4,708 research outputs found
Moments of spectral functions: Monte Carlo evaluation and verification
The subject of the present study is the Monte Carlo path-integral evaluation
of the moments of spectral functions. Such moments can be computed by formal
differentiation of certain estimating functionals that are
infinitely-differentiable against time whenever the potential function is
arbitrarily smooth. Here, I demonstrate that the numerical differentiation of
the estimating functionals can be more successfully implemented by means of
pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial
interpolant), which utilize information from the entire interval . The algorithmic detail that leads to robust numerical
approximations is the fact that the path integral action and not the actual
estimating functional are interpolated. Although the resulting approximation to
the estimating functional is non-linear, the derivatives can be computed from
it in a fast and stable way by contour integration in the complex plane, with
the help of the Cauchy integral formula (e.g., by Lyness' method). An
interesting aspect of the present development is that Hamburger's conditions
for a finite sequence of numbers to be a moment sequence provide the necessary
and sufficient criteria for the computed data to be compatible with the
existence of an inversion algorithm. Finally, the issue of appearance of the
sign problem in the computation of moments, albeit in a milder form than for
other quantities, is addressed.Comment: 13 pages, 2 figure
DVCS amplitude at tree level: Transversality, twist-3, and factorization
We study the virtual Compton amplitude in the generalized Bjorken region (q^2
-> Infinity, t small) in QCD by means of a light-cone expansion of the product
of e.m. currents in string operators in coordinate space. Electromagnetic gauge
invariance (transversality) is maintained by including in addition to the
twist-2 operators 'kinematical' twist-3 operators which appear as total
derivatives of twist-2 operators. The non-forward matrix elements of the
elementary twist-2 operators are parametrized in terms of two-variable spectral
functions (double distributions), from which twist-2 and 3 skewed distributions
are obtained through reduction formulas. Our approach is equivalent to a
Wandzura-Wilczek type approximation for the twist-3 skewed distributions. The
resulting Compton amplitude is manifestly transverse up to terms of order
t/q^2. We find that in this approximation the tensor amplitude for longitudinal
polarization of the virtual photon is finite, while the one for transverse
polarization contains a divergence already at tree level. However, this
divergence has zero projection on the polarization vector of the final photon,
so that the physical helicity amplitudes are finite.Comment: 34 pages, revtex, 1 eps figure included using epsf. Misprints
corrected, one reference adde
Non-Abelian brane cosmology
We discuss isotropic and homogeneous D-brane-world cosmology with non-Abelian
Born-Infeld (NBI) matter on the brane. In the usual Friedmann-Robertson-Walker
(FRW) model the scale non-invariant NBI matter gives rise to an equation of
state which asymptotes to the string gas equation and ensures a
start-up of the cosmological expansion with zero acceleration. We show that the
same state equation in the brane-world setup leads to the Tolman type evolution
as if the conformal symmetry was effectively restored. This is not precisely so
in the NBI model with symmetrized trace, but the leading term in the expansion
law is still the same. A cosmological sphaleron solution on the D-brane is
presented.Comment: 6 pages, latex, 1 figure. Submitted to the Proceedings of the VFC
workshop at JENAM2002, Portu, Portugal, 1-6 september 200
Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei
Important contributions to the cross sections of
low-lying orbital excitations are found in heavy deformed nuclei, arising
from the small energy separation between the two excitations with and 1, respectively. They are studied microscopically in QRPA using
DWBA. The accompanying response is negligible at small momentum transfer
but contributes substantially to the cross sections measured at for fm ( MeV)
and leads to a very good agreement with experiment. The electric response is of
longitudinal type for but becomes almost purely
transverse for larger backward angles. The transverse response
remains comparable with the response for fm
( MeV) and even dominant for MeV. This happens even at
large backward angles , where the dominance is
limited to the lower region.Comment: RevTeX, 19 pages, 8 figures included Accepted for publication in Phys
Rev
Gaussian resolutions for equilibrium density matrices
A Gaussian resolution method for the computation of equilibrium density
matrices rho(T) for a general multidimensional quantum problem is presented.
The variational principle applied to the ``imaginary time'' Schroedinger
equation provides the equations of motion for Gaussians in a resolution of
rho(T) described by their width matrix, center and scale factor, all treated as
dynamical variables.
The method is computationally very inexpensive, has favorable scaling with
the system size and is surprisingly accurate in a wide temperature range, even
for cases involving quantum tunneling. Incorporation of symmetry constraints,
such as reflection or particle statistics, is also discussed.Comment: 4 page
Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
We investigate the set a) of positive, trace preserving maps acting on
density matrices of size N, and a sequence of its nested subsets: the sets of
maps which are b) decomposable, c) completely positive, d) extended by identity
impose positive partial transpose and e) are superpositive. Working with the
Hilbert-Schmidt (Euclidean) measure we derive tight explicit two-sided bounds
for the volumes of all five sets. A sample consequence is the fact that, as N
increases, a generic positive map becomes not decomposable and, a fortiori, not
completely positive.
Due to the Jamiolkowski isomorphism, the results obtained for quantum maps
are closely connected to similar relations between the volume of the set of
quantum states and the volumes of its subsets (such as states with positive
partial transpose or separable states) or supersets. Our approach depends on
systematic use of duality to derive quantitative estimates, and on various
tools of classical convexity, high-dimensional probability and geometry of
Banach spaces, some of which are not standard.Comment: 34 pages in Latex including 3 figures in eps, ver 2: minor revision
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