1,795 research outputs found
Resummation of fermionic in-medium ladder diagrams to all orders
A system of fermions with a short-range interaction proportional to the
scattering length is studied at finite density. At any order , we
evaluate the complete contributions to the energy per particle
arising from combined (multiple) particle-particle and hole-hole rescatterings
in the medium. This novel result is achieved by simply decomposing the
particle-hole propagator into the vacuum propagator plus a medium-insertion and
correcting for certain symmetry factors in the -th power of the
in-medium loop. Known results for the low-density expansion up to and including
order are accurately reproduced. The emerging series in can be
summed to all orders in the form of a double-integral over an arctangent
function. In that representation the unitary limit can be taken
and one obtains the value for the universal Bertsch parameter. We
discuss also applications to the equation of state of neutron matter at low
densities and mention further extensions of the resummation method.Comment: 12 pages, 7 figures, submitted to Nuclear Physics
Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction
A recent work on the resummation of fermionic in-medium ladder diagrams to
all orders is extended by considering the effective range correction in the
s-wave interaction and a (spin-independent) p-wave contact-interaction. A
two-component recursion generates the in-medium T-matrix at any order when
off-shell terms spoil the factorization of multi-loop diagrams. The resummation
to all orders is achieved in the form of a geometrical series for the
particle-particle ladders, and through an arctangent-function for the combined
particle-particle and hole-hole ladders. One finds that the effective range
correction changes the results in the limit of large scattering length
considerably, with the effect that the Bertsch parameter nearly
doubles. Applications to the equation of state of neutron matter at low density
are also discussed. For the p-wave contact-interaction the resummation to all
orders is facilitated by decomposing tensorial loop-integrals with a
transversal and a longitudinal projector. The enhanced attraction provided by
the p-wave ladder series has its origin mainly in the coherent sum of Hartree
and Fock contributions.Comment: 17 pages, 7 figures, to be published in Eur. Phys. J.
Single-particle potential from resummed ladder diagrams
A recent work on the resummation of fermionic in-medium ladder diagrams to
all orders is extended by calculating the complex single-particle potential
for momenta . The on-shell
single-particle potential is constructed by means of a complex-valued in-medium
loop that includes corrections from a test-particle of momentum added
to the filled Fermi sea. The single-particle potential at the
Fermi surface as obtained from the resummation of the combined particle and
hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem. The
perturbative contributions at various orders in the scattering length are
deduced and checked against the known analytical results at order and
. The limit is studied as a special case and a strong
momentum dependence of the real (and imaginary) single-particle potential is
found. This indicates an instability against a phase transition to a state with
an empty shell inside the Fermi sphere such that the density gets reduced by
about 5%. For comparison, the same analysis is performed for the resummed
particle-particle ladder diagrams alone. In this truncation an instability for
hole-excitations near the Fermi surface is found at strong coupling. For the
set of particle-hole ring diagrams the single-particle potential is calculated
as well. Furthermore, the resummation of in-medium ladder diagrams to all
orders is studied for a two-dimensional Fermi gas with a short-range two-body
contact-interaction.Comment: 28 pages, 19 figures, to be published in European Physical Journal
Transformation of two and three-dimensional regions by elliptic systems
Finite difference methods for composite grids were analyzed. It was observed that linear interpolation between grids would suffice only where low order accuracy was required. In the context of fluid flow, this would be in regions where the flow was essentially free stream. Higher order interpolation schemes were also investigated. The well known quadratic and cubic interpolating polynomials would increase the formal accuracy of the overall numerical algorithm. However, it can also be shown that the stability of the algorithm may be adversely affected. Further numerical results are needed in order to assess the nature of this instability induced by the interpolation procedure. Finally, error analysis and the order of difference expressions on general curvilinear coordinates are discussed
Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels
Photons propagating in strong magnetic fields are subject to a phenomenon
called the "vacuum birefringence" where refractive indices of two physical
modes both deviate from unity and are different from each other. We compute the
vacuum polarization tensor of a photon in a static and homogeneous magnetic
field by utilizing Schwinger's proper-time method, and obtain a series
representation as a result of double integrals analytically performed with
respect to proper-time variables. The outcome is expressed in terms of an
infinite sum of known functions which is plausibly interpreted as summation
over all the Landau levels of fermions. Each contribution from infinitely many
Landau levels yields a kinematical condition above which the contribution has
an imaginary part. This indicates decay of a sufficiently energetic photon into
a fermion-antifermion pair with corresponding Landau level indices. Since we do
not resort to any approximation, our result is applicable to the calculation of
refractive indices in the whole kinematical region of a photon momentum and in
any magnitude of the external magnetic field.Comment: To appear in Ann. Phys., 47 pages, 7 figure
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