The Specific Heat of a Trapped Fermi Gas: an Analytical Approach

We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kT>hw and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.Comment: To be published in Physics Letters A. 7 pages (RevTex) and 2 figures (postscript

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.Comment: 20 pages, 4 figure

Non-Fermi-liquid behavior in the Kondo lattices induced by peculiarities of magnetic ordering and spin dynamics

A scaling consideration of the Kondo lattices is performed with account of singularities in the spin excitation spectral function. It is shown that a non-Fermi-liquid (NFL) behavior between two critical values of the bare $s-f$ coupling constant occurs naturally for complicated magnetic structures with several magnon branches. This may explain the fact that a NFL behavior takes place often in the heavy-fermion systems with peculiar spin dynamics. Another kind of a NFL-like state (with different critical exponents) can occur for simple antiferromagnets with account of magnon damping, and for paramagnets, especially with two-dimensional character of spin fluctuations. The mechanisms proposed lead to some predictions about behavior of specific heat, resistivity, magnetic susceptibility, and anisotropy parameter, which can be verified experimentally.Comment: 16 pages, RevTeX, 4 Postscript figures. Extended versio

Effect of annealing on glassy dynamics and non-Fermi liquid behavior in UCu_4Pd

Longitudinal-field muon spin relaxation (LF-muSR) experiments have been performed in unannealed and annealed samples of the heavy-fermion compound UCu_4Pd to study the effect of disorder on non-Fermi liquid behavior in this material. The muon spin relaxation functions G(t,H) obey the time-field scaling relation G(t,H) = G(t/H^gamma) previously observed in this compound. The observed scaling exponent gamma = 0.3 pm 0.1, independent of annealing. Fits of the stretched-exponential relaxation function G(t) = exp[-(Lambda t)^K] to the data yielded stretching exponentials K < 1 for all samples. Annealed samples exhibited a reduction of the relaxation rate at low temperatures, indicating that annealing shifts fluctuation noise power to higher frequencies. There was no tendency of the inhomogeneous spread in rates to decrease with annealing, which modifies but does not eliminate the glassy spin dynamics reported previously in this compound. The correlation with residual resistivity previously observed for a number of NFL heavy-electron materials is also found in the present work.Comment: 4 pages, 3 figures, submitted to 10th International Conference on Muon Spin Rotation, Relaxation, and Resonance, Oxford, UK, August 200

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure

Are species occurrence data in global online repositories fit for modeling species distributions? The case of the Global Biodiversity Information Facility (GBIF). Final Report of the Task Group on GBIF Data Fitness for Use in Distribution Modelling.

Primary Biodiversity Data (PBD) are defined as the basic attributes of observations or records of the occurrences of species. PBD is a fundamental concept of biodiversity informatics since it is substantial in quantity and provides the links to organize other large and independent bodies of data concerning species (= taxonomic information) and environments. In fact, PBD is at the core of the exploding field of biodiversity informatics, which in some sense now underlies biogeography, macroecology, landscape ecology and several other subdisciplines of biology. A principal - and rapidly growing - class of research that can be performed using PBD is the estimation of a species' environmental requirements and the projection of these in both environmental and geographic spaces to estimate niches or distributional ranges, generally by using models of ecological niches and species' distributions (often called ENMs or SDMs, respectively). The largest point of access to PBD in the world is the Global Biodiversity Information Facility (GBIF), and hundreds of papers have now used GBIF-mediated data to fit and apply ENM/SDM. Experience has shown that GBIF, like other aggregated data research infrastructures, holds a number of potential problems related to incomplete or difficult access to all the fields in its schema, inconsistent information among fields, or simply erroneous or incomplete data. These drawbacks complicate ENM/SDM analyses considerably, and detract from the enormous scientific value of this information storehouse. Three overlapping communities participate in GBIF's data process: providers (museums, herbaria, and observer's networks), users (scientists, analysts working for governments, NGOs or the private sector, the public) and the technical staff managing the huge databases, web services and servers at GBIF. Each can play a different role in fixing data issues of GBIF. Our main recommendations for the GBIF Secretariat are the following: GBIF.org should serve indicators of precision, quality, and uncertainty of data that can be calculated practically, and preferably "on the fly", as well as summaries and metrics of completeness of inventories, at scales and for regions defined by the user. The summaries should display maps and graphs of completeness by region, time-period and taxa. The implementation of the GBIF information resource should go beyond unique identifiers of queries (DOIs for downloads, including the capability to re-run queries, http://www.gbif.org/publishing-data/summary#supporteddatasettypes), and to include identifiers of the individual data that make up the queried data. GBIF.org should include applications or functionalities enabling users to annotate errors or problems, and communicate those changes directly to providers, as it may be practical and appropriate. This point may need to be discussed with providers. A procedure enabling users to make accessible versions of their databases that have been improved and annotated should be supported, but this functionality should not lose the vital tie back to the original data records and the actual data provider. GBIF should partner with and/or support initiatives to do more for training and guiding users on the proper use of the data; such initiatives should incorporate actual expert uses in ENM/SDM to assure that current best practices are followed

Trapping of Projectiles in Fixed Scatterer Calculations

We study multiple scattering off nuclei in the closure approximation. Instead of reducing the dynamics to one particle potential scattering, the scattering amplitude for fixed target configurations is averaged over the target groundstate density via stochastic integration. At low energies a strong coupling limit is found which can not be obtained in a first order optical potential approximation. As its physical explanation, we propose it to be caused by trapping of the projectile. We analyse this phenomenon in mean field and random potential approximations. (PACS: 24.10.-i)Comment: 15 page

Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark description

This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.Comment: 8 pages, 6 figures, submitted to PR

Superconductivity and crystalline electric field effects in the filled skutterudite series Pr(Os1−x_{1-x}Rux_x)4_4Sb12_{12}

X-ray powder diffraction, magnetic susceptibility $\chi(T)$, and electrical resistivity $\rho(T)$ measurements were made on single crystals of the filled skutterudite series Pr(Os$_{1-x}$Ru$_x$)$_4$Sb$_{12}$. One end of the series ($x = 0$) is a heavy fermion superconductor with a superconducting critical temperature $T_{c} = 1.85$ K, while the other end ($x = 1$) is a conventional superconductor with $T_{c} \approx 1$ K. The lattice constant $a$ decreases approximately linearly with increasing Ru concentration $x$. As Ru (Os) is substituted for Os (Ru), $T_{c}$ decreases nearly linearly with substituent concentration and exhibits a minimum with a value of $T_{c} = 0.75$ K at $x = 0.6$, suggesting that the two types of superconductivity compete with one another. Crystalline electric field (CEF) effects in $\chi_\mathrm{dc}(T)$ and $\rho(T)$ due to the splitting of the Pr$^{3+}$ nine-fold degenerate Hund's rule $J = 4$ multiplet are observed throughout the series, with the splitting between the ground state and the first excited state increasing monotonically as $x$ increases. The fits to the $\chi_\mathrm{dc}(T)$ and $\rho(T)$ data are consistent with a $\Gamma_{3}$ doublet ground state for all values of x, although reasonable fits can be obtained for a $\Gamma_{1}$ ground state for $x$ values near the end member compounds ($x = 0$ or $x = 1$).Comment: 10 pages, 8 figures, submitted to Phys. Rev.

The Isospin Makeup of the Giant Resonances from (p,n) Reaction Studies at Intermediate Energies

This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit