Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory

We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well with those from numerical Dynamical Density-Matrix Renormalization Group (DDMRG) calculations. The density of states of the lower Hubbard band also agrees very well with DDMRG data, apart from a resonance contribution at the upper band edge which cannot be reproduced in low-order perturbation theory.Comment: 40 pages, 7 figure

Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions

We use Brueckner-Goldstone perturbation theory to calculate the ground-state energy of the half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbard interaction. We obtain the momentum distribution as a functional derivative of the ground-state energy with respect to the bare dispersion relation. The resulting expressions agree with those from Rayleigh-Schroedinger perturbation theory. Our results for the momentum distribution and the quasi-particle weight agree very well with those obtained earlier from Feynman-Dyson perturbation theory for the single-particle self-energy. We give the correct fourth-order coefficient in the ground-state energy which was not calculated accurately enough from Feynman-Dyson theory due to the insufficient accuracy of the data for the self-energy, and find a good agreement with recent estimates from Quantum Monte-Carlo calculations.Comment: 15 pages, 8 fugures, submitted to JSTA

The Feynman propagator for spin foam quantum gravity

We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence. Using the technology of evolution kernels for quantum fields/particles on Lie groups/homogeneous spaces, we construct a generalised version of spin foam models, introducing an extra proper time variable and prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of QFT or as a covariant definition of the inner product between quantum gravity states; and a new class of causal models, corresponding to the quantum gravity analogue of the Feynman propagator in QFT, non-trivial function of the orientation data, and implying a notion of ''timeless ordering''.Comment: RevTex, 5 pages, no figures; v2-3:minor typos correcte

Primordial helium recombination III: Thomson scattering, isotope shifts, and cumulative results

Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background (CMB) at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of HeI and HeII recombination. Here we describe the effect of Thomson scattering, the $^3$He isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and $^3$He scattering modify the free electron fraction $x_e$ at the level of several $\times 10^{-4}$. The uncertainty in the $2^3P^o-1^1S$ rate is significant, and for conservative estimates gives uncertainties in $x_e$ of order $10^{-3}$. We describe several convergence tests for the atomic level code and its inputs, derive an overall $C_\ell$ error budget, and relate shifts in $x_e(z)$ to the changes in $C_\ell$, which are at the level of 0.5% at $\ell =3000$. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is $\sim 0.3$ in $x_e$.Comment: 19 pages, 15 figures, to be submitted to PR

New CMB Power Spectrum Constraints from MSAMI

We present new cosmic microwave background (CMB) anisotropy results from the combined analysis of the three flights of the first Medium Scale Anisotropy Measurement (MSAM1). This balloon-borne bolometric instrument measured about 10 square degrees of sky at half-degree resolution in 4 frequency bands from 5.2 icm to 20 icm with a high signal-to-noise ratio. Here we present an overview of our analysis methods, compare the results from the three flights, derive new constraints on the CMB power spectrum from the combined data and reduce the data to total-power Wiener-filtered maps of the CMB. A key feature of this new analysis is a determination of the amplitude of CMB fluctuations at $\ell \sim 400$. The analysis technique is described in a companion paper by Knox.Comment: 9 pages, 6 included figure

Landform type mediates compositional change in a hurricane-disturbed sub-tropical forest

Background Categorization of topographical features into landform type is a long-standing method for understanding physiographic patterns in the environment. Differences in forest composition between landform types are driven primarily by concurrent differences in soil composition and moisture, but also disturbance regime. Many studies have focused on the interaction between fire disturbance, succession, and landforms, but the effects of hurricane disturbance on compositional differences between landforms are poorly understood. In the study presented here, we assess compositional and structural differences between landform types in the tree community of a young sub-tropical forest that is frequently subjected to hurricanes. Specifically, we ask whether the tree community (1) changed structurally over the study period, (2) experienced compositional change over the study period, (3) is compositionally different between landform types, and (4) exhibits compositional change mediated by landform type. Results The tree community experienced significant structural change over the course of our study, but compositional change was only significant for some landforms. Conclusion Despite large-scale, intense, and frequent hurricane disturbance to our study system, compositional change in the tree community was localized and only significant for some landform types

Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations as well. In order to compute the rate of formation of massive objects we employ the Spherical Collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the Pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations as well. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift.Comment: 21 pages, 8 figures. Matches published version, with caption of Fig. 6 correcte

Carbon stock increases up to old growth forest along a secondary succession in Mediterranean island ecosystems

The occurrence of old-growth forests is quite limited in Mediterranean islands, which have been subject to particularly pronounced human impacts. Little is known about the carbon stocks of such peculiar ecosystems compared with different stages of secondary succession. We investigated the carbon variation in aboveground woody biomass, in litter and soil, and the nitrogen variation in litter and soil, in a 100 years long secondary succession in Mediterranean ecosystems. A vineyard, three stages of plant succession (high maquis, maquis-forest, and forest-maquis), and an old growth forest were compared. Soil samples at two soil depths (0-15 and 15-30 cm), and two litter types, relatively undecomposed and partly decomposed, were collected. Carbon stock in aboveground woody biomass increased from 6 Mg ha-1 in the vineyard to 105 Mg ha-1 in old growth forest. Along the secondary succession, soil carbon considerably increased from about 33 Mg ha-1 in the vineyard to about 69 Mg ha-1 in old growth forest. Soil nitrogen has more than doubled, ranging from 4.1 Mg ha-1 in the vineyard to 8.8 Mg ha-1 in old growth forest. Both soil parameters were found to be affected by successional stage and soil depth but not by their interaction. While the C/N ratio in the soil remained relatively constant during the succession, the C/N ratio of the litter strongly decreased, probably following the progressive increase in the holm oak contribution. While carbon content in litter decreased along the succession, nitrogen content slightly increased. Overall, carbon stock in aboveground woody biomass, litter and soil increased from about 48 Mg ha-1 in the vineyard to about 198 Mg ha-1 in old growth forest. The results of this study indicate that, even in Mediterranean environments, considerable amounts of carbon may be stored through secondary succession processes up to old growth forest.The occurrence of old-growth forests is quite limited in Mediterranean islands, which have been subject to particularly pronounced human impacts. Little is known about the carbon stocks of such peculiar ecosystems compared with different stages of secondary succession. We investigated the carbon variation in aboveground woody biomass, in litter and soil, and the nitrogen variation in litter and soil, in a 100 years long secondary succession in Mediterranean ecosystems. A vineyard, three stages of plant succession (high maquis, maquis-forest, and forest-maquis), and an old growth forest were compared. Soil samples at two soil depths (0-15 and 15-30 cm), and two litter types, relatively undecomposed and partly decomposed, were collected. Carbon stock in aboveground woody biomass increased from 6 Mg ha(-1) in the vineyard to 105 Mg ha(-1) in old growth forest. Along the secondary succession, soil carbon considerably increased from about 33 Mg ha(-1) in the vineyard to about 69 Mg ha(-1) in old growth forest. Soil nitrogen has more than doubled, ranging from 4.1 Mg ha(-1) in the vineyard to 8.8 Mg ha(-1) in old growth forest. Both soil parameters were found to be affected by successional stage and soil depth but not by their interaction. While the C/N ratio in the soil remained relatively constant during the succession, the C/N ratio of the litter strongly decreased, probably following the progressive increase in the holm oak contribution. While carbon content in litter decreased along the succession, nitrogen content slightly increased. Overall, carbon stock in aboveground woody biomass, litter and soil increased from about 48 Mg ha(-1) in the vineyard to about 198 Mg ha(-1) in old growth forest. The results of this study indicate that, even in Mediterranean environments, considerable amounts of carbon may be stored through secondary succession processes up to old growth forest