403 research outputs found
Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry
We study a set of static solutions of the Einstein equations in presence of a
massless scalar field and establish their connection to the Kantowski-Sachs
cosmological solutions based on some kind of duality transformations. The
physical properties of the limiting case of an empty hyperbolic spacetime
(pseudo-Schwarzschild geometry) are analyzed in some detail.Comment: 13 pages, 4 figure
Universality of random matrices in the microscopic limit and the Dirac operator spectrum
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of the soft spectrum of the Dirac operator is briefly discussed
Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field
We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work
is motivated by recent experiments on the compound (C5H12N)2CuBr4 (BPCB). We
use a combination of numerical and analytical methods, in particular the
density matrix renormalization group (DMRG) technique, to explore the phase
diagram and the excitation spectra of such a system. We give detailed results
on the temperature dependence of the magnetization and the specific heat, and
the magnetic field dependence of the nuclear magnetic resonance (NMR)
relaxation rate of single ladders. For coupled ladders, treating the weak
interladder coupling within a mean-field or quantum Monte Carlo approach, we
compute the transition temperature of triplet condensation and its
corresponding antiferromagnetic order parameter. Existing experimental
measurements are discussed and compared to our theoretical results. Furthermore
we compute, using time dependent DMRG, the dynamical correlations of a single
spin ladder. Our results allow to directly describe the inelastic neutron
scattering cross section up to high energies. We focus on the evolution of the
spectra with the magnetic field and compare their behavior for different
couplings. The characteristic features of the spectra are interpreted using
different analytical approaches such as the mapping onto a spin chain, a
Luttinger liquid (LL) or onto a t-J model. For values of parameters for which
such measurements exist, we compare our results to inelastic neutron scattering
experiments on the compound BPCB and find excellent agreement. We make
additional predictions for the high energy part of the spectrum that are
potentially testable in future experiments.Comment: 35 pages, 26 figure
Phase transitions in the boson-fermion resonance model in one dimension
We study 1D fermions with photoassociation or with a narrow Fano-Feshbach
resonance described by the Boson-Fermion resonance model. Using thebosonization
technique, we derive a low-energy Hamiltonian of the system. We show that at
low energy, the order parameters for the Bose Condensation and fermion
superfluidity become identical, while a spin gap and a gap against the
formation of phase slips are formed. As a result of these gaps, charge density
wave correlations decay exponentially in contrast with the phases where only
bosons or only fermions are present. We find a Luther-Emery point where the
phase slips and the spin excitations can be described in terms of
pseudofermions. This allows us to provide closed form expressions of the
density-density correlations and the spectral functions. The spectral functions
of the fermions are gapped, whereas the spectral functions of the bosons remain
gapless. The application of a magnetic field results in a loss of coherence
between the bosons and the fermion and the disappearance of the gap. Changing
the detuning has no effect on the gap until either the fermion or the boson
density is reduced to zero. Finally, we discuss the formation of a Mott
insulating state in a periodic potential. The relevance of our results for
experiments with ultracold atomic gases subject to one-dimensional confinement
is also discussed.Comment: 31 pages, 8 EPS figures, RevTeX 4, long version of cond-mat/050570
Bosonizing one-dimensional cold atomic gases
We present results for the long-distance asymptotics of correlation functions
of mesoscopic one-dimensional systems with periodic and open (Dirichlet)
boundary conditions, as well as at finite temperature in the thermodynamic
limit. The results are obtained using Haldane's harmonic-fluid approach (also
known as ``bosonization''), and are valid for both bosons and fermions, in
weakly and strongly interacting regimes. The harmonic-fluid approach and the
method to compute the correlation functions using conformal transformations are
explained in great detail. As an application relevant to one-dimensional
systems of cold atomic gases, we consider the model of bosons interacting with
a zero-range potential. The Luttinger-liquid parameters are obtained from the
exact solution by solving the Bethe-ansatz equations in finite-size systems.
