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

Translation-invariant quasi-free states for fermionic systems and the BCS approximation

We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but includes also direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity.Comment: 31 pages, 2 figure

Gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation. The gravitational potential U(r) which determines the lensing is directly give by the rotation curve U(r)=−v 2(r). This allows to test general relativity on the scale of galaxies where dark matter is relevan

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

Exact gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation and corrections to it.Comment: 12 pages, 1 figur

Wheat zinc finger protein TaZF interacts with both the powdery mildew AvrPm2 protein and the corresponding wheat Pm2a immune receptor

Plant defense responses to pathogens are induced after direct or indirect perception of effector proteins or their activity on host proteins. In fungal-plant interactions, relatively little is known about whether, in addition to avirulence effectors and immune receptors, other proteins contribute to specific recognition. The nucleotide-binding leucine-rich repeat (NLR) immune receptor Pm2a in wheat recognizes the fungal powdery mildew effector AvrPm2. We found that the predicted wheat zinc finger TaZF interacts with both the fungal avirulence protein AvrPm2 and the wheat NLR Pm2a. We further demonstrated that the virulent AvrPm2-H2 variant does not interact with TaZF. TaZF silencing in wheat resulted in a reduction but not a loss of Pm2a-mediated powdery mildew resistance. Interaction studies showed that the leucine-rich repeat domain of Pm2a is the mediator of the interaction with TaZF. TaZF recruits both Pm2a and AvrPm2 from the cytosol to the nucleus, resulting in nuclear localization of Pm2a, TaZF, and AvrPm2 in wheat. We propose that TaZF acts as a facilitator of Pm2a-dependent AvrPm2 effector recognition. Our findings highlight the importance of identifying effector host targets for characterization of NLR-mediated effector recognition

Effect of two different neuroprotection systems on microembolization during carotid artery stenting

ObjectivesThis study sought to compare the efficacy of two different cerebral protection systems for the prevention of embolization during carotid artery stenting (CAS) using a transcranial Doppler (TCD) monitoring with the detection of microembolic signals (MES).BackgroundDespite the introduction of cerebral protection systems, neurologic complications during CAS cannot completely be prevented. Transcranial Doppler and detection of MES may aid in assessing the efficacy of different neuroprotection systems.MethodsA total of 42 patients with internal carotid artery stenoses were treated by CAS using either a filter (E.P.I. FilterWire, Boston Scientific Corp., Santa Clara, California) (n = 21) or a proximal endovascular clamping device (MO.MA system, Invatec s.r.l., Roncadelle, Italy) (n = 21). Microembolic signal counts were compared during five phases: placement of the protection device, passage of the stenosis, stent deployment, balloon dilation, and retrieval of the protection device.ResultsThere were no significant differences in clinical or angiographic outcomes between the two groups. Compared to the filter device, the MO.MA system significantly reduced MES counts during the procedural phases of wire passage of the stenosis, stent deployment, balloon dilation, and in total (MES counts for the filter device were 25 ± 22, 73 ± 49, 70 ± 31, and 196 ± 84 during the three phases and in total, MES counts for the MO.MA system were 1.8 ± 3.2, 11 ± 19, 12 ± 21, and 57 ± 41, respectively; p < 0.0001).ConclusionsIn comparison to a filter device the MO.MA system led to significantly lower MES counts during CAS. The detection of MES by TCD may facilitate the evaluation and comparison of different neuroprotection systems

Mathematical Aspects of the BCS Theory of Superconductivity and Related Theories

The present work starts with a introduction to the BCS theory, describing superconductivity and superfluidity. The main part consist of a collection of three publications and a paper included in a conference proceedings. The introduction (Chapter 1) includes a brief historical review of the research in the field of superconductivity and superfluidity. It ends with a short summary of the technical applications of superconductivity. In Chapter 2, a derivation of the BCS functional from quantum statistics is presented. Chapter 3 explains the results of the publications mentioned above. In a first work, the validity of the negligence of the direct and exchange energy in the derivation of the BCS functional is examined. Another work addresses the connection between the BCS theory and the Gross-Pitaevskii equation.Die vorliegende Arbeit beginnt mit einer Einführung in die der Supraleitung und Superfluidität zugrunde liegenden BCS-Theorie. Der Hauptteil besteht aus einer Zusammenfassung von drei Publikationen und einem Beitrag zu einem Tagungsband. Die Einführung (Kapitel 1) beinhaltet einen kurzen historischen Rückblick auf die Forschung im Gebiet der Supraleitung und der Superfluidität, beginnend mit den Umständen, die dazu führten, dass Kamerlingh Onnes im Jahr 1911 die Supraleitung entdeckte. Abgeschlossen wird der erste Teil mit einem kurzen Überblick über die technischen Anwendungen der Supraleitung. Kapitel 2 beginnt mit einer Zusammenfassung der bekannten Konzepte aus der Quantenmechanik und der Quantenstatistik, auf die die BCS-Theorie aufbaut. Der Hauptteil dieses Kapitels ist die Herleitung des BCS-Funktionals aus der Quantenstatistik. Kapitel 3 erklärt die Ergebnisse aus den oben erwähnten Publikationen. In einer erste Arbeit wird die Gültigkeit einer Näherung bei der Herleitung des BCS-Funktionals untersucht. Es handelt sich dabei um die Vernachlässigung der so genannten direkten und Austausch- Energie im Energie- Funktional. In einer weiteren Arbeit wird der Zusammenhang mit der Gross-Pitaevskii-Theorie untersucht