32,904 research outputs found
Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states
A model Hamiltonian that exhibits asymptotic freedom and a bound state, is
used to show on example that similarity renormalization group procedure can be
tuned to improve convergence of perturbative derivation of effective
Hamiltonians, through adjustment of the generator of the similarity
transformation. The improvement is measured by comparing the eigenvalues of
perturbatively calculated renormalized Hamiltonians that couple only a
relatively small number of effective basis states, with the exact bound state
energy in the model. The improved perturbative calculus leads to a few-percent
accuracy in a systematic expansion.Comment: 6 pages of latex, 4 eps figure
Light-front Hamiltonians for heavy quarks and gluons
A boost-invariant light-front Hamiltonian formulation of canonical quantum
chromodynamics provides a heuristic picture of the binding mechanism for
effective heavy quarks and gluons.Comment: 10 pages, 6 figures, Invited talk at the Workshop on Light-Cone QCD
and Nonperturbative Hadron Physics (LC2005), Cairns, Australia, 7-15 Jul 200
Stable higher order finite-difference schemes for stellar pulsation calculations
Context: Calculating stellar pulsations requires a sufficient accuracy to
match the quality of the observations. Many current pulsation codes apply a
second order finite-difference scheme, combined with Richardson extrapolation
to reach fourth order accuracy on eigenfunctions. Although this is a simple and
robust approach, a number of drawbacks exist thus making fourth order schemes
desirable. A robust and simple finite-difference scheme, which can easily be
implemented in either 1D or 2D stellar pulsation codes is therefore required.
Aims: One of the difficulties in setting up higher order finite-difference
schemes for stellar pulsations is the so-called mesh-drift instability. Current
ways of dealing with this defect include introducing artificial viscosity or
applying a staggered grids approach. However these remedies are not well-suited
to eigenvalue problems, especially those involving non-dissipative systems,
because they unduly change the spectrum of the operator, introduce
supplementary free parameters, or lead to complications when applying boundary
conditions.
Methods: We propose here a new method, inspired from the staggered grids
strategy, which removes this instability while bypassing the above
difficulties. Furthermore, this approach lends itself to superconvergence, a
process in which the accuracy of the finite differences is boosted by one
order.
Results: This new approach is shown to be accurate, flexible with respect to
the underlying grid, and able to remove mesh-drift.Comment: 15 pages, 11 figures, accepted for publication in A&
Very Large-Scale Singular Value Decomposition Using Tensor Train Networks
We propose new algorithms for singular value decomposition (SVD) of very
large-scale matrices based on a low-rank tensor approximation technique called
the tensor train (TT) format. The proposed algorithms can compute several
dominant singular values and corresponding singular vectors for large-scale
structured matrices given in a TT format. The computational complexity of the
proposed methods scales logarithmically with the matrix size under the
assumption that both the matrix and the singular vectors admit low-rank TT
decompositions. The proposed methods, which are called the alternating least
squares for SVD (ALS-SVD) and modified alternating least squares for SVD
(MALS-SVD), compute the left and right singular vectors approximately through
block TT decompositions. The very large-scale optimization problem is reduced
to sequential small-scale optimization problems, and each core tensor of the
block TT decompositions can be updated by applying any standard optimization
methods. The optimal ranks of the block TT decompositions are determined
adaptively during iteration process, so that we can achieve high approximation
accuracy. Extensive numerical simulations are conducted for several types of
TT-structured matrices such as Hilbert matrix, Toeplitz matrix, random matrix
with prescribed singular values, and tridiagonal matrix. The simulation results
demonstrate the effectiveness of the proposed methods compared with standard
SVD algorithms and TT-based algorithms developed for symmetric eigenvalue
decomposition
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
A finite element method using B-splines is presented and compared with a
conventional finite element method of Lagrangian type. The efficiency of both
methods has been investigated at the example of a coupled non-linear system of
Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which
describe a nuclear system in the framework of relativistic mean field theory.
Although, FEM has been applied with great success in nuclear RMF recently, a
well known problem is the appearance of spurious solutions in the spectra of
the Dirac equation. The question, whether B-splines lead to a reduction of
spurious solutions is analyzed. Numerical expenses, precision and behavior of
convergence are compared for both methods in view of their use in large scale
computation on FEM grids with more dimensions. A B-spline version of the object
oriented C++ code for spherical nuclei has been used for this investigation.Comment: 27 pages, 30 figure
- …