179 research outputs found
Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover
We derive a nonlinear differential equation for the gap parameter of a
superfluid Fermi system by performing a suitable coarse graining of the
Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the
aim of replacing the time-consuming solution of the original BdG equations by
the simpler solution of this novel equation. We perform a favorable numerical
test on the validity of this new equation over most of the temperature-coupling
phase diagram, by an explicit comparison with the full solution of the original
BdG equations for an isolated vortex. We also show that the new equation
reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling
close to the critical temperature and to the Gross-Pitaevskii equation for
composite bosons in strong coupling at low temperature.Comment: 12 pages, 8 figure
Non-local equation for the superconducting gap parameter
The properties are considered in detail of a non-local (integral) equation
for the superconducting gap parameter, which is obtained by a coarse-graining
procedure applied to the Bogoliubov-deGennes (BdG) equations over the whole
coupling-vs-temperature phase diagram associated with the superfluid phase. It
is found that the limiting size of the coarse-graining procedure, which is
dictated by the range of the kernel of this integral equation, corresponds to
the size of the Cooper pairs over the whole coupling-vs-temperature phase
diagram up to the critical temperature, even when Cooper pairs turn into
composite bosons on the BEC side of the BCS-BEC crossover. A practical method
is further implemented to solve numerically this integral equation in an
efficient way, which is based on a novel algorithm for calculating the Fourier
transforms. Application of this method to the case of an isolated vortex,
throughout the BCS-BEC crossover and for all temperatures in the superfluid
phase, helps clarifying the nature of the length scales associated with a
single vortex and the kinds of details that are in practice disposed off by the
coarse-graining procedure on the BdG equations
Temperature dependence of a vortex in a superfluid Fermi gas
The temperature dependence of an isolated quantum vortex, embedded in an
otherwise homogeneous fermionic superfluid of infinite extent, is determined
via the Bogoliubov-de Gennes (BdG) equations across the BCS-BEC crossover.
Emphasis is given to the BCS side of this crossover, where it is physically
relevant to extend this study up to the critical temperature for the loss of
the superfluid phase, such that the size of the vortex increases without bound.
To this end, two novel techniques are introduced. The first one solves the BdG
equations with "free boundary conditions", which allows one to determine with
high accuracy how the vortex profile matches its asymptotic value at a large
distance from the center, thus avoiding a common practice of constraining the
vortex in a cylinder with infinite walls. The second one improves on the
regularization procedure of the self-consistent gap equation when the
inter-particle interaction is of the contact type, and permits to considerably
reduce the time needed for its numerical integration, by drawing elements from
the derivation of the Gross-Pitaevskii equation for composite bosons starting
from the BdG equations.Comment: 18 pgaes, 16 figure
Josephson effect at finite temperature along the BCS-BEC crossover
The Josephson current-phase characteristics, that arise when a supercurrent flows across two fermionic superfluids separated by a potential barrier, can be controlled by varying either the interparticle coupling or the temperature. While the coupling dependence has been addressed in detail both theoretically and experimentally for an attractive Fermi gas undergoing the BCS-BEC crossover, a corresponding study of the temperature dependence of the Josephson characteristics is still lacking in this context. Here, we investigate the combined coupling and temperature dependence of the Josephson characteristics in a systematic way for a wide set of barriers, within ranges of height and width that can be experimentally explored. Our study smoothly connects the two limiting cases, of nonoverlapping composite bosons at low temperature described by the Gross-Piatevskii equation, and of strongly overlapping Cooper pairs near the critical temperature described by the Ginzburg-Landau equation. In this way, we are able to explore several interesting effects related to how the current-phase characteristics evolve along the BCS-BEC crossover as a function of temperature and of barrier shape. These effects include the coherence length outside the barrier and the pair penetration length inside the barrier (which is related to the proximity effect), as well as the temperature evolution of the Landau criterion in the limit of a vanishingly small barrier. A comparison is also presented between the available experimental data for the critical current and our theoretical results over a wide range of couplings along the BCS-BEC crossover
BCS-BEC crossover at finite temperature in the broken-symmetry phase
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry
phase between zero temperature and the critical temperature. This study bridges
two regimes where quantum and thermal fluctuations are, respectively,
