1,827 research outputs found
Precise numerical results for limit cycles in the quantum three-body problem
The study of the three-body problem with short-range attractive two-body
forces has a rich history going back to the 1930's. Recent applications of
effective field theory methods to atomic and nuclear physics have produced a
much improved understanding of this problem, and we elucidate some of the
issues using renormalization group ideas applied to precise nonperturbative
calculations. These calculations provide 11-12 digits of precision for the
binding energies in the infinite cutoff limit. The method starts with this
limit as an approximation to an effective theory and allows cutoff dependence
to be systematically computed as an expansion in powers of inverse cutoffs and
logarithms of the cutoff. Renormalization of three-body bound states requires a
short range three-body interaction, with a coupling that is governed by a
precisely mapped limit cycle of the renormalization group. Additional
three-body irrelevant interactions must be determined to control subleading
dependence on the cutoff and this control is essential for an effective field
theory since the continuum limit is not likely to match physical systems ({\it
e.g.}, few-nucleon bound and scattering states at low energy). Leading order
calculations precise to 11-12 digits allow clear identification of subleading
corrections, but these corrections have not been computed.Comment: 37 pages, 8 figures, LaTeX, uses graphic
The Applicability of Remote Sensing in the Field of Air Pollution
This report prepared by KNMI and JRC is the final result of a study on the applicability of remote sensing in the field of air pollution requested by the DG Environment. The objectives of this study were to:
Have an assessment of presently available scientific information on the feasibility of utilising remote sensing techniques in the implementation of existing legislation, and describe opportunities for realistic streamlining of monitoring in air quality and emissions, based on greater use of remote sensing.
Have recommendations for the next policy cycle on the use of remote sensing through development of appropriate provisions and new concepts, including, if appropriate, new environmental objectives, more suited to the use of remote sensing.
Have guidance on how to effectively engage with GMES and other initiatives in the air policy field projects Satellite remote sensing of the troposphere is a rapidly developing field. Today several satellite sensors are in orbit that measure trace gases and aerosol properties relevant to air quality. Satellite remote sensing data have the following unique properties:
Near-simultaneous view over a large area;
Global coverage;
Good spatial resolution.
The properties of satellite data are highly complementary to ground-based in-situ networks, which provide detailed measurements at specific locations with a high temporal resolution.
Although satellite data have distinct benefits, the interpretation is often less straightforward as compared to traditional in-situ measurements.
Maps of air pollution measured from space are widespread in the scientific community as well as in the media, and have had a strong impact on the general public and the policy makers. The next step is to make use of satellite data in a quantitative way. Applications based solely on satellite data are foreseen, however an integrated approach using satellite data, ground-based data and models combined with data assimilation, will make the best use of the satellite remote-sensing potential, as well as of the synergy with ground-based observations.JRC.H.4-Transport and air qualit
Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach
Renormalization of Hamiltonian field theory is usually a rather painful
algebraic or numerical exercise. By combining a method based on the coupled
cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian
approach to renormalization, we show that a powerful and elegant method exist
to solve such problems. The method is in principle non-perturbative, and is not
necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear
in JHE
Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model
We have studied electron correlations in the doped two-dimensional (2D)
Hubbard model by using the coupled-cluster method (CCM) to investigate whether
or not the method can be applied to correct the independent particle
approximations actually used in ab-initio band calculations. The double
excitation version of the CCM, implemented using the approximate coupled pair
(ACP) method, account for most of the correlation energies of the 2D Hubbard
model in the weak () and the intermediate regions (). The error is always less than 1% there. The ACP approximation gets
less accurate for large () and/or near half-filling.
Further incorporation of electron correlation effects is necessary in this
region. The accuracy does not depend on the system size and the gap between the
lowest unoccupied level and the highest occupied level due to the finite size
effect. Hence, the CCM may be favorably applied to ab-initio band calculations
on metals as well as semiconductors and insulators.Comment: RevTeX3.0, 4 pages, 4 figure
Current-density functional for disordered systems
The effective action for the current and density is shown to satisfy an
evolution equation, the functional generalization of Callan-Symanzik equation.
