218 research outputs found
Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap
An asymptotically exact many body theory for spin polarized interacting
fermions in a one-dimensional harmonic atom trap is developed using the
bosonization method and including backward scattering. In contrast to the
Luttinger model, backscattering in the trap generates one-particle potentials
which must be diagonalized simultaneously with the two-body interactions.
Inclusion of backscattering becomes necessary because backscattering is the
dominant interaction process between confined identical one-dimensional
fermions. The bosonization method is applied to the calculation of one-particle
matrix elements at zero temperature. A detailed discussion of the validity of
the results from bosonization is given, including a comparison with direct
numerical diagonalization in fermionic Hilbert space. A model for the
interaction coefficients is developed along the lines of the Luttinger model
with only one coupling constant . With these results, particle densities,
the Wigner function, and the central pair correlation function are calculated
and displayed for large fermion numbers. It is shown how interactions modify
these quantities. The anomalous dimension of the pair correlation function in
the center of the trap is also discussed and found to be in accord with the
Luttinger model.Comment: 19 pages, 5 figures, journal-ref adde
Searches for Supersymmetry with the ATLAS Detector
This is a review of searches for supersymmetry (SUSY) with the ATLAS detector
in proton-proton collisions at a center-of-mass energy of 7 TeV at the Large
Hadron Collider at CERN. The review covers results that have been published, or
submitted for publication, up to September 2012, many of which cover the full 7
TeV data-taking period. No evidence for SUSY has been seen; some possibilities
for future directions are discussed.Comment: 15 pages, 2 figures. Invited review article for Modern Physics
Letters A. Electronic version of an article published as Mod. Phys. Lett. A,
Vol. 27, No. 32 (2012) 1230033 DOI: 10.1142/S0217732312300339 copyright World
Scientific Publishing Company http://www.worldscientific.com/worldscinet/mpl
Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature
We present an exact closed form expression for the {\em finite temperature}
first-order density matrix of a harmonically trapped ideal Fermi gas in any
dimension. This constitutes a much sought after generalization of the recent
results in the literature, where exact expressions have been limited to
quantities derived from the {\em diagonal} first-order density matrix. We
compare our exact results with the Thomas-Fermi approximation (TFA) and
demonstrate numerically that the TFA provides an excellent description of the
first-order density matrix in the large-N limit. As an interesting application,
we derive a closed form expression for the finite temperature Hartree-Fock
exchange energy of a two-dimensional parabolically confined quantum dot. We
numerically test this exact result against the 2D TF exchange functional, and
comment on the applicability of the local-density approximation (LDA) to the
exchange energy of an inhomogeneous 2D Fermi gas.Comment: 12 pages, 3 figures included in the text, RevTeX4. Text before
Eq.(25) corrected. Additional equation following Eq.(25) has been adde
Some exact results for a trapped quantum gas at finite temperature
We present closed analytical expressions for the particle and kinetic energy
spatial densities at finite temperatures for a system of noninteracting
fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For
d=2 and 3, exact expressions for the N-particle densities are used to calculate
perturbatively the temperature dependence of the splittings of the energy
levels in a given shell due to a very weak interparticle interaction in a
dilute Fermi gas. In two dimensions, we obtain analytically the surprising
result that the |l|-degeneracy in a harmonic oscillator shell is not lifted in
the lowest order even when the exact, rather than the Thomas-Fermi expression
for the particle density is used. We also demonstrate rigorously (in two
dimensions) the reduction of the exact zero-temperature fermionic expressions
to the Thomas-Fermi form in the large-N limit.Comment: 14 pages, 4 figures include
Optimisation of variables for studying dilepton transverse momentum distributions at hadron colliders
In future measurements of the dilepton () transverse momentum,
\Qt, at both the Tevatron and LHC, the achievable bin widths and the ultimate
precision of the measurements will be limited by experimental resolution rather
than by the available event statistics. In a recent paper the variable \at,
which corresponds to the component of \Qt\ that is transverse to the dilepton
thrust axis, has been studied in this regard. In the region, \Qt\ 30 GeV,
\at\ has been shown to be less susceptible to experimental resolution and
efficiency effects than the \Qt. Extending over all \Qt, we now demonstrate
that dividing \at\ (or \Qt) by the measured dilepton invariant mass further
