Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Green's function of a finite chain and the discrete Fourier transform

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20, No. 5 (2006) 593-60

RXTE monitoring observations of Markarian 3

We present Rossi X-ray Timing Explorer, monitoring observations of the Seyfert 2 galaxy Markarian 3 spanning a 200 day period during which time the source flux varied by a factor $\sim 2$ in the 4-20 keV bandpass. In broad agreement with earlier Ginga results, the average spectrum can be represented in terms of a simple spectral model consisting of a very hard power-law continuum ($\Gamma \approx 1.1$) modified below $\sim 6$ keV by a high absorbing column ($N_H\sim 6\times 10^{23}$ \cunits) together with a high equivalent width Fe-K emission feature at 6.4 keV. The abnormally flat spectral index is probably the signature of a strong reflection component and we consider two models incorporating such emission. In the first the reflected signal suffers the same absorption as the intrinsic continuum, whereas in the second the reflection is treated as an unabsorbed spectral component. In the former case, we require a very strong reflection signal ($R ~< 3$) in order to match the data; in addition variability of both the intrinsic power-law and the reflection component is required. The unabsorbed reflection model requires a somewhat higher line-of-sight column density to the nuclear source ($\sim 10^{24}$ \cunits), but in this case the reflected signal remains constant whilst the level of the intrinsic continuum varies. The latter description is consistent with the reflection originating from the illuminated far inner wall of a molecular torus, the nearside of which screens our direct view of the central continuum source.Comment: 7 pages, submitted to the MNRA

Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $\phi^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP 20-11-9

Monitoring RXTE Observations of Markarian 348: the origin of the column density variations

We analyze 37 RXTE observations of the type 2 Seyfert galaxy Mrk348 obtained during a period of 14 months. We confirm the spectral variability previous reported by Smith et al., in the sense that thecolumn density decreases by a factor of ~3 as the count rate increases. Column density variations could possibly originate either due to the random drift of clouds within the absorption screen, or due to photoionization processes. Our modeling of the observed variations implies that the first scenario is more likely. These clouds should lie in a distance of >2 light years from the source, having a diameter of a few light days and a density of >10^7 cm^(-3), hence probably residing outside the Broad Line Region.Comment: 6 pages, 3 figures, to appear in MNRA

FIBONACCI SUPERLATTICES OF NARROW-GAP III-V SEMICONDUCTORS

We report theoretical electronic structure of Fibonacci superlattices of narrow-gap III-V semiconductors. Electron dynamics is accurately described within the envelope-function approximation in a two-band model. Quasiperiodicity is introduced by considering two different III-V semiconductor layers and arranging them according to the Fibonacci series along the growth direction. The resulting energy spectrum is then found by solving exactly the corresponding effective-mass (Dirac-like) wave equation using tranfer-matrix techniques. We find that a self-similar electronic spectrum can be seen in the band structure. Electronic transport properties of samples are also studied and related to the degree of spatial localization of electronic envelope-functions via Landauer resistance and Lyapunov coefficient. As a working example, we consider type II InAs/GaSb superlattices and discuss in detail our results in this system.Comment: REVTeX 3.0, 16 pages, 8 figures available upon request. To appear in Semiconductor Science and Technolog

Refinement of metabolite detection in cystic fibrosis sputum reveals heme correlates with lung function decline

The bacterial growth environment within cystic fibrosis (CF) sputum is complex, dynamic, and shaped by both host and microbial processes. Characterization of the chemical parameters within sputum that stimulate the in vivo growth of airway pathogens (e.g. Pseudomonas aeruginosa) and their associated virulence factors may lead to improved CF treatment strategies. Motivated by conflicting reports of the prevalence and abundance of P. aeruginosa-derived metabolites known as phenazines within CF airway secretions, we sought to quantify these metabolites in sputum using quadrupole time-of-flight mass spectrometry. In contrast to our previous work, all phenazines tested (pyocyanin (PYO), phenazine-1-carboxylic acid (PCA), phenazine-1-carboxamide, and 1-hydroxyphenazine) were below detection limits of the instrument (0.1 μM). Instead, we identified a late-eluting compound that shared retention time and absorbance characteristics with PCA, yet generated mass spectra and a fragmentation pattern consistent with ferriprotoporphyrin IX, otherwise known as heme B. These data suggested that UV-vis chromatographic peaks previously attributed to PCA and PYO in sputum were mis-assigned. Indeed, retrospective analysis of raw data from our prior study found that the heme B peak closely matched the peaks assigned to PCA, indicating that the previous study likely uncovered a positive correlation between pulmonary function (percent predicted forced expiratory volume in 1 second, or ppFEV1) and heme B, not PCA or any other phenazine. To independently test this observation, we performed a new tandem mass-spectrometry analysis of 71 additional samples provided by the Mountain West CF Consortium Sputum Biomarker study and revealed a positive correlation (ρ = −0.47, p<0.001) between sputum heme concentrations and ppFEV1. Given that hemoptysis is strongly associated with airway inflammation, pulmonary exacerbations and impaired lung function, these new data suggest that heme B may be a useful biomarker of CF pathophysiology

Exact results for some Madelung type constants in the finite-size scaling theory

A general formula is obtained from which the madelung type constant: $$C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}]$$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $\nu$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added

Exact Zeros of the Partition Function for a Continuum System with Double Gaussian Peaks

We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two separate loci of zeros which used to give first-order transition touch each other, with density of zeros vanishing at the contact point on the positive real axis. Instead of the second-order transition of Ehrenfast classification as one might naively expect, one finds a critical behavior in this limit.Comment: 13 pages, 6 figures, revtex, minor changes in fig.2, to be published in Physical Review

Supersymmetric quantum mechanics with nonlocal potentials

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.Comment: 4 pages, REVTeX, Minor revisions for clarificatio