Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium

A newly developed hypergeometric resummation technique [H. Mera et al., Phys. Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain conserving approximations within the self-consistent nonequilibrium many-body perturbation theory. We demonstrate the usefulness of this technique by calculating the phonon-limited electronic current in a model of a single-molecule junction within the self-consistent Born approximation for the electron-phonon interacting system, where the perturbation expansion for the nonequilibrium Green function in powers of the free bosonic propagator typically consists of a series of non-crossing \sunset" diagrams. Hypergeometric resummation preserves conservation laws and it is shown to provide substantial convergence acceleration relative to more standard approaches to self-consistency. This result strongly suggests that the convergence of the self-consistent \sunset" series is limited by a branch-cut singularity, which is accurately described by Gauss hypergeometric functions. Our results showcase an alternative approach to conservation laws and self-consistency where expectation values obtained from conserving perturbation expansions are \summed" to their self-consistent value by analytic continuation functions able to mimic the convergence-limiting singularity structure.Comment: 13 pages, 6 figure

DFT study of graphene antidot lattices: The roles of geometry relaxation and spin

Graphene sheets with regular perforations, dubbed as antidot lattices, have theoretically been predicted to have a number of interesting properties. Their recent experimental realization with lattice constants below 100 nanometers stresses the urgency of a thorough understanding of their electronic properties. In this work we perform calculations of the band structure for various hydrogen-passivated hole geometries using both spin-polarized density functional theory (DFT) and DFT based tight-binding (DFTB) and address the importance of relaxation of the structures using either method or a combination thereof. We find from DFT that all structures investigated have band gaps ranging from 0.2 eV to 1.5 eV. Band gap sizes and general trends are well captured by DFTB with band gaps agreeing within about 0.2 eV even for very small structures. A combination of the two methods is found to offer a good trade-off between computational cost and accuracy. Both methods predict non-degenerate midgap states for certain antidot hole symmetries. The inclusion of spin results in a spin-splitting of these states as well as magnetic moments obeying the Lieb theorem. The local spin texture of both magnetic and non-magnetic symmetries is addressed

Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants

We demonstrate that a Meijer-G-function-based resummation approach can be successfully applied to approximate the Borel sum of divergent series, and thus to approximate the Borel-\'Ecalle summation of resurgent transseries in quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Pad\'e and Borel-Pad\'e-\'Ecalle summation methods. The resulting Meijer-G approximants are easily parameterized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-Hypergeometric method [Mera {\it et al.} Phys. Rev. Lett. {\bf 115}, 143001 (2015)]. Here we illustrate the ability of this technique in various examples from QFT, traditionally employed as benchmark models for resummation, such as: 0-dimensional $\phi^4$ theory, $\phi^4$ with degenerate minima, self-interacting QFT in 0-dimensions, and the computation of one- and two-instanton contributions in the quantum-mechanical double-well problem.Comment: 18 pages, 9 figures, PDFTe

Stark effect in low-dimension hydrogen

Studies of atomic systems in electric fields are challenging because of the diverging perturbation series. However, physically meaningful Stark shifts and ionization rates can be found by analytical continuation of the series using appropriate branch cut functions. We apply this approach to low-dimensional hydrogen atoms in order to study the effects of reduced dimensionality. We find that modifications by the electric field are strongly suppressed in reduced dimensions. This finding is explained from a Landau-type analysis of the ionization process

Determining the Optimal Number of Pistons for Offshore Digital Winch Drives

In offshore winch drive applications, determining the required number of pistons in digital displacement motors is critical for minimizing torque ripples. Digital displacement motors have shown promise for improving energy efficiency for offshore operations, such as placing equipment on the seabed or mineral drilling. However, they are known for exhibiting significant torque ripples, which can affect load-handling precision. This paper estimates the required number of pistons for realizing a digital hydraulic winch drive based on information from a commercial winch. The proposed drive employs full-stroke displacement strategies at high speeds and partial-stroke at low speeds. By simulating steady-state operations, this study correlates torque output with position oscillations. The results show that 37 pistons are required to keep position oscillations below a benchmark threshold of 10 mm throughout the drive’s operating range to avoid hindering the drive’s performance. However, such a high piston count could result in high costs due to the large, expensive valves required for partial-stroke operations. Therefore, this paper suggests an alternative drive topology for future research, which could potentially reduce the number of pistons that are operated with partial strokes

The Interaction Effect Between Previous Stroke and Hip Fracture on Postoperative Mortality:A Nationwide Cohort Study

PURPOSE: It remains uncertain how a history of stroke impacts the prognosis for patients with hip fracture. This study aimed to evaluate mortality following hip fracture surgery by comparing patients with and without a history of stroke. PATIENTS AND METHODS: All patients aged 65 years or above in Denmark receiving hip fracture surgery between 2010 and 2018. For every patient, 10 individuals from the general population without hip fracture were sampled. Comparators had a similar stroke history, age, and sex on the date of hip fracture surgery (index date). We established four cohorts: hip fracture patients with/without stroke and non-hip fracture patients with/without stroke. Outcomes were all-cause mortality at 0–30 days, 31–365 days and 1 to 5 years. Direct standardized mortality rates (MR) with 95% confidence intervals (CI) were computed. We calculated the interaction contrast to estimate excess absolute mortality among patients with both hip fracture and stroke. Through a Cox proportional hazards model, we estimated the hazard ratio (HR) and the attributable proportion as a measure of excess relative mortality attributable to interaction. RESULTS: Of the hip fracture patients, 8433 had a stroke history and 44,997 did not. Of the non-hip fracture patients, 84,330 had a stroke history and 449,962 did not. Corresponding 30-day MRs/100 person years were 148.4 (95% CI: 138.8–158.7), 124.3 (95% CI: 120.7–128.1), 14.3 (95% CI: 13.4–15.2) and 8.4 (95% CI: 8.1–8.7). The interaction contrast was 18.2 (95% CI: 7.5–28.8), and the attributable proportion was 9.0% (95% CI: 2.9–15.1). No interaction was present beyond 30 days. CONCLUSION: We observed excess short-term mortality in patients with stroke and hip fracture, but the effect disappeared at later follow-up periods. Clinicians are encouraged to pay rigorous attention to early complications among hip fracture patients with stroke, as this may serve as a way to reduce mortality