointlike
topological defects. The Majorana fermions associated with these modes have
non-Abelian exchange statistics, despite the fact that the braid group is
trivial in three dimensions. This can occur because the defects are associated
with an orientation that can undergo topologically nontrivial rotations. A new
feature of three dimensional systems is that there are "braidless" operations
in which it is possible to manipulate the groundstate associated with a set of
defects without moving or measuring them. To illustrate these effects we
analyze specific architectures involving topological insulators and
superconductors.Comment: 4 pages, 2 figures, published versio
Spectral density analysis of time correlation functions in lattice QCD using the maximum entropy method
We study various aspects of extracting spectral information from time
correlation functions of lattice QCD by means of Bayesian inference with an
entropic prior, the maximum entropy method (MEM). Correlator functions of a
heavy-light meson-meson system serve as a repository for lattice data with
diverse statistical quality. Attention is given to spectral mass density
functions, inferred from the data, and their dependence on the parameters of
the MEM. We propose to employ simulated annealing, or cooling, to solve the
Bayesian inference problem, and discuss practical issues of the approach.Comment: 11 pages, 30 figure files (eps), some references added and updated,
requires REVTeX 4.0 and prerequisites (AMS-LaTeX 2.0, graphicx, dcolumn, bm)
see http://publish.aps.org/revtex4
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