improves the resolution. In addition, we propose a new variable, \phistarEta,
that is determined exclusively from the measured lepton directions; this is
even more precisely determined experimentally than the above variables and is
similarly sensitive to the \Qt. The greater precision achievable using such
variables will enable more stringent tests of QCD and tighter constraints on
Monte Carlo event generator tunes.Comment: 8 pages, 5 figures, 2 table
Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions
We present a Green's function method for the evaluation of the particle
density profile and of the higher moments of the one-body density matrix in a
mesoscopic system of N Fermi particles moving independently in a linear
potential. The usefulness of the method is illustrated by applications to a
Fermi gas confined in a harmonic potential well, for which we evaluate the
momentum flux and kinetic energy densities as well as their quantal mean-square
fluctuations. We also study some properties of the kinetic energy functional
E_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic
energy density yields a multi-valued function, an exact single-valued
relationship between the density derivative of E_{kin}[n(x)] and the particle
density n(x) is demonstrated and evaluated for various values of the number of
particles in the system.Comment: 10 pages, 5 figure
Luttinger model approach to interacting one-dimensional fermions in a harmonic trap
A model of interacting one--dimensional fermions confined to a harmonic trap
is proposed. The model is treated analytically to all orders of the coupling
constant by a method analogous to that used for the Luttinger model. As a first
application, the particle density is evaluated and the behavior of Friedel
oscillations under the influence of interactions is studied. It is found that
attractive interactions tend to suppress the Friedel oscillations while strong
repulsive interactions enhance the Friedel oscillations significantly. The
momentum distribution function and the relation of the model interaction to
realistic pair interactions are also discussed.Comment: 12 pages latex, 1 eps-figure in 1 tar file, extended Appendix, added
and corrected references, new eq. (53), corrected typos, accepted for PR
Hadronic final states in deep-inelastic scattering with Sherpa
We extend the multi-purpose Monte-Carlo event generator Sherpa to include
processes in deeply inelastic lepton-nucleon scattering. Hadronic final states
in this kinematical setting are characterised by the presence of multiple
kinematical scales, which were up to now accounted for only by specific
resummations in individual kinematical regions. Using an extension of the
recently introduced method for merging truncated parton showers with
higher-order tree-level matrix elements, it is possible to obtain predictions
which are reliable in all kinematical limits. Different hadronic final states,
defined by jets or individual hadrons, in deep-inelastic scattering are
analysed and the corresponding results are compared to HERA data. The various
sources of theoretical uncertainties of the approach are discussed and
quantified. The extension to deeply inelastic processes provides the
opportunity to validate the merging of matrix elements and parton showers in
multi-scale kinematics inaccessible in other collider environments. It also
allows to use HERA data on hadronic final states in the tuning of hadronisation
models.Comment: 32 pages, 22 figure
Top Quark Physics at the LHC: A Review of the First Two Years
This review summarizes the highlights in the area of top quark physics
obtained with the two general purpose detectors ATLAS and CMS during the first
two years of operation of the Large Hadron Collider LHC. It covers the 2010 and
2011 data taking periods, where the LHC provided pp collisions at a
center-of-mass energy of sqrt(s)=7 TeV. Measurements are presented of the total
and differential top quark pair production cross section in many different
channels, the top quark mass and various other properties of the top quark and
its interactions, for instance the charge asymmetry. Measurements of single top
quark production and various searches for new physics involving top quarks are
also discussed. The already very precise experimental data are in good
agreement with the standard model.Comment: 107 pages, invited review for Int. J. Mod. Phys. A, v2 is identical
to v1 except for the addition of the table of content
Coherent Parton Showers with Local Recoils
We outline a new formalism for dipole-type parton showers which maintain
exact energy-momentum conservation at each step of the evolution. Particular
emphasis is put on the coherence properties, the level at which recoil effects
do enter and the role of transverse momentum generation from initial state
radiation. The formulated algorithm is shown to correctly incorporate coherence
for soft gluon radiation. Furthermore, it is well suited for easing matching to
next-to-leading order calculations.Comment: 24 pages, 3 figure
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