5,188 research outputs found
Variational Calculations using Low-Momentum Potentials with Smooth Cutoffs
Recent variational calculations of the deuteron and the triton illustrate
that simple wave function ansatze become more effective after evolving the
nucleon-nucleon potential to lower momentum (``V_lowk''). However, wave
function artifacts from the use of sharp cutoffs in relative momentum decrease
effectiveness for small cutoffs (< 2 fm^-1) and slow down convergence in
harmonic oscillator bases. These sharp cutoff artifacts are eliminated when
V_lowk is generated using a sufficiently smooth cutoff regulator.Comment: 11 pages, 4 figure
Weinberg Eigenvalues and Pairing with Low-Momentum Potentials
The nonperturbative nature of nucleon-nucleon interactions evolved to low
momentum has recently been investigated in free space and at finite density
using Weinberg eigenvalues as a diagnostic. This analysis is extended here to
the in-medium eigenvalues near the Fermi surface to study pairing. For a fixed
value of density and cutoff Lambda, the eigenvalues increase arbitrarily in
magnitude close to the Fermi surface, signaling the pairing instability. When
using normal-phase propagators, the Weinberg analysis with complex energies
becomes a form of stability analysis and the pairing gap can be estimated from
the largest attractive eigenvalue. With Nambu-Gorkov Green's functions, the
largest attractive eigenvalue goes to unity close to the Fermi surface,
indicating the presence of bound states (Cooper pairs), and the corresponding
eigenvector leads to the self-consistent gap function.Comment: 16 pages, 9 figure
Low-momentum interactions with smooth cutoffs
Nucleon-nucleon potentials evolved to low momentum, which show great promise
in few- and many-body calculations, have generally been formulated with a sharp
cutoff on relative momenta. However, a sharp cutoff has technical disadvantages
and can cause convergence problems at the 10-100 keV level in the deuteron and
triton. This motivates using smooth momentum-space regulators as an
alternative. We generate low-momentum interactions with smooth cutoffs both
through energy-independent renormalization group methods and using a multi-step
process based on the Bloch-Horowitz approach. We find greatly improved
convergence for calculations of the deuteron and triton binding energies in a
harmonic oscillator basis compared to results with a sharp cutoff. Even a
slight evolution of chiral effective field theory interactions to lower momenta
is beneficial. The renormalization group preserves the long-range part of the
interaction, and consequently the renormalization of long-range operators, such
as the quadrupole moment, the radius and 1/r, is small. This demonstrates that
low-energy observables in the deuteron are reproduced without short-range
correlations in the wave function.Comment: 29 pages, 19 figure
Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model
A simple class of unitary renormalization group transformations that force
hamiltonians towards a band-diagonal form produce few-body interactions in
which low- and high-energy states are decoupled, which can greatly simplify
many-body calculations. One such transformation has been applied to
phenomenological and effective field theory nucleon-nucleon interactions with
success, but further progress requires consistent treatment of at least the
three-nucleon interaction. In this paper we demonstrate in an extremely simple
model how these renormalization group transformations consistently evolve two-
and three-body interactions towards band-diagonal form, and introduce a
diagrammatic approach that generalizes to the realistic nuclear problem.Comment: 25 pages, 18 figures, minor typos corrected and references update
Convergence of the Born Series with Low-Momentum Interactions
The nonperturbative nature of nucleon-nucleon interactions as a function of a
momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This
investigation extends an earlier study of the perturbative convergence of the
Born series to partial waves beyond the 3S1-3D1 channel and to positive
energies. As the cutoff is lowered using renormalization-group or model-space
techniques, the evolution of nonperturbative features at large cutoffs from
strong short-range repulsion and the iterated tensor interaction are monitored
via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit
circle, the expansion of the scattering amplitude in terms of the interaction
is perturbative, with the magnitude of the largest eigenvalue setting the rate
of convergence. Major decreases in the magnitudes of repulsive eigenvalues are
observed as the Argonne v18, CD-Bonn or Nijmegen potentials are evolved to low
momentum, even though two-body observables are unchanged. For chiral EFT
potentials, running the cutoff lower tames the impact of the tensor force and
of new nonperturbative features entering at N3LO. The efficacy of separable
approximations to nuclear interactions derived from the Weinberg analysis is
studied as a function of cutoff, and the connection to inverse scattering is
demonstrated.Comment: 21 pages, 15 figures, minor additions, to appear in Nucl. Phys.
Similarity Renormalization Group for Few-Body Systems
Internucleon interactions evolved via flow equations yield soft potentials
that lead to rapid variational convergence in few-body systems.Comment: 3 pages, 6 figures. To appear in the proceedings of the 20th European
Conference on Few-Body Problems in Physics (EFB20), Pisa, September 10-14,
200
Algebraic characterization of differential operators of Calabi-Yau type
We give an algebraic characterization of Picard-Fuchs operators attached to
families of Calabi-Yau manifolds with a point of maximally unipotent monodromy
and discuss possibilities for their differential Galois groups.Comment: 20 page
Generalizations of polylogarithms for Feynman integrals
In this talk, we discuss recent progress in the application of
generalizations of polylogarithms in the symbolic computation of multi-loop
integrals. We briefly review the Maple program MPL which supports a certain
approach for the computation of Feynman integrals in terms of multiple
polylogarithms. Furthermore we discuss elliptic generalizations of
polylogarithms which have shown to be useful in the computation of the massive
two-loop sunrise integral.Comment: Talk presented at ACAT 2016 at UTFSM, Valpara\'iso, Chil
Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
A one-dimensional system of bosons with short-range repulsion and mid-range
attraction is used as a laboratory to explore the evolution of many-body forces
by the Similarity Renormalization Group (SRG). The free-space SRG is
implemented for few-body systems in a symmetrized harmonic oscillator basis
using a recursive construction analogous to no-core shell model
implementations. This approach, which can be directly generalized to
three-dimensional nuclei, is fully unitary up to induced A-body forces when
applied with an A-particle basis (e.g., A-body bound-state energies are exactly
preserved). The oscillator matrix elements for a given A can then be used in
larger systems. Errors from omitted induced many-body forces show a hierarchy
of decreasing contribution to binding energies. An analysis of individual
contributions to the growth of many-body forces demonstrates such a hierarchy
and provides an understanding of its origins.Comment: 23 pages, 11 figures, Changed section on analysis of three-body
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