Palm pairs and the general mass-transport principle

We consider a lcsc group G acting properly on a Borel space S and measurably on an underlying sigma-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form.Comment: 26 page

Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation

Milagrito: a TeV air-shower array

Milagrito, a large, covered water-Cherenkov detector, was the world's first air-shower-particle detector sensitive to cosmic gamma rays below 1 TeV. It served as a prototype for the Milagro detector and operated from February 1997 to May 1998. This paper gives a description of Milagrito, a summary of the operating experience, and early results that demonstrate the capabilities of this technique.Comment: 38 pages including 24 figure

Bonding, Moment Formation, and Magnetic Interactions in Ca14MnBi11 and Ba14MnBi11

The ``14-1-11'' phase compounds based on magnetic Mn ions and typified by Ca14MnBi11 and Ba14MnBi11 show unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local orbital based method within the local spin density approximation to study the electronic structure, we find a gap between a bonding valence band complex and an antibonding conduction band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the MnBi4 tetrahedral unit and partially compensates the high spin d^5 Mn moment, leaving a net spin near 4 \mu_B that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating `jungle gym' networks of spin 4/2 MnBi4^{9-} units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. Ca14MnBi11 is calculated to be ferromagnetic as observed, while for Ba14MnBi11 (which is antiferromagnetic) the ferro- and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic.Comment: 17 pages, containing 10 postscript figures and 5 tables. Two additional figures (Fig.8 and 11 of the paper) are provided in JPG format in separate files. Submitted to Phys. Rev. B on September 20th 200

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d=3, it is given by a Levy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d=2, it is given by a marginal Gaussian distribution intermediate between Gaussian and Levy laws. In d=1, it is exactly given by the Bernouilli distribution (for any particle number N) which becomes Gaussian for N>>1. Therefore, the dimension d=2 is critical regarding the statistics of the gravitational force. We generalize these results for inhomogeneous systems with arbitrary power-law density profile and arbitrary power-law force in a d-dimensional universe

Weak lensing, dark matter and dark energy

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.Comment: Invited review article for the GRG special issue on gravitational lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). V3: subsection on three-point function and some references added. Matches the published versio

Langevin equations for interacting fermions and Cooper-like pairing in trapped one-dimensional fermions

Momentum correlations in a one-dimensional equilibrium ensemble of trapped fermions, with a point interaction between particles of opposite spin have been studied. In the degenerate regime correlations were observed between fermions with opposite spins and momenta, similar to Cooper pairing. These correlations appear as soon as the temperature is below the Fermi energy, which is a much less stringent condition than that of the BCS transition proper. Calculations are carried out in both perturbative and non-perturbative regimes. To achieve the latter. it is shown that interacting fermionic dynamics may be solved as a stochastic linear transformation of Grassmann algebra generators, much in the way random c-number paths are introduced in the conventional quantum stochastics of bosons. Importantly, the method thus emerging is inherently free of the sign problem

Highly Charged Ions in Rare Earth Permanent Magnet Penning Traps

A newly constructed apparatus at the National Institute of Standards and Technology (NIST) is designed for the isolation, manipulation, and study of highly charged ions. Highly charged ions are produced in the NIST electron-beam ion trap (EBIT), extracted through a beamline that selects a single mass/charge species, then captured in a compact Penning trap. The magnetic field of the trap is generated by cylindrical NdFeB permanent magnets integrated into its electrodes. In a room-temperature prototype trap with a single NdFeB magnet, species including Ne10+ and N7+ were confined with storage times of order 1 second, showing the potential of this setup for manipulation and spectroscopy of highly charged ions in a controlled environment. Ion capture has since been demonstrated with similar storage times in a more-elaborate Penning trap that integrates two coaxial NdFeB magnets for improved B-field homogeneity. Ongoing experiments utilize a second-generation apparatus that incorporates this two-magnet Penning trap along with a fast time-of-flight MCP detector capable of resolving the charge-state evolution of trapped ions. Holes in the two-magnet Penning trap ring electrode allow for optical and atomic beam access. Possible applications include spectroscopic studies of one-electron ions in Rydberg states, as well as highly charged ions of interest in atomic physics, metrology, astrophysics, and plasma diagnostics.Comment: Proceedings of CDAMOP-2011, 13-16 Dec 2011, Delhi, India. To be published by Springer Verla

Quantum Dot in the Kondo Regime coupled to p-wave superconductors

This paper studies the physics of junctions containing superconducting $(S)$ and normal $(N)$ leads weakly coupled to an Anderson impurity in the Kondo regime $(K)$. Special attention is devoted to the case where one of the leads is a $p-wave$ superconductor where mid-gap surface states play an important role in the tunneling processes and help the formation of Kondo resonance. The novel physics in these systems beyond that encountered in quantum dots coupled only to to normal leads is that electron transport at finite bias $eV$ in $SKN$ and $SKS$ junctions is governed by Andreev reflections. These enable the occurrence of dissipative current even when the bias $eV$ is smaller than the superconducting gap $\Delta$. Using the slave boson mean field approximation the current, shot-noise power and Fano factor are calculated as functions of the applied bias voltage in the sub-gap region $eV < \Delta$ and found to be strongly dependent on the ratio $t_K$ between the Kondo temperature $T_{K}$ and the superconducting gap $\Delta$. In particular, for large values of $t_K$ the attenuation of current due to the existence of the superconducting gap is compensated by the Kondo effect. This scenario is manifested also in the behavior of the Josephson current as function of temperature.Comment: 7 pages, 5 .eps figure