The solution describes the dependence of the one-particle irreducible vertex
functions on the strength of the quenched disorder and the annealed Coulomb
interaction. The result is non-perturbative, no small parameter is assumed. The
a.c. conductivity is obtained by the numerical solution of the evolution
equation on finite lattices in the absence of the Coulomb interaction. The
static limit is performed and the conductivity is found to be vanishing beyond
a certain threshold of the impurity strength.Comment: final version, 28 pages, 17 figures, to appear in Phys. Rev.
Flow equation for Halpern-Huang directions of scalar O(N) models
A class of asymptotically free scalar theories with O(N) symmetry, defined
via the eigenpotentials of the Gaussian fixed point (Halpern-Huang directions),
are investigated using renormalization group flow equations. Explicit solutions
for the form of the potential in the nonperturbative infrared domain are found
in the large-N limit. In this limit, potentials without symmetry breaking
essentially preserve their shape and undergo a mass renormalization which is
governed only by the renormalization group distance parameter; as a
consequence, these scalar theories do not have a problem of naturalness.
Symmetry-breaking potentials are found to be ``fine-tuned'' in the large-N
limit in the sense that the nontrivial minimum vanishes exactly in the limit of
vanishing infrared cutoff: therefore, the O(N) symmetry is restored in the
quantum theory and the potential becomes flat near the origin.Comment: 18 pages, 4 figures, LaTeX, references added, presentation improved,
final version to appear in Phys. Rev.
More on the infrared renormalization group limit cycle in QCD
We present a detailed study of the recently conjectured infrared
renormalization group limit cycle in QCD using chiral effective field theory.
It was conjectured that small increases in the up and down quark masses can
move QCD to the critical trajectory for an infrared limit cycle in the
three-nucleon system. At the critical quark masses, the binding energies of the
deuteron and its spin-singlet partner are tuned to zero and the triton has
infinitely many excited states with an accumulation point at the three-nucleon
threshold. We exemplify three parameter sets where this effect occurs at
next-to-leading order in the chiral counting. For one of them, we study the
structure of the three-nucleon system in detail using both chiral and contact
effective field theories. Furthermore, we investigate the matching of the
chiral and contact theories in the critical region and calculate the influence
of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version
to appear in EPJ
Resummation of mass terms in perturbative massless quantum field theory
The neutral massless scalar quantum field in four-dimensional
space-time is considered, which is subject to a simple bilinear
self-interaction. Is is well-known from renormalization theory that adding a
term of the form to the Lagrangean has the formal
effect of shifting the particle mass from the original zero value to m after
resummation of all two-leg insertions in the Feynman graphs appearing in the
perturbative expansion of the S-matrix. However, this resummation is
accompanied by some subtleties if done in a proper mathematical manner.
Although the model seems to be almost trivial, is shows many interesting
features which are useful for the understanding of the convergence behavior of
perturbation theory in general. Some important facts in connection with the
basic principles of quantum field theory and distribution theory are
highlighted, and a remark is made on possible generalizations of the
distribution spaces used in local quantum field theory. A short discussion how
one can view the spontaneous breakdown of gauge symmetry in massive gauge
theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde
A class of ansatz wave functions for 1D spin systems and their relation to DMRG
We investigate the density matrix renormalization group (DMRG) discovered by
White and show that in the case where the renormalization eventually converges
to a fixed point the DMRG ground state can be simply written as a ``matrix
product'' form. This ground state can also be rederived through a simple
variational ansatz making no reference to the DMRG construction. We also show
how to construct the ``matrix product'' states and how to calculate their
properties, including the excitation spectrum. This paper provides details of
many results announced in an earlier letter.Comment: RevTeX, 49 pages including 4 figures (macro included). Uuencoded with
uufiles. A complete postscript file is available at
http://fy.chalmers.se/~tfksr/prb.dmrg.p
String-localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with
irreducible representations of the Poincar\'e group and localized in
semi-infinite strings extending to spacelike infinity. Among these are fields
that generate the irreducible representations of mass zero and infinite spin
that are known to be incompatible with point-like localized fields. For the
massive representation and the massless representations of finite helicity, all
string-localized free fields can be written as an integral, along the string,
of point-localized tensor or spinor fields. As a special case we discuss the
string-localized vector fields associated with the point-like electromagnetic
field and their relation to the axial gauge condition in the usual setting.Comment: minor correction
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