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 $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ 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 $s$ 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