A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition

The Gutzwiller semiclassical trace formula links the eigenvalues of the Scrodinger operator ^H with the closed orbits of the corresponding classical mechanical system, associated with the Hamiltonian H, when the Planck constant is small ("semiclassical regime"). Gutzwiller gave a heuristic proof, using the Feynman integral representation for the propagator of ^H. Later on mathematicians gave rigorous proofs of this trace formula, under different settings, using the theory of Fourier Integral Operators and Lagrangian manifolds. Here we want to show how the use of coherent states (or gaussian beams) allows us to give a simple and direct proof.Comment: 17 pages, LaTeX, available on http://qcd.th.u-psud.f

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity

Quantum tomography for collider physics: Illustrations with lepton pair production

Quantum tomography is a method to experimentally extract all that is observable about a quantum mechanical system. We introduce quantum tomography to collider physics with the illustration of the angular distribution of lepton pairs. The tomographic method bypasses much of the field-theoretic formalism to concentrate on what can be observed with experimental data, and how to characterize the data. We provide a practical, experimentally-driven guide to model-independent analysis using density matrices at every step. Comparison with traditional methods of analyzing angular correlations of inclusive reactions finds many advantages in the tomographic method, which include manifest Lorentz covariance, direct incorporation of positivity constraints, exhaustively complete polarization information, and new invariants free from frame conventions. For example, experimental data can determine the $entanglement$ $entropy$ of the production process, which is a model-independent invariant that measures the degree of coherence of the subprocess. We give reproducible numerical examples and provide a supplemental standalone computer code that implements the procedure. We also highlight a property of $complex$ $positivity$ that guarantees in a least-squares type fit that a local minimum of a $\chi^{2}$ statistic will be a global minimum: There are no isolated local minima. This property with an automated implementation of positivity promises to mitigate issues relating to multiple minima and convention-dependence that have been problematic in previous work on angular distributions.Comment: 25 pages, 3 figure

A DISTRIBUTIONAL ANALYSIS OF THE COSTS OF FOODBORNE ILLNESS: WHO ULTIMATELY PAYS?

This paper traces the economic impact of the costs of foodborne illness on the U.S. economy using a Social Accounting Matrix (SAM) framework. Previous estimates of the costs of seven foodborne pathogens are disaggregated by type, and distributed across the population using data from the National Health Interview Survey. Initial income losses resulting from premature death cause a decrease in economic activity. Medical costs, in contrast, result in economic growth, though this growth does not outweigh the total costs of premature death. A SAM accounting of how the costs of illness are diffused through the economy provides useful information for policy makers.Cost of illness, Foodborne illness, Social Accounting Matrix, Food Consumption/Nutrition/Food Safety,

Decay of the Maxwell field on the Schwarzschild manifold

We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$ for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the Regge-Wheeler tortoise coordinate is large, $r_*>\epsilon t$, we obtain decay for the null components with rates of $|\phi_+| \sim |\alpha| < C r^{-5/2}$, $|\phi_0| \sim |\rho| + |\sigma| < C r^{-2} |t-r_*|^{-1/2}$, and $|\phi_{-1}| \sim |\underline{\alpha}| < C r^{-1} |t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$, and when $t+r_*1$, all components (normalized with respect to an ingoing null basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior region.Comment: 37 pages, 5 figure

Evidence for Adsorption of Chlorine Species on Iron(III) (hydr)oxides in the Sheepbed Mudstone, Gale Crater, Mars

Chlorine is a widespread element on Mars present in dust, soils and rocks, including the Sheepbed mudstone at Yellowknife Bay, Gale crater. Combined elemental and volatile analyses of two drilled samples, Cumberland and John Klein, indicated that chloride (Cl-) and perchlorate (ClO4 -) are likely present in the mudstone. The nature of chlorine species in Sheepbed mudstone is still not well constrained. It has been proposed that both are present as amorphous or crystalline salts physically mixed with mudstone minerals. We alternatively hypothesize that adsorbed perchlorate and chloride exist in the mudstone and adsorption could occur, in particular, on Fe(III) (hydr)oxide phases as supported by laboratory observations on terrestrial materials. Mineralogical and compositional analyses of the drilled Cumberland mudstone sample revealed the presence of ~30 wt% of a Fe-rich X-ray amorphous phase. Ferrihydrite has been proposed as a component of the Fe-rich X-ray amorphous material. The objectives of this work were to determine adsorption of perchlorate and chloride on ferrihydrite and to enable data comparison by characterizing adsorbed chloride and perchlorate with thermal and evolved gas analysis run under operating conditions similar to the SAM instrument onboard the Curiosity rover

Analysis Tools for Discovering Strong Parity Violation at Hadron Colliders

Several arguments suggest parity violation may be observable in high energy strong interactions. We introduce new analysis tools for describing the azimuthal dependence of multi-particle distributions, or "azimuthal flow." Analysis uses the representations of the orthogonal group O(2) and dihedral groups $D_{N}$ necessary to define parity correctly in two dimensions. Classification finds that collective angles used in event-by-event statistics represent inequivalent tensor observables that cannot generally be represented by a single "reaction plane". Many new parity-violating observables exist that have never been measured, while many new parity-conserving observables formerly lumped together are now distinguished. We use the concept of "event shape sorting" to suggest separating right- and left-handed events, and we discuss the effects of transverse and longitudinal spin. The analysis tools are statistically robust, and can be applied equally to low or high multiplicity events at the Tevatron, $RHIC$ or $RHIC\, Spin$, and the $LHC$.Comment: 18 pages, 2 figures. Final version, accepted for publication in PRD. Updated references. Modified presentation and discussion of previous wor

Efficient numerical diagonalization of hermitian 3x3 matrices

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an analytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published version, typo in Eq. (39) corrected; software library available at http://www.mpi-hd.mpg.de/~globes/3x3

Lunar surface dynamics: Some general conclusions and new results from Apollo 16 and 17

Exposure ages of Apollo 17 rocks as measured by tracks and the Kr-Kr rare gas method are reported. Concordant ages of 22 - or + 1 million year (my) are obtained for the station 6 boulder sample 76315. This value is interpreted as the time when the station 6 boulder was emplaced in its present position. Reasonable agreement is also obtained by the two methods for another station 6 boulder, sample 76015. Discordant ages (respectively 5 and 28 my by the track and rare gas methods) are obtained for the station 7 boulder sample, 77135, indicating that the boulder was emplaced at least 5 my ago. The 72 my exposure age of 75035, in general agreement with previous measurements of approximately 85 my for another Camelot boulder, may well date the formation of Camelot. Rock 76015 was split and one surface exposed to the sky through a very small solid angle