8,150 research outputs found
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
The equation for the gap parameter represents the main equation of the
pairing theory of superconductivity. Although it is formally defined through a
single-particle property, physically it reflects the pairing correlations
between opposite-spin fermions. Here, we exploit this physical connection and
cast the gap equation in an alternative form which explicitly highlights these
two-particle correlations, by showing that it is equivalent to a
Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct
connection is established in this way between the treatment of the condensate
fraction in condensate systems of fermions and bosons. At a practical level,
the use of this alternative form of the gap equation is expected to make easier
the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept
of the new method, we apply the modified form of the gap equation to the
long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov
correction across the whole BCS-BEC crossover, from the BCS limit of strongly
overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for
all temperatures in the superfluid phase. Our numerical calculations yield
excellent agreement with the recently determined experimental values of the gap
parameter for an ultra-cold Fermi gas in the intermediate regime between BCS
and BEC, as well as with the available quantum Monte Carlo data in the same
regime.Comment: 24 pages, 13 figure
Dark Matter Annihilation in Substructures Revised
Upcoming -ray satellites will search for Dark Matter annihilations in
Milky Way substructures (or 'clumps'). The prospects for detecting these
objects strongly depend on the assumptions made on the distribution of Dark
Matter in substructures, and on the distribution of substructures in the Milky
Way halo. By adopting simplified, yet rather extreme, prescriptions for these
quantities, we compute the number of sources that can be detected with upcoming
experiments such as GLAST, and show that, for the most optimistic particle
physics setup ( GeV and annihilation cross section cm s), the result ranges from zero to
hundred sources, all with mass above . However, for a fiducial DM
candidate with mass GeV and cm s,
at most a handful of large mass substructures can be detected at ,
with a 1-year exposure time, by a GLAST-like experiment. Scenarios where
micro-clumps (i.e. clumps with mass as small as ) can be
detected are severely constrained by the diffuse -ray background
detected by EGRET.Comment: Version accepted for publication in MNRAS. Other subhalos mass
function slopes added. All-sky analysis performed. Boost factors added. High
resolution figures for all models in http://www2.iap.fr/users/bertone/Clumps
Anisotropy probe of galactic and extra-galactic Dark Matter annihilations
We study the flux and the angular power spectrum of gamma-rays produced by
Dark Matter (DM) annihilations in the Milky Way (MW) and in extra-galactic
halos. The annihilation signal receives contributions from: a) the smooth MW
halo, b) resolved and unresolved substructures in the MW, c) external DM halos
at all redshifts, including d) their substructures. Adopting a self-consistent
description of local and extra-galactic substructures, we show that the
annihilation flux from substructures in the MW dominates over all the other
components for angles larger than O(1) degrees from the Galactic Center, unless
an extreme prescription is adopted for the substructures concentration. We also
compute the angular power spectrum of gamma-ray anisotropies and find that, for
an optimistic choice of the particle physics parameters, an interesting
signature of DM annihilations could soon be discovered by the Fermi LAT
satellite at low multipoles, l<100, where the dominant contribution comes from
MW substructures with mass M>10^4 solar masses. For the substructures models we
have adopted, we find that the contribution of extra-galactic annihilations is
instead negligible at all scales.Comment: 14 pages, 7 figure
Cross-correlating CMB temperature fluctuations with high-energy γ-ray flux from Dark-Matter annihilation
In this paper we compute the Integrated Sachs-Wolfe effect due to the presence of dark-matter structures on cosmological scale. We cross-correlate the CMB temperature fluctuations with the extragalactic high-energy γ-ray flux map obtained with FERMI-LAT. We find a null signal consistent with the theory and conclude that the presence of halos and subhalos at galactic and extragalactic scale,
if not excluded, will be hardly discoverable
Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover
The theoretical description of the critical temperature Tc of a Fermi
superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who
addressed it for a weakly-coupled (dilute) superfluid in the BCS
(weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that
particle-particle (pairing) excitations, which are responsible for
superfluidity to occur below Tc, and particle-hole excitations, which give rise
to screening also in a normal system, get effectively disentangled from each
other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value
of Tc obtained when neglecting screening effects. Subsequent work on this
topic, aimed at extending the original GMB argument away from the BCS limit
with diagrammatic methods, has kept this disentangling between pairing and
screening throughout the BCS-BEC crossover, without realising that the
conditions for it to be valid are soon violated away from the BCS limit. Here,
we reconsider this problem from a more general perspective and argue that
pairing and screening are intrinsically entangled with each other along the
whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a
detailed numerical calculation of the GMB diagrammatic contribution extended to
the whole BCS-BEC crossover, where the full wave-vector and frequency
dependence occurring in the repeated in-medium two-particle scattering is duly
taken into account. Our numerical calculations are tested against analytic
results available in both the BCS and BEC limits, and the contribution of the
GMB diagrammatic term to the scattering length of composite bosons in the BEC
limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find
that it agrees quite well with Quantum Monte Carlo calculations and
experimental data available in the unitarity regime.Comment: 21 pages, 11 figure
Pairing fluctuation effects on the single-particle spectra for the superconducting state
Single-particle spectra are calculated in the superconducting state for a
fermionic system with an attractive interaction, as functions of temperature
and coupling strength from weak to strong. The fermionic system is described by
a single-particle self-energy that includes pairing-fluctuation effects in the
superconducting state. The theory reduces to the ordinary BCS approximation in
weak coupling and to the Bogoliubov approximation for the composite bosons in
strong coupling. Several features of the single-particle spectral function are
shown to compare favorably with experimental data for cuprate superconductors.Comment: 4 pages, 4 figure
Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories
We investigate both numerically and analytically the behaviour of a spin-1
antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic
field. Extensive DMRG studies of chains up to N=80 sites extend previous
analyses and exhibit the well known phenomenon of the closure of the Haldane
gap at a lower critical field H_c1. We obtain an estimate of the gap below
H_c1. Above the lower critical field, when the correlation functions exhibit
algebraic decay, we obtain the critical exponent as a function of the net
magnetization as well as the magnetization curve up to the saturation (upper
critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry
of the model is explicitly broken by the field, the Haldane phase of the model
is still well described by an SO(3) nonlinear sigma-model. A mean-field theory
is developed for the latter and its predictions are compared with those of the
numerical analysis and with the existing literature.Comment: 11 pages, 4 eps figure
Popov approximation for composite bosons in the BCS-BEC crossover
Theoretical treatments of the BCS-BEC crossover need to provide as accurate
as possible descriptions of the two regimes where the diluteness condition
applies, either in terms of the constituent fermions (BCS limit) or of the
composite bosons which form as bound-fermion pairs (BEC limit). This has to
occur via a single fermionic theory that bridges across these two limiting
representations. In this paper, we set up successive improvements of the
fermionic theory, that result into composite bosons described at the level of
either the Bogoliubov or the Popov approximations for point-like bosons. This
work bears on the recent experimental advances on the BCS-BEC crossover with
trapped Fermi atoms, which show the need for accurate theoretical descriptions
of BEC side of the crossover.Comment: 13 pages, 4 figure
- …