Minimal Position-Velocity Uncertainty Wave Packets in Relativistic and Non-relativistic Quantum Mechanics

We consider wave packets of free particles with a general energy-momentum dispersion relation $E(p)$. The spreading of the wave packet is determined by the velocity v = \p_p E. The position-velocity uncertainty relation $\Delta x \Delta v \geq {1/2} ||$ is saturated by minimal uncertainty wave packets $\Phi(p) = A \exp(- \alpha E(p) + \beta p)$. In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation $E(p) = p^2/2m$, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation $E(p) = - \cos(p a)/m a^2$ as well as for the relativistic dispersion relation $E(p) = \sqrt{p^2 + m^2}$. The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed

Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor - planar case

We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. The masses of the $W$, $Z$ and Higgs bosons are assumed to be degenerate. This work is a continuation of our previous evaluation of master integrals containing at most 1 massive propagator. The 1/\epsilon poles and the finite parts are computed exactly in terms of a {\it new} class of 1-dimensional harmonic polylogarithms of the variable x, with \epsilon=2-D/2 and D the pace-time dimension. Since thresholds and pseudothresholds in s=\pm 4m^2 do appear in addition to the old ones in s=0,\pm m^2, an extension of the basis function set involving complex constants and radicals is introduced, together with a set of recursion equations to reduce integrals with semi-integer powers. It is shown that the basic properties of the harmonic polylogarithms are maintained by the generalization. We derive small-momentum expansions |s| << m^2 of all the 6-denominator amplitudes. We also present large momentum expansions |s| >> m^2 of all the 6-denominator amplitudes which can be represented in terms of ordinary harmonic polylogarithms. Comparison with previous results in the literature is performed finding complete agreement.Comment: 68 pages, 7 figure

Systems analysis of bioenergetics and growth of the extreme halophile Halobacterium salinarum

Halobacterium salinarum is a bioenergetically flexible, halophilic microorganism that can generate energy by respiration, photosynthesis, and the fermentation of arginine. In a previous study, using a genome-scale metabolic model, we have shown that the archaeon unexpectedly degrades essential amino acids under aerobic conditions, a behavior that can lead to the termination of growth earlier than necessary. Here, we further integratively investigate energy generation, nutrient utilization, and biomass production using an extended methodology that accounts for dynamically changing transport patterns, including those that arise from interactions among the supplied metabolites. Moreover, we widen the scope of our analysis to include phototrophic conditions to explore the interplay between different bioenergetic modes. Surprisingly, we found that cells also degrade essential amino acids even during phototropy, when energy should already be abundant. We also found that under both conditions considerable amounts of nutrients that were taken up were neither incorporated into the biomass nor used as respiratory substrates, implying the considerable production and accumulation of several metabolites in the medium. Some of these are likely the products of forms of overflow metabolism. In addition, our results also show that arginine fermentation, contrary to what is typically assumed, occurs simultaneously with respiration and photosynthesis and can contribute energy in levels that are comparable to the primary bioenergetic modes, if not more. These findings portray a picture that the organism takes an approach toward growth that favors the here and now, even at the cost of longer-term concerns. We believe that the seemingly "greedy" behavior exhibited actually consists of adaptations by the organism to its natural environments, where nutrients are not only irregularly available but may altogether be absent for extended periods that may span several years. Such a setting probably predisposed the cells to grow as much as possible when the conditions become favorable

Perturbative quantum gauge invariance: Where the ghosts come from

A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories which are then subject to quantization, but it is also possible to recover the classical group structure and coupling properties from purely quantum mechanical principles. As a main tool we use a free field version of the Becchi-Rouet-Stora-Tyutin gauge transformation, which contains no interaction terms related to a coupling constant. This free gauge transformation can be formulated in an analogous way for quantum electrodynamics, Yang-Mills theories with massless or massive gauge bosons and quantum gravity.Comment: 28 pages, LATEX. Some typos corrected, version to be publishe

Jack of All Trades, Master of All: A Positive Association between Habitat Niche Breadth and Foraging Performance in Pit-Building Antlion Larvae

