538 research outputs found
Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations
We study weakly interacting Bose gases using the functional renormalization
group with a hydrodynamic effective action. We use a scale-dependent
parametrization of the boson fields that interpolates between a Cartesian
representation at high momenta and an amplitude-phase one for low momenta. We
apply this to Bose gases in two and three dimensions near the superfluid phase
transition where they can be described by statistical O(2) models. We are able
to give consistent physical descriptions of the infrared regime in both two and
three dimensions. In particular, and in contrast to previous studies using the
functional renormalization group, we find a stable superfluid phase at finite
temperatures in two dimensions. We compare our results for the superfluid and
boson densities with Monte-Carlo simulations, and we find they are in
reasonable agreement.Comment: 21 pages, 10 figures, to appear in Phys. Rev.
Relativistic Faddeev approach to a non-local NJL model
The diquark and nucleon are studied in a non-local NJL model. We solve the
relativistic Faddeev equation and compare the results with the ordinary NJL
model. Although the model is quark confining, it is not diquark confining in
the rainbow-ladder approximation. We show that the off-shell contribution to
the diquark matrix is crucial for the structure of the nucleon: without its
inclusion the attraction in the scalar channel is too weak to form a three-body
bound state.Comment: 5 pages (AIP style), 3 figures, Talk presented at the " Xth
International Conference on Hadron Spectroscopy (HADRON '03) ", August
31-September 6, 2003, Aschaffenburg, German
Renormalization group, dimer-dimer scattering, and three-body forces
We study the ratio between the fermion-fermion scattering length and the
dimer-dimer scattering length for systems of nonrelativistic fermions, using
the same functional renormalisation technique as previously applied to
fermionic matter. We find a strong dependence on the cutoff function used in
the renormalisation flow for a two-body truncation of the action. Adding a
simple three-body term substantially reduces this dependence.Comment: 5 pages, 2 picture
Exact renormalization group and many-fermion systems
The exact renormalization group methods is applied to many fermion systems
with short-range attractive force. The strength of the attractive
fermion-fermion interaction is determined from the vacuum scattering length. A
set of approximate flow equations is derived including fermionic and bosonic
fluctuations. The numerical solutions show a phase transition to a gapped
phase. The inclusion of bosonic fluctuations is found to be significant only in
the small-gap regime.Comment: Talk, given by B. Krippa on the International Workshop "Meson2004",
Cracow, Poland, 3 page
Off-shell effects and consistency of many-body treatments of dense matter
Effective field theory requires all observables to be independent of the
representation used for the quantum field operators. It means that off-shell
properties of the interactions should not lead to any observable effects. We
analyse this issue in the context of many-body approaches to nuclear matter,
where it should be possible to shift the contributions of lowest order in
purely off-shell two-body interactions into three-body forces. We show that
none of the commonly used truncations of the two-body scattering amplitude such
as the ladder, Brueckner-Hartree-Fock or parquet approximations respect this
requirement.Comment: 5 pages, RevTeX, 6 figure
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action
The functional renormalization group for the effective action is used to
construct an effective hydrodynamic description of weakly interacting Bose
gases. We employ a scale-dependent parametrization of the boson fields
developed previously to start the renormalization evolution in a Cartesian
representation at high momenta and interpolate to an amplitude-phase one in the
low-momentum regime. This technique is applied to Bose gases in one, two and
three dimensions, where we study thermodynamic quantities such as the pressure
and energy per particle. The interpolation leads to a very natural description
of the Goldstone modes in the physical limit, and compares well to analytic and
Monte-Carlo simulations at zero temperature. The results show that our method
improves aspects of the description of low-dimensional systems, with stable
results for the superfluid phase in two dimensions and even in one dimension.Comment: 35 pages, 10 figures; matched to the published versio
Baryon structure in a quark-confining non-local NJL model
We study the nucleon and diquarks in a non-local Nambu-Jona-Lasinio model.
For certain parameters the model exhibits quark confinement, in the form of a
propagator without real poles. After truncation of the two-body channels to the
scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon
bound states is solved in the covariant diquark-quark picture. The dependence
of the nucleon mass on diquark masses is studied in detail. We find parameters
that lead to a simultaneous reasonable description of pions and nucleons. Both
the diquarks contribute attractively to the nucleon mass. Axial-vector diquark
correlations are seen to be important, especially in the confining phase of the
model. We study the possible implications of quark confinement for the
description of the diquarks and the nucleon. In particular, we find that it
leads to a more compact nucleon.Comment: 21 pages (RevTeX), 18 figures (eps
Colour superconductivity in finite systems
In this paper we study the effect of finite size on the two-flavour colour
superconducting state. As well as restricting the quarks to a box, we project
onto states of good baryon number and onto colour singlets, these being
necessary restrictions on any observable ``quark nuggets''. We find that
whereas finite size alone has a significant effect for very small boxes, with
the superconducting state often being destroyed, the effect of projection is to
restore it again. The infinite-volume limit is a good approximation even for
quite small systems.Comment: 14 pages RevTeX4, 12 eps figure
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