The double well potential in quantum mechanics: a simple, numerically exact formulation

The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum mechanic

Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere

Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork' structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the modes beyond the instrumental horizon (EoR/CD window). We show that this structure largely arises due to strong instrumental polarization leakage ($\sim30\%$) towards {Cas\,A} ($\sim21$ kJy at 81 MHz, brightest source in northern sky), which is far away from primary field of view. We measure an extremely small ionospheric diffractive scale ($r_{\text{diff}} \approx 430$ m at 60 MHz) towards {Cas\,A} resembling pure Kolmogorov turbulence compared to $r_{\text{diff}} \sim3 - 20$ km towards zenith at 150 MHz for typical ionospheric conditions. This is one of the smallest diffractive scales ever measured at these frequencies. Our work provides insights in understanding the nature of aforementioned effects and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA) in the same frequency window.Comment: 20 pages, 11 figures, accepted for publication in MNRA

Prospects for detecting the 21cm forest from the diffuse intergalactic medium with LOFAR

We discuss the feasibility of the detection of the 21cm forest in the diffuse IGM with the radio telescope LOFAR. The optical depth to the 21cm line has been derived using simulations of reionization which include detailed radiative transfer of ionizing photons. We find that the spectra from reionization models with similar total comoving hydrogen ionizing emissivity but different frequency distribution look remarkably similar. Thus, unless the reionization histories are very different from each other (e.g. a predominance of UV vs. x-ray heating) we do not expect to distinguish them by means of observations of the 21cm forest. Because the presence of a strong x-ray background would make the detection of 21cm line absorption impossible, the lack of absorption could be used as a probe of the presence/intensity of the x-ray background and the thermal history of the universe. Along a random line of sight LOFAR could detect a global suppression of the spectrum from z>12, when the IGM is still mostly neutral and cold, in contrast with the more well-defined, albeit broad, absorption features visible at lower redshift. Sharp, strong absorption features associated with rare, high density pockets of gas could be detected also at z~7 along preferential lines of sight.Comment: 12 pages, 13 figures. MNRAS, in pres

Recovering the H II region size statistics from 21-cm tomography

We introduce a novel technique, called ‘granulometry’, to characterize and recover the mean size and the size distribution of H II regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well-defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of H II region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of Square Kilometre Array 1 (SKA1) low and a future extension to SKA2. We show that the technique allows the recovery of the H II region size distribution with a moderate signal-to-noise ratio from wide-field imaging (SNR 3), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field of view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21-cm power spectra, we suggest an observing strategy using wide- field imaging (several tens of square degrees) by an interferometric mosaicking/multibeam observation with additional intermediate baselines (∼2−4 km) in an SKA phase 2

Foregrounds for observations of the cosmological 21 cm line: I. First Westerbork measurements of Galactic emission at 150 MHz in a low latitude field

We present the first results from a series of observations conducted with the Westerbork telescope in the 140--160 MHz range with a 2 arcmin resolution aimed at characterizing the properties of the foregrounds for epoch of reionization experiments. For the first time we have detected fluctuations in the Galactic diffuse emission on scales greater than 13 arcmin at 150 MHz, in the low Galactic latitude area known as Fan region. Those fluctuations have an $rms$ of 14 K. The total intensity power spectrum shows a power--law behaviour down to $\ell \sim 900$ with slope $\beta^I_\ell = -2.2 \pm 0.3$. The detection of diffuse emission at smaller angular scales is limited by residual point sources. We measured an $rms$ confusion noise of $\sim$3 mJy beam$^{-1}$. Diffuse polarized emission was also detected for the first time at this frequency. The polarized signal shows complex structure both spatially and along the line of sight. The polarization power spectrum shows a power--law behaviour down to $\ell \sim 2700$ with slope $\beta^P_\ell = -1.65 \pm 0.15$. The $rms$ of polarization fluctuations is 7.2 K on 4 arcmin scales. By extrapolating the measured spectrum of total intensity emission, we find a contamination on the cosmological signal of $\delta T= \sqrt{\ell (\ell+1) C^I_\ell / 2\pi} \sim 5.7$ K on 5 arcmin scales and a corresponding $rms$ value of $\sim$18.3 K at the same angular scale. The level of the polarization power spectrum is $\delta T \sim 3.3$ K on 5 arcmin scales. Given its exceptionally bright polarized signal, the Fan region is likely to represent an upper limit on the sky brightness at moderate and high Galactic latitude.Comment: Minor corrections made to match the final version printed on A&A. A version with high resolution figures is available at http://www.astro.rug.nl/~bernardi/FAN/fan.pd

Interactions between heterometallic bridged cis-or trans-Pt(II)-Zn(II)complexes and calf thymus DNA

