288 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
Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit
We study the zero-temperature spin fluctuations of a two-dimensional
itinerant-electron system with an incommensurate magnetic ground state
described by a single-band Hubbard Hamiltonian. We introduce the
(broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through
a \emph{spiral spin configuration} with characteristic wave vector
\gmathbf{Q} different in general from the antiferromagnetic wave vector
\gmathbf{Q_{AF}}, and consider spin fluctuations over and above it within the
electronic random-phase (RPA) approximation. We obtain a \emph{closed} system
of equations for the generalized wave vector and frequency dependent
susceptibilities, which are equivalent to the ones reported recently by Brenig.
We obtain, in addition, analytic results for the spin-wave dispersion relation
in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite
doping the spin-wave dispersion relation has a \emph{hybrid form} between that
associated with the (localized) Heisenberg model and that associated with the
(long-range) RKKY exchange interaction. We also find an instability of the
spin-wave spectrum in a finite region about the center of the Brillouin zone,
which signals a physical instability toward a different spin- or, possibly,
charge-ordered phase, as, for example, the stripe structures observed in the
high-Tc materials. We expect, however, on physical grounds that for wave
vectors external to this region the spin-wave spectrum that we have determined
should survive consideration of more sophisticated mean-field solutions.Comment: 30 pages, 4 eps figure
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
Density and spin response of a strongly-interacting Fermi gas in the attractive and quasi-repulsive regime
Recent experimental advances in ultra-cold Fermi gases allow for exploring
response functions under different dynamical conditions. In particular, the
issue of obtaining a "quasi-repulsive" regime starting from a Fermi gas with an
attractive inter-particle interaction while avoiding the formation of the
two-body bound state is currently debated. Here, we provide a calculation of
the density and spin response for a wide range of temperature and coupling both
in the attractive and quasi-repulsive regime, whereby the system is assumed to
evolve non-adiabatically toward the "upper branch" of the Fermi gas. A
comparison is made with the available experimental data for these two
quantities.Comment: 8 pages, 7 figures, to appear on Phys. Rev. Let
From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature
We investigate the density, current, and spin response functions above the
critical temperature for a system of three-dimensional fermions interacting via
an attractive short-range potential. In the strong-coupling (bosonic) limit of
this interaction, we identify the dominant diagrammatic contributions for a
``dilute'' system of composite bosons which form as bound-fermion pairs, and
compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and
density-of-states) terms occurring in the theory of superconducting
fluctuations above the critical temperature for a clean system in the
weak-coupling limit. We show that, at the zeroth order in the diluteness
parameter for the composite bosons, the Aslamazov-Larkin term still represents
formally the dominant contribution to the density and current response
functions, while the Maki-Thompson and density-of-states terms are strongly
suppressed. Corrections to the Aslamazov-Larkin term are then considered at the
next order in the diluteness parameter for the composite bosons. The spin
response function is also examined, and it is found to be exponentially
suppressed in the bosonic limit only when appropriate sets of diagrams are
considered simultaneously.Comment: 10 pages, 6 figure
Extracting the condensate density from projection experiments with Fermi gases
A debated issue in the physics of the BCS-BEC crossover with trapped Fermi
atoms is to identify characteristic properties of the superfluid phase.
Recently, a condensate fraction was measured on the BCS side of the crossover
by sweeping the system in a fast (nonadiabatic) way from the BCS to the BEC
sides, thus ``projecting'' the initial many-body state onto a molecular
condensate. We analyze here the theoretical implications of these projection
experiments, by identifying the appropriate quantum-mechanical operator
associated with the measured quantities and relating them to the many-body
correlations occurring in the BCS-BEC crossover. Calculations are presented
over wide temperature and coupling ranges, by including pairing fluctuations on
top of mean field.Comment: 4 pages, 4 figure
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
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