Order parameter, correlation functions, and fidelity susceptibility for the BCS model in the thermodynamic limit

The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A “canonical” order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground-state energy, level occupations, and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for interlevel correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist nonperturbative corrections to the BCS predictions in the thermodynamic limit

Exceptional and regular spectra of a generalized Rabi model

We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in a magnetic field with Rashba and Dresselhaus spin-orbit couplings. Like in case of the Rabi model, the spectrum of the generalized Rabi model consists of the regular and the exceptional parts. The latter is represented by the energy levels which cross at certain parameters' values which we determine explicitly. The wave functions of these exceptional states are given by finite order polynomials in the Bargmann representation. The roots of these polynomials satisfy a Bethe ansatz equation of the Gaudin type. At the exceptional points the model is therefore quasi-exactly solvable. An analytical approximation is derived for the regular part of the spectrum in the weak- and strong-coupling limits. In particular, in the strong-coupling limit the spectrum consists of two quasi-degenerate equidistant ladders.Comment: 15 pages, 9 figure

Egyptians\u27 attitudes toward secularism

This research study examined Egyptians\u27 attitudes towards Egypt\u27s possible evolution into a secular state. Our hypotheses were that Christianity, less religiosity in Islam, more religious tolerance, higher Westernization and more liberal thinking would predict more positive attitudes towards Egypt becoming a secular state. In addition, we conducted exploratory research on the demographics including gender and socio-economic status including education, to see whether they have a relationship with secularism attitudes. The convenience sample consisted of 234 individuals who completed a series of questionnaires either at an Internet website or on paper in our local neighborhoods. Our findings confirmed our hypotheses except that religious tolerance and secularism were inversely related

Spin polarization through Floquet resonances in a driven central spin model

Adiabatically varying the driving frequency of a periodically-driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.Comment: 6+4 page

Lipohypertrophy in children and adolescents with type 1 diabetes and the associated factors

<p>Abstract</p> <p>Background</p> <p>Despite the important implications of lipohypertrophy for diabetes control, there is a dearth of information and research about the subject in children. The aim of this study was to study the prevalence of lipohypertrophy in children with type 1 diabetes, and to evaluate the associated factors.</p> <p>Findings</p> <p>119 children coming for regular follow up in the diabetes clinic were examined for the presence of lipohypertrophy by inspection and palpation. The last 4 readings of glycated hemoglobin (HbA1c) levels and other factors that may affect lipohypertrophy were documented. RESULTS: The patient's age ranged from 2 months to 21 years with a median of 10 years (inter-quartile range = 6). Lipohypertrophy occurred in 54.9% of patients, more commonly in males (62.7%) vs. females (48.4%) (P = 0.074). Grade 1 lipohypertrophy occurred in 42.5% and grade 2 in 12.4%. Lipohypertrophy was related significantly to the dose of insulin units per kg of body weight (Odds ratio [OR] = 16.4; 95% CI, 2.2 - 124.6; P = 0.007), the duration of diabetes, [OR] = 1.16; 95% CI, 1.05 - 1.32; P = 0.004)), and the body mass index (BMI) [OR] = 1.68; 95% CI, 1.25 - 2.15; P = 0.006). The mean HbA1c levels of patients with grade 1 and grade 2 lipohypertrophy did not differ from diabetics without lipohypertrophy (F = 0.178, P = 0.837)</p> <p>Conclusions</p> <p>The presence of lipohypertrophy was significantly associated with the duration of diabetes and the body mass index. Children with lipohypertrophy needed a significantly higher dose of insulin units/kg of body weight to achieve fair control compared to children without lipohypertrophy. Further studies are needed to ascertain the clinical meaning of these findings.</p

Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models

In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non negligible fraction, they also allow to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce a new inversion method based on a basis of barycentric polynomials which leads to a more stable and efficient root extraction which most importantly avoids the necessity of working with arbitrary precision. As an example we show the results of our procedure applied to the Richardson model on a square lattice.Comment: 10 pages, 3 figures, published versio

Competing interactions in semiconductor quantum dots

We introduce an integrability-based method enabling the study of semiconductor quantum dot models incorporating both the full hyperfine interaction as well as a mean-field treatment of dipole-dipole interactions in the nuclear spin bath. By performing free induction decay and spin echo simulations we characterize the combined effect of both types of interactions on the decoherence of the electron spin, for external fields ranging from low to high values. We show that for spin echo simulations the hyperfine interaction is the dominant source of decoherence at short times for low fields, and competes with the dipole-dipole interactions at longer times. On the contrary, at high fields the main source of decay is due to the dipole-dipole interactions. In the latter regime an asymmetry in the echo is observed. Furthermore, the non-decaying fraction previously observed for zero field free induction decay simulations in quantum dots with only hyperfine interactions, is destroyed for longer times by the mean-field treatment of the dipolar interactions.Comment: 10 pages, 5 figures [v2: subsection and references added

Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the coupling strength no longer appear explicitly. The problem is thus reduced to a set of quadratic algebraic equations. The required inverse transformation can then be realized using only linear operations and a standard polynomial root finding algorithm. The method is applied to Richardson's fermionic pairing model, the central spin model and generalized Dicke model.Comment: 10 pages, 3 figures, published versio

Peptidomimetic and Non- Peptidomimetic Derivatives as Possible SARS-CoV-2 Main Protease (Mpro) Inhibitors

To design novel inhibitors of the SARS-CoV-2 main protease (Mpro), we investigated the binding mode of the recently reported α-ketoamide inhibitors of this enzyme. Following, we utilized in-silico screening to identify 168 peptidomimetic and non-peptidomimetic compounds that are high probability Mpro binding candidates. The compounds were synthesized in 5 to 10 mg for initial screening for their potential inhibition of Mpro using Fluorescence Resonance Energy Transfer (FRET) assay. The study was conducted using the main protease, MBP-tagged (SARS-CoV-2) Assay Kit (BPS Bioscience, #79955-2), and the fluorescence due to enzymatic cleavage of substrate measured using BMG LABTECH CLARIOstar™, a fluorescent microplate reader, with an excited/emission wavelength of 360 nm/460 nm, respectively. The FRET assay showed 29 compounds to exhibit lower fluorescence compared to the positive control, indicating inhibitory activity, with three of the compounds exhibiting over 50% enzymatic inhibition. The assay average scores were plotted as dose inhibition curves using variable parameter nonlinear regression to calculate the IC50 values. To design more potent inhibitors, an in-silico molecular docking simulation using the SARS-CoV-2 Mpro crystal structure was conducted to investigate on a molecular level the key binding residues at the active site, as well as the possible binding modes and affinity of the lead inhibitors. Additionally, an in-silico study of the compounds\u27 molecular properties and physicochemical profiles was performed to predict their pharmacokinetic properties and assess their suitability as potential orally active drug candidates.https://scholarscompass.vcu.edu/gradposters/1139/thumbnail.jp