19,434 research outputs found
Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence
Using a Schmidt orthogonalization transformation, a family of Hermitian
low-momentum NN interactions is derived from the non-Hermitian Lee-Suzuki (LS)
low-momentum NN interaction. As special cases, our transformation reproduces
the Hermitian interactions for Okubo and Andreozzi. Aside from their common
preservation of the deuteron binding energy, these Hermitian interactions are
shown to be phase shift equivalent, all preserving the empirical phase shifts
up to decimation scale Lambda. Employing a solvable matrix model, the Hermitian
interactions given by different orthogonalization transformations are studied;
the interactions can be very different from each other particularly when there
is a strong intruder state influence. However, because the parent LS
low-momentum NN interaction is only slightly non-Hermitian, the Hermitian
low-momentum nucleon interactions given by our transformations, including the
Okubo and Andreozzi ones, are all rather similar to each other. Shell model
matrix elements given by the LS and several Hermitian low-momentum interactions
are compared.Comment: 10 pages, 7 figure
Lorentz transformation and vector field flows
The parameter changes resulting from a combination of Lorentz transformation
are shown to form vector field flows. The exact, finite Thomas rotation angle
is determined and interpreted intuitively. Using phase portraits, the
parameters evolution can be clearly visualized. In addition to identifying the
fixed points, we obtain an analytic invariant, which correlates the evolution
of parameters.Comment: 11 pages, 3 figures. Section IV revised and title change
Hermitian quark mass matrices with four texture zeros
We provide a complete and systematic analysis of hermitian, hierarchical
quark mass matrices with four texture zeros. Using triangular mass matrices,
each pattern of texture zeros is readily shown to lead to a definite relation
between the CKM parameters and the quark masses. Nineteen pairs are found to be
consistent with present data, and one other is marginally acceptable. In
particular, no parallel structure between the up and down mass matrices is
found to be favorable with data.Comment: 18 pages, no figure, references [8] and [10] adde
Gravity waves over topographical bottoms: Comparison with the experiment
In this paper, the propagation of water surface waves over one-dimensional
periodic and random bottoms is investigated by the transfer matrix method. For
the periodic bottoms, the band structure is calculated, and the results are
compared to the transmission results. When the bottoms are randomized, the
Anderson localization phenomenon is observed. The theory has been applied to an
existing experiment (Belzons, et al., J. Fluid Mech. {\bf 186}, 530 (1988)). In
general, the results are compared favorably with the experimental observation.Comment: 15 pages, 7 figure
Nuclear Lattice Simulations with Chiral Effective Field Theory
We study nuclear and neutron matter by combining chiral effective field
theory with non-perturbative lattice methods. In our approach nucleons and
pions are treated as point particles on a lattice. This allows us to probe
larger volumes, lower temperatures, and greater nuclear densities than in
lattice QCD. The low energy interactions of these particles are governed by
chiral effective theory and operator coefficients are determined by fitting to
zero temperature few-body scattering data. Any dependence on the lattice
spacing can be understood from the renormalization group and absorbed by
renormalizing operator coefficients. In this way we have a realistic simulation
of many-body nuclear phenomena with no free parameters, a systematic expansion,
and a clear theoretical connection to QCD. We present results for hot neutron
matter at temperatures 20 to 40 MeV and densities below twice nuclear matter
density.Comment: 41 pages, 23 figure
Rigorous treatment of electrostatics for spatially varying dielectrics based on energy minimization
A novel energy minimization formulation of electrostatics that allows
computation of the electrostatic energy and forces to any desired accuracy in a
system with arbitrary dielectric properties is presented. An integral equation
for the scalar charge density is derived from an energy functional of the
polarization vector field. This energy functional represents the true energy of
the system even in non-equilibrium states. Arbitrary accuracy is achieved by
solving the integral equation for the charge density via a series expansion in
terms of the equation's kernel, which depends only on the geometry of the
dielectrics. The streamlined formalism operates with volume charge
distributions only, not resorting to introducing surface charges by hand.
Therefore, it can be applied to any spatial variation of the dielectric
susceptibility, which is of particular importance in applications to
biomolecular systems. The simplicity of application of the formalism to real
problems is shown with analytical and numerical examples.Comment: 27 pages, 5 figure
Hot new directions for quasi-Monte Carlo research in step with applications
This article provides an overview of some interfaces between the theory of
quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC
theoretical settings: first order QMC methods in the unit cube and in
, and higher order QMC methods in the unit cube. One important
feature is that their error bounds can be independent of the dimension
under appropriate conditions on the function spaces. Another important feature
is that good parameters for these QMC methods can be obtained by fast efficient
algorithms even when is large. We outline three different applications and
explain how they can tap into the different QMC theory. We also discuss three
cost saving strategies that can be combined with QMC in these applications.
Many of these recent QMC theory and methods are developed not in isolation, but
in close connection with applications
Gravitons and Lightcone Fluctuations II: Correlation Functions
A model of a fluctuating lightcone due to a bath of gravitons is further
investigated. The flight times of photons between a source and a detector may
be either longer or shorter than the light propagation time in the background
classical spacetime, and will form a Gaussian distribution centered around the
classical flight time. However, a pair of photons emitted in rapid succession
will tend to have correlated flight times. We derive and discuss a correlation
function which describes this effect. This enables us to understand more fully
the operational significance of a fluctuating lightcone. Our results may be
combined with observational data on pulsar timing to place some constraints on
the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps
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