important. The theory is implemented on physical grounds, by adopting a
fermionic self-energy in the broken-symmetry phase that represents fermions
coupled to superconducting fluctuations in weak coupling and to bosons
described by the Bogoliubov theory in strong coupling. This extension of the
theory beyond mean field proves important at finite temperature, to connect
with the results in the normal phase. The order parameter, the chemical
potential, and the single-particle spectral function are calculated numerically
for a wide range of coupling and temperature. This enables us to assess the
quantitative importance of superconducting fluctuations in the broken-symmetry
phase over the whole BCS-BEC crossover. Our results are relevant to the
possible realizations of this crossover with high-temperature cuprate
superconductors and with ultracold fermionic atoms in a trap.Comment: 21 pages, 15 figure
Evolution of the Normal State of a Strongly Interacting Fermi Gas from a Pseudogap Phase to a Molecular Bose Gas
Wave-vector resolved radio frequency (rf) spectroscopy data for an ultracold
trapped Fermi gas are reported for several couplings at Tc, and extensively
analyzed in terms of a pairing-fluctuation theory. We map the evolution of a
strongly interacting Fermi gas from the pseudogap phase into a fully gapped
molecular Bose gas as a function of the interaction strength, which is marked
by a rapid disappearance of a remnant Fermi surface in the single-particle
dispersion. We also show that our theory of a pseudogap phase is consistent
with a recent experimental observation as well as with Quantum Monte Carlo data
of thermodynamic quantities of a unitary Fermi gas above Tc.Comment: 9 pages, 9 figures. Substantially revised version (to appear in Phys.
Rev. Lett.
VOC Air Pollution in Urban Areas – A Microscale Model experimentally validated
Previous theoretical and experimental studies (S. T. A.- Università di Pisa (DIMNP), 1998; Agostini E., M. Corezzi, I. Ciucci, M. Mazzini 2003; Agostini E., I. Ciucci, M. Mazzini, S. Strinati, 2003) even if partial, evidenced the problem of atmospheric pollution by Volatile Organic Compounds (VOC) in Livorno (Tuscany). This pollution is caused mainly by the presence of an important refinery, other industries and traffic. Other relevant VOC emission sources are linked to port activities and to numerous small companies using paints and solvents. Figure 1 shows the map of Livorno, situated on the Tyrrhenian sea. This is a simple site from the orography point of view, except for the southern zone where a promontory and a chain of hills impose a more complex pattern of air fluxes. The industrial zone is localized in the north of the map and the harbour activities along the coast (west area). It’s difficult to define a specific zone for the companies using solvents and paints, even though a grater concentration is present around the axis Viale Carducci – Piazza Repubblica – Via Grande.
The map outlines also the air pollution measurement stations managed by ARPAT (points) and the meteorological stations (crosses).
The simulation of the emission scenario, was done by using ISC3 (U. S. Environmental Protection Agency) code for treating diffuse sources and CALINE4 (California Department of Transportation) for those related to traffic on main roads.
The research work focuses the attention on the results of model validation by experimental data obtained along the roads of the studied area. The possibility to extend the application of this model to sites with similar orography and town-planning characteristics is also discussed in the aim of obtaining information about the level of atmospheric pollution on sites where there aren’t measurement stations
Elimination of unoccupied state summations in it ab initio self-energy calculations for large supercells
We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for 8 or more silicon atoms per unit cell
Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover
Theoretical predictions for the BCS-BEC crossover of trapped Fermi atoms are
compared with recent experimental results for the density profiles of Li.
The calculations rest on a single theoretical approach that includes pairing
fluctuations beyond mean field. Excellent agreement with experimental results
is obtained. Theoretical predictions for the zero-temperature chemical
potential and gap at the unitarity limit are also found to compare extremely
well with Quantum Monte Carlo simulations and with recent experimental results.Comment: 4 pages, 3 eps figure
Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation
The linear response to a space- and time-dependent external disturbance of a
system of dilute condensed composite bosons at zero temperature, as obtained
from the linearized version of the time-dependent Gross-Pitaevskii equation, is
shown to result also from the strong-coupling limit of the time-dependent BCS
(or broken-symmetry RPA) approximation for the constituent fermions subject to
the same external disturbance. In this way, it is possible to connect
excited-state properties of the bosonic and fermionic systems by placing the
Gross-Pitaevskii equation in perspective with the corresponding fermionic
approximationsComment: 4 pages, 1 figur
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