Species utilizing a wide range of resources are intuitively expected to be less efficient in exploiting each resource type compared to species which have developed an optimal phenotype for utilizing only one or a few resources. We report here the results of an empirical study whose aim was to test for a negative association between habitat niche breadth and foraging performance. As a model system to address this question, we used two highly abundant species of pit-building antlions varying in their habitat niche breadth: the habitat generalist Myrmeleon hyalinus, which inhabits a variety of soil types but occurs mainly in sandy soils, and the habitat specialist Cueta lineosa, which is restricted to light soils such as loess. Both species were able to discriminate between the two soils, with each showing a distinct and higher preference to the soil type providing higher prey capture success and characterizing its primary habitat-of-origin. As expected, only small differences in the foraging performances of the habitat generalist were evident between the two soils, while the performance of the habitat specialist was markedly reduced in the alternative sandy soil. Remarkably, in both soil types, the habitat generalist constructed pits and responded to prey faster than the habitat specialist, at least under the temperature range of this study. Furthermore, prey capture success of the habitat generalist was higher than that of the habitat specialist irrespective of the soil type or prey ant species encountered, implying a positive association between habitat niche-breadth and foraging performance. Alternatively, C. lineosa specialization to light soils does not necessarily confer upon its superiority in utilizing such habitats. We thus suggest that habitat specialization in C. lineosa is either an evolutionary dead-end, or, more likely, that this species' superiority in light soils can only be evident when considering additional niche axes

XMM-Newton discovery of an X-ray filament in Coma

XMM-Newton observations of the outskirts of the Coma cluster of galaxies confirm the existence of a soft X-ray excess claimed previously and show it comes from warm thermal emission. Our data provide a robust estimate of its temperature (~0.2 keV) and oxygen abundance (~0.1 solar). Using a combination of XMM-Newton and ROSAT All-Sky Survey data, we rule out a Galactic origin of the soft X-ray emission. Associating this emission with a 20 Mpc region in front of Coma, seen in the skewness of its galaxy velocity distribution, yields an estimate of the density of the warm gas of ~50 f_baryon rho_critical, where f_baryon is the baryon fraction of the gas and rho_critical is the critical density needed to halt the expansion of the universe. Our measurement of the gas mass associated with the warm emission strongly support its nonvirialized nature, suggesting that we are observing the warm-hot intergalactic medium (WHIM). Our measurements provide a direct estimate of the O, Ne and Fe abundance of the WHIM. Differences with the reported Ne/O ratio for some OVI absorbers hints at a different origin of the OVI absorbers and the Coma filament. We argue that the Coma filament has likely been preheated, but at a substantially lower level compared to what is seen in the outskirts of groups. The thermodynamic state of the gas in the Coma filament reduces the star-formation rate in the embedded spiral galaxies, providing an explanation for the presence of passive spirals observed in this and other clusters.Comment: 9 pages, 5 figures, accepted by A&

The Role of the Environment in Chaotic Quantum Dynamics

We study how the interaction with an external incoherent environment induces a crossover from quantum to classical behavior for a particle whose classical motion is chaotic. Posing the problem in the semiclassical regime, we find that noise produced by the bath coupling rather than dissipation is primarily responsible for the dephasing that results in the ``classicalization'' of the particle. We find that the bath directly alters the phase space structures that signal the onset of classical chaos. This dephasing is shown to have a semiclassical interpretation: the noise renders the interfering paths indistinguishable and therefore incoherent. The noise is also shown to contribute to the quantum inhibition of mixing by creating new paths that interfere coherently.Comment: 10 pages RevTex. Three figures in Postscript as a uuencoded compressed tar file have been submitted as wel

The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.Comment: 42 pages, 1 figur

Signature of Chaotic Diffusion in Band Spectra

We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors with the winding number as a spatial argument. For times smaller than the Heisenberg time, they are related to the full space-time dependence of the classical diffusion propagator. They approach constant asymptotes via a regime, reflecting quantal ballistic motion, where they decay by a factor proportional to the number of unit cells. We derive a universal scaling function for the long-time behaviour. Our results are substantiated by a numerical study of the kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps