On the BCS gap equation for superfluid fermionic gases

We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.Comment: Contribution to the proceedings of QMath12, Berlin, September 10-13, 201

Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit

We consider the Bogolubov-Hartree-Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose-Einstein condensate of fermion pairs. The latter can be described by means of the Gross-Pitaevskii energy functional.Comment: 24 page

Equivalence of Topological and Scattering Approaches to Quantum Pumping

The Schrödinger equation with a potential periodically varying in time is used to model adiabatic quantum pumps. The systems considered may be either infinitely extended and gapped or finite and connected to gapless leads. Correspondingly, two descriptions of the transported charge, one relating to a Chern number and the other to a scattering matrix, have been available for some time. Here we generalize the first one and establish its equivalence to the secon

Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit

We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional

Age-Stratified Outcomes after Radical Prostatectomy in a Randomized Setting (LAP-01): Do Younger Patients Have More to Lose?

Objective Age is known to have an impact on outcomes after radical prostatectomy (RP). However, age differences can be investigated from a cross-sectional as well as from a longitudinal perspective. This study combines both perspectives. Materials and methods LAP-01 is the first multicenter randomized patient blinded trial comparing outcomes after robotic-assisted and laparoscopic RP. This study stratified the entire population that received nerve-sparing surgery and was potent at baseline by the following ages: ≤ 60 years, 61–65 years, and > 65 years. Potency was assessed using the IIEF-5. The EORTC QLQ-C30 was used for global health perception and the EORTC QLQ-PR25 for urinary symptoms. Continence was assessed by the number of pads used. Longitudinal change was assessed using either validated anchor-based criteria or the 1 or 0.5-standard-deviation criterion. Worsening of continence was measured by increasing numbers of pads. Results 310 patients were included into this study. Older patients had a significantly higher risk for worsening of continence at 3 and 6 months (OR 2.21, 95% CI [1.22, 4.02], p = 0.009 and OR 2.00, 95% CI [1.16, 3.46], p = 0.013, respectively); at 12 months, the odds of worsening did not differ significantly between age groups. Potency scores were better in younger patients from a cross-sectional perspective, but longitudinal change did not differ between the age groups. In contrast, global health perception was better in older patients from a cross-sectional perspective and longitudinal decreases were significantly more common among the youngest patients, at 12 months (36.9% vs. 24.4%, p = 0.038). Conclusion From a cross-sectional perspective, function scores were better in younger patients, but from a longitudinal perspective, age differences were found in continence only. In contrast, global health scores were better in older patients from a cross-sectional and longitudinal perspective

Study of atmospheric carbon monoxide and methane

The analysis of isotope ratios is widely used for the investigation of atmospheric trace gases. We measured the stable isotopes d13C and dD of atmospheric CH4 as well as d13C, d18O and the 14CO concentrations of atmospheric CO at Izana, Tenerife, from 1996 to 1999. We report the first directly measured dD seasonality for atmospheric background CH4. The large seasonal cycles in mixing and isotopic ratios of CH4 and CO enable inferences about the underlying source and sink processes. The large synoptic scale variations occurring for these trace gases at Izana made it possible to study source regions such as North America, Europe, as well as background conditions over the North Atlantic and Africa. We also measured d13C and dD on firn air samples from two Antarctic sites. From these measurements the atmospheric trends of d13C and dD of CH4 over the past fifty years have been reconstructed with the help of a firn air diffusion model. We find that parallel to increasing CH4 mixing ratios d13C increases, which is evidence for a growing contribution of the heavier anthropogenic CH4 sources. For dD we find a period of decline previous to 1975, followed by a gradual increase. This dD minimum is due to the non-equilibrium state between CH4 and its sources and sinks and has for the first time been detected for dD