The range of applicability of the approach is discussed, and the prefactor of
the one-body density matrix of bosons is fixed by finding an appropriate
parametrization of the weak-coupling result. The formula thus obtained is shown
to be accurate, when compared with recent diffusion Montecarlo calculations,
within less than 10%. The experimental implications of these results for Bragg
scattering experiments at low and high momenta are also discussed.Comment: 39 pages + 14 EPS figures; typos corrected, references update
Universal correlations of trapped one-dimensional impenetrable bosons
We calculate the asymptotic behaviour of the one body density matrix of
one-dimensional impenetrable bosons in finite size geometries. Our approach is
based on a modification of the Replica Method from the theory of disordered
systems. We obtain explicit expressions for oscillating terms, similar to
fermionic Friedel oscillations. These terms are universal and originate from
the strong short-range correlations between bosons in one dimension.Comment: 18 pages, 3 figures. Published versio
Integrable model for interacting electrons in metallic grains
We find an integrable generalization of the BCS model with non-uniform
Coulomb and pairing interaction. The Hamiltonian is integrable by construction
since it is a functional of commuting operators; these operators, which
therefore are constants of motion of the model, contain the anisotropic Gaudin
Hamiltonians. The exact solution is obtained diagonalizing them by means of
Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the
``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible
applications of this model to a single grain and to a system of few interacting
grains.Comment: 4 pages, revtex. Revised version to be published in Phys. Rev. Let
Ghost spins and novel quantum critical behavior in a spin chain with local bond-deformation
We study the boundary impurity-induced critical behavior in an integrable
SU(2)-invariant model consisting of an open Heisenberg chain of arbitrary
spin- (Takhatajian-Babujian model) interacting with an impurity of spin
located at one of the boundaries. For or , the
impurity interaction has a very simple form which
describes the deformed boundary bond between the impurity and the
first bulk spin with an arbitrary strength . With a weak
coupling , the impurity is completely compensated,
undercompensated, and overcompensated for , and as in the
usual Kondo problem. While for strong coupling , the
impurity spin is split into two ghost spins. Their cooperative effect leads to
a variety of new critical behaviors with different values of .Comment: 16 pages revtex, no figur
The Gaia-ESO Survey : The analysis of high-resolution UVES spectra of FGK-type stars
Date of Acceptance: 01/09/2014Context. The ongoing Gaia-ESO Public Spectroscopic Survey is using FLAMES at the VLT to obtain high-quality medium-resolution Giraffe spectra for about 105 stars and high-resolution UVES spectra for about 5000 stars. With UVES, the Survey has already observed 1447 FGK-type stars. Aims. These UVES spectra are analyzed in parallel by several state-of-the-art methodologies. Our aim is to present how these analyses were implemented, to discuss their results, and to describe how a final recommended parameter scale is defined. We also discuss the precision (method-to-method dispersion) and accuracy (biases with respect to the reference values) of the final parameters. These results are part of the Gaia-ESO second internal release and will be part of its first public release of advanced data products. Methods. The final parameter scale is tied to the scale defined by the Gaia benchmark stars, a set of stars with fundamental atmospheric parameters. In addition, a set of open and globular clusters is used to evaluate the physical soundness of the results. Each of the implemented methodologies is judged against the benchmark stars to define weights in three different regions of the parameter space. The final recommended results are the weighted medians of those from the individual methods. Results. The recommended results successfully reproduce the atmospheric parameters of the benchmark stars and the expected Teff-log g relation of the calibrating clusters. Atmospheric parameters and abundances have been determined for 1301 FGK-type stars observed with UVES. The median of the method-to-method dispersion of the atmospheric parameters is 55 K for Teff, 0.13 dex for log g and 0.07 dex for [Fe/H]. Systematic biases are estimated to be between 50-100 K for Teff, 0.10-0.25 dex for log g and 0.05-0.10 dex for [Fe/H]. Abundances for 24 elements were derived: C, N, O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Mo, Ba, Nd, and Eu. The typical method-to-method dispersion of the abundances varies between 0.10 and 0.20 dex. Conclusions. The Gaia-ESO sample of high-resolution spectra of FGK-type stars will be among the largest of its kind analyzed in a homogeneous way. The extensive list of elemental abundances derived in these stars will enable significant advances in the areas of stellar evolution and Milky Way formation and evolution.Peer reviewe
Gaia FGK benchmark stars: abundances of α and iron-peak elements
Context. In the current era of large spectroscopic surveys of the Milky Way, reference stars for calibrating astrophysical parameters and chemical abundances are of paramount importance. Aims. We determine elemental abundances of Mg, Si, Ca, Sc, Ti, V, Cr, Mn, Co, and Ni for our predefined set of Gaia FGK benchmark stars. Methods. By analysing high-resolution spectra with a high signal-to-noise ratio taken from several archive datasets, we combined results of eight different methods to determine abundances on a line-by-line basis. We performed a detailed homogeneous analysis of the systematic uncertainties, such as differential versus absolute abundance analysis. We also assessed errors that are due to non-local thermal equilibrium and the stellar parameters in our final abundances. Results. Our results are provided by listing final abundances and the different sources of uncertainties, as well as line-by-line and method-by-method abundances. Conclusions. The atmospheric parameters of the Gaia FGK benchmark stars are already being widely used for calibration of several pipelines that are applied to different surveys. With the added reference abundances of ten elements, this set is very suitable for calibrating the chemical abundances obtained by these pipelines
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