More recently scientific attention is paid on non platinum based drug especially on bio essential metal ions Design of the heterometallic complexes is possible way to overcome limitation of platinum based drugs T he four novel complexes cis PtCl (NH 3 μ 4 4 bipyridyl) ZnCl terpy )}](ClO 4 2 trans PtCl (NH 3 μ 4 4 bipyridyl) ZnCl terpy )}](ClO 4 2 cis PtCl (NH 3 μ pyrazine) ZnCl terpy )}](ClO 4 2 and trans PtCl (NH 3 μ pyrazine) ZnCl terpy )}](ClO 4 2 (where terpy 2 2 6 2 terpyridine) were synthesized and characterized The binding of the heterometallic bridged cis or trans Pt(II) Zn(II) complexes to calf thymus DNA (CT DNA) was studied using UV absorption and fluorescence emission spectroscopy The results indicate that the complexes bind strongly to DNA K b in the order of 10 4 M 1 through groove binding, hydrogen bonds, and hydrophobic or electrostatic interaction According to Stern Volmer quenching constant K SV and binding constant (K the cis PtCl (NH 3 μ 4 4 bipyridyl) ZnCl terpy )}](ClO 4 2 complex interacts with CT DNA EB more strongly than the rest of the studied complexes.Publishe

Polymorphism of alpha-1-antitrypsin in hematological malignancies

Alpha-1-antitrypsin (AAT) or serine protease inhibitor A1 (SERPINA1) is an important serine protease inhibitor in humans. The main physiological role of AAT is to inhibit neutrophil elastase (NE) released from triggered neutrophils, with an additional lesser role in the defense against damage inflicted by other serine proteases, such as cathepsin G and proteinase 3. Although there is a reported association between AAT polymorphism and different types of cancer, this association with hematological malignancies (HM) is, as yet, unknown. We identified AAT phenotypes by isoelectric focusing (in the pH 4.2-4.9 range) in 151 serum samples from patients with HM (Hodgkins lymphomas, non-Hodgkins lymphomas and malignant monoclonal gammopathies). Healthy blood-donors constituted the control group (n = 272). The evaluated population of patients as well as the control group, were at Hardy-Weinberg equilibrium for the AAT gene (χ2 = 4.42, d.f.11, p = 0.96 and χ2 = 4.71, d.f.11, p = 0.97, respectively). There was no difference in the frequency of deficient AAT alleles (Pi Z and Pi S) between patients and control. However, we found a significantly higher frequency of PiM1M1 homozygote and PiM1 allele in HM patients than in control (for phenotype: f = 0.5166 and 0.4118 respectively, p = 0.037; for allele: f = 0.7020 and 0.6360 respectively, p = 0.05). In addition, PiM homozygotes in HM-patients were more numerous than in controls (59% and 48%, respectively, p = 0.044). PiM1 alleles and PiM1 homozygotes are both associated with hematological malignancies, although this is considered a functionally normal AAT variant

LOFAR insights into the epoch of reionization from the cross-power spectrum of 21 cm emission and galaxies

<p>Using a combination of N-body simulations, semi-analytic models and radiative transfer calculations, we have estimated the theoretical cross-power spectrum between galaxies and the 21 cm emission from neutral hydrogen during the epoch of reionization. In accordance with previous studies, we find that the 21 cm emission is initially correlated with haloes on large scales (greater than or similar to 30 Mpc), anticorrelated on intermediate (similar to 5 Mpc) and uncorrelated on small (less than or similar to 3 Mpc) scales. This picture quickly changes as reionization proceeds and the two fields become anticorrelated on large scales. The normalization of the cross-power spectrum can be used to set constraints on the average neutral fraction in the intergalactic medium and its shape can be a powerful tool to study the topology of reionization. When we apply a drop-out technique to select galaxies and add to the 21 cm signal the noise expected from the LOw Frequency ARray (LOFAR) telescope, we find that while the normalization of the cross-power spectrum remains a useful tool for probing reionization, its shape becomes too noisy to be informative. On the other hand, for an Ly alpha Emitter (LAE) survey both the normalization and the shape of the cross-power spectrum are suitable probes of reionization. A closer look at a specific planned LAE observing program using Subaru Hyper-Suprime Cam reveals concerns about the strength of the 21 cm signal at the planned redshifts. If the ionized fraction at z similar to 7 is lower than the one estimated here, then using the cross-power spectrum may be a useful exercise given that at higher redshifts and neutral fractions it is able to distinguish between two toy models with different topologies.</p>

Review of experience of family medicine in Europe and Central Asia : Executive summary

This report summarizes the findings of four case studies that review the experience of family medicine in Europe and Central Asia (ECA) Region. It is part of a study comprising five volumes that review the experience of family medicine in four countries in ECA--Armenia, Bosnia and Herzegovina, Kyrgyz Republic and Moldova. The report reviews the experience, draws lessons, and establishes an evidence base for detailed analysis. The study presents best practices for policy dialogue and future investments by the World Bank and other financial institutions. The detailed case studies compare these countries and draw common themes and issues. Comparisons are made with best-developed or existing models in the OECD and other countries in the Europe and Central Asia Region that have already undertaken family medicine reform