Optical Resonances in Reflectivity near Crystal Modes with Spatial Dispersion

We study the effect of spatial dispersion of crystal modes on optical properties such as the reflectivity $R$. As an example for isotropic media, we investigate the simplest model for phonons in ionic crystals and compare with previous results for highly anisotropic plasmons, which are now understood from a more general point of view. As a consequence of the wave vector dependence of the dielectric function small changes in the lineshape are predicted. Beyond that, if the frequency of minimal $R$ is near a pole of the dispersionless dielectric function, the relative amplitude of dips in $R$ with normal and anomalous dispersion differ significantly, if dissipation and disorder are low.Comment: 4 pages, 7 eps figures, minor change

Wigner crystalization about ν\nu=3

We measure a resonance in the frequency dependence of the real diagonal conductivity, Re[$\sigma_{xx}$], near integer filling factor, $\nu=3$. This resonance depends strongly on $\nu$, with peak frequency $f_{pk} \approx 1.7$ GHz at $\nu=3.04$ or 2.92 close to integer $\nu$, but $f_{pk} \approx$ 600 MHz at $\nu=3.19$ or 2.82, the extremes of where the resonance is visible. The dependence of $f_{pk}$ upon $n^*$, the density of electrons in the partially filled level, is discussed and compared with similar measurments by Chen {\it et al.}\cite{yong} about $\nu=1$ and 2. We interpret the resonance as due to a pinned Wigner crystal phase with density $n^*$ about the $\nu=3$ state.Comment: for proceedings of EP2DS-15 (Nara) to appear in Physica

Relativistic Coulomb Sum Rules for (e,e′)(e,e^\prime)

A Coulomb sum rule is derived for the response of nuclei to $(e,e^\prime)$ scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the most direct connection with experiments; an immediate consequence is that excitations involving antinucleons, e.g., $N{\bar N}$ pair production, are approximately eliminated from the sum rule. Relativistic recoil and Fermi motion of target nucleons are correctly incorporated. The sum rule decomposes into one- and two-body parts, with correlation information in the second. The one-body part requires information on the nucleon momentum distribution function, which is incorporated by a moment expansion method. The sum rule given through the second moment (RCSR-II) is tested in the Fermi gas model, and is shown to be sufficiently accurate for applications to data.Comment: 32 pages (LaTeX), 4 postscript figures available from the author

Evaluation of the low-lying energy levels of two- and three-electron configurations for multi-charged ions

Accurate QED evaluations of the one- and two-photon interelectron interaction for low lying two- and three-electron configurations for ions with nuclear charge numbers $60\le Z \le 93$ are performed. The three-photon interaction is also partly taken into account. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations. A detailed investigation of the behaviour of the energy levels of the configurations $1s_{1/2}2s_{1/2} {}^1 S_0$, $1s_{1/2}2p_{1/2} {}^3 P_0$ near the crossing points Z=64 and Z=92 is carried out. The crossing points are important for the future experimental search for parity nonconserving (PNC) effects in highly charged ions

High momentum transfer inelastic muon scattering and test of scale invariance at NAL

We propose a relatively simple first stage experiment with muons in the 50-150 GeV range. The experiment is designed to optimize conditions for testing scale invariance while providing some information about the final state, as a test of various theories of high energy interactions. The proposed use of an iron spectrometer and of a high Z (>1) target with a low intensity ({approx}10{sup 6}/sec) muon beam should greatly reduce the cost and complexity of the experiment and especially ease the construction of the beam. It may even be possible to make an adequate muon beam for this purpose from the planned 3.5 mrad high intensity pion beam. A higher intensity muon beam can be used to extend the range in q{sup 2}. Information gained in this first experiment could greatly assist the planning of a more sophisticated experiment proposed for the high intensity {mu} beam

Optical Properties of Layered Superconductors near the Josephson Plasma Resonance

We study the optical properties of crystals with spatial dispersion and show that the usual Fresnel approach becomes invalid near frequencies where the group velocity of the wave packets inside the crystal vanishes. Near these special frequencies the reflectivity depends on the atomic structure of the crystal provided that disorder and dissipation are very low. This is demonstrated explicitly by a detailed study of layered superconductors with identical or two different alternating junctions in the frequency range near the Josephson plasma resonance. Accounting for both inductive and charge coupling of the intrinsic junctions, we show that multiple modes are excited inside the crystal by the incident light, determine their relative amplitude by the microscopic calculation of the additional boundary conditions and finally obtain the reflectivity. Spatial dispersion also provides a novel method to stop light pulses, which has possible applications for quantum information processing and the artificial creation of event horizons in a solid.Comment: 25 pages, 20 figures, submitted to Phys. Rev.

Sensitivity analysis of reactive ecological dynamics

Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.Financial support provided by NSF grant DEB-0343820, NOAA grant NA03-NMF4720491, the Ocean Life Institute of the Woods Hole Oceanographic Institution, and the Academic Programs Office of the MIT-WHOI Joint Program in Oceanography

Study of the Linked Dipole Chain Model in heavy quark production at the Tevatron

We present calculations of charm and beauty production at Tevatron within the framework of kT-factorization, using the unintegrated gluon distributions as obtained from the Linked Dipole Chain model. The analysis covers transverse momentum and rapidity distributions and the azimuthal correlations between b and bbar quarks (or rather muons from their decay) which are powerful tests for the different unintegrated gluon distributions. We compare the theoretical results with recent experimental data taken by D0 and CDF collaborations at the Tevatron Run I and II.Comment: 16 page

Density-functional calculation of ionization energies of current-carrying atomic states

Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be numerically feasible. Different parametrizations for the current-dependence of the density functional are critically compared. Orbital currents in open-shell atoms turn out to produce a small shift in the ionization energies. We find that modern density functionals have reached an accuracy at which small current-related terms appearing in open-shell configurations are not negligible anymore compared to the remaining difference to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.

An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice

The lattice spin model with $Q$--component discrete spin variables restricted to have orientations orthogonal to the faces of $Q$-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole--dipole and quadrupole--quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations which allows to calculate all thermodynamic characteristics of the model is obtained. The correspondence between thermodynamic phases and different types of fixed points of the RR is established. Using the technique of simple iterations the plots of the zero field magnetization and quadrupolar moment are obtained. Analyzing the regions of stability of different types of fixed points of the system of recurrent relations the phase diagrams of the model are plotted. For $Q \leq 2$ the phase diagram of the model is found to have three tricritical points, whereas for $Q> 2$ there are one triple and one tricritical points.Comment: 20 pages, 7 figure