5,341 research outputs found
Thermodynamics in the NC disc
We study the thermodynamics of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. We explicitly obtain expressions for thermodynamic potentials of gases of particles obeying different statistics. In order to do that, we derive an asymptotic expansion for the density of the zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein condensation in the noncommutative disc does not take place.Fil: Franchino Viñas, Sebastián Alberto. Universitat Jena; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Pisani, P.. Facultad de Ciencias Exactas, Universidad Nacional de la Plata; Argentin
Spectral functions of non essentially selfadjoint operators
One of the many problems to which J.S. Dowker devoted his attention is the
effect of a conical singularity in the base manifold on the behavior of the
quantum fields. In particular, he studied the small- asymptotic expansion of
the heat-kernel trace on a cone and its effects on physical quantities, as the
Casimir energy. In this article we review some peculiar results found in the
last decade, regarding the appearance of non-standard powers of , and even
negative integer powers of , in this asymptotic expansion for the
selfadjoint extensions of some symmetric operators with singular coefficients.
Similarly, we show that the -function associated to these selfadjoint
extensions presents an unusual analytic structure.Comment: 57 pages, 1 figure. References added. Version to appear in the
special volume of Journal of Physics A in honor of Stuart Dowker's 75th
birthday. PACS numbers: 02.30.Tb, 02.30.Sa, 03.65.D
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
Semi-transparent Boundary Conditions in the Worldline Formalism
The interaction of a quantum field with a background containing a Dirac delta
function with support on a surface of codimension 1 represents a particular
kind of matching conditions on that surface for the field. In this article we
show that the worldline formalism can be applied to this model. We obtain the
asymptotic expansion of the heat-kernel corresponding to a scalar field on
in the presence of an arbitrary regular potential and
subject to this kind of matching conditions on a flat surface. We also consider
two such surfaces and compute their Casimir attraction due to the vacuum
fluctuations of a massive scalar field weakly coupled to the corresponding
Dirac deltas.Comment: 12 page
The EAGLE. A model for policy analysis of macroeconomic interdependence in the euro area
Building on the New Area Wide Model, we develop a 4-region macroeconomic model of the euro area and the world economy. The model (EAGLE, Euro Area and Global Economy model) is microfounded and designed for conducting quantitative policy analysis of macroeconomic interdependence across regions belonging to the euro area and between euro area regions and the world economy. Simulation analysis shows the transmission mechanism of region-specific or common shocks, originating in the euro area and abroad.
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
The Orbital Structure of Dark Matter Halos with Gas
With the success of the Chandra and XMM missions and the maturation of
gravitational lensing techniques, powerful constraints on the orbital structure
of cluster dark matter halos are possible. I show that the X-ray emissivity and
mass of a galaxy cluster uniquely specify the anisotropy and velocity
dispersion profiles of its dark matter halo. I consider hydrostatic as well as
cooling flow scenarios, and apply the formalism to the lensing cluster
CL0024+16 and the cooling flow cluster Abell 2199. In both cases, the model
predicts a parameter-free velocity dispersion profile that is consistent with
independent optical redshift surveys of the clusters.Comment: 17 pages, 12 figures; to appear in the Astrophysical Journa
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