Critical Temperature and Energy Gap for the BCS Equation

We derive upper and lower bounds on the critical temperature $T_c$ and the energy gap $\Xi$ (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two-body interaction potential $\lambda V(x)$. At weak coupling $\lambda \ll 1$ and under appropriate assumptions on $V(x)$, our bounds show that $T_c \sim A \exp(-B/\lambda)$ and $\Xi \sim C \exp(-B/\lambda)$ for some explicit coefficients $A$, $B$ and $C$ depending on the interaction $V(x)$ and the chemical potential $\mu$. The ratio $A/C$ turns out to be a universal constant, independent of both $V(x)$ and $\mu$. Our analysis is valid for any $\mu$; for small $\mu$, or low density, our formulas reduce to well-known expressions involving the scattering length of $V(x)$.Comment: RevTeX4, 23 pages. Revised version, to appear in Phys. Rev.

The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

Onsager's Inequality, the Landau-Feynman Ansatz and Superfluidity

We revisit an inequality due to Onsager, which states that the (quantum) liquid structure factor has an upper bound of the form (const.) x |k|, for not too large modulus of the wave vector k. This inequality implies the validity of the Landau criterion in the theory of superfluidity with a definite, nonzero critical velocity. We prove an auxiliary proposition for general Bose systems, together with which we arrive at a rigorous proof of the inequality for one of the very few soluble examples of an interacting Bose fluid, Girardeau's model. The latter proof demonstrates the importance of the thermodynamic limit of the structure factor, which must be taken initially at k different from 0. It also substantiates very well the heuristic density functional arguments, which are also shown to hold exactly in the limit of large wave-lengths. We also briefly discuss which features of the proof may be present in higher dimensions, as well as some open problems related to superfluidity of trapped gases.Comment: 28 pages, 2 figure, uses revtex

Pictures of Synthetic Biology: A reflective discussion of the representation of Synthetic Biology (SB) in the German-language media and by SB experts

This article is concerned with the representation of Synthetic Biology in the media and by biotechnology experts. An analysis was made of German-language media articles published between 2004 and 2008, and interviews with biotechnology-experts at the Synthetic Biology conference SB 3.0 in Zurich 2007. The results have been reflected in terms of the definition of Synthetic Biology, applications of Synthetic Biology and the perspectives of opportunities and risks. In the media, Synthetic Biology is represented as a new scientific field of biology with an engineering-like thinking, while the scientists interviewed mostly define Synthetic Biology as contrary to nature and the natural system. Media articles present Synthetic Biology broadly with positive potential and inform the publics less about the potential risks than about the benefits of Synthetic Biology. In contrast, the experts interviewed reflect more on the risks than the opportunities of Synthetic Biology. Both used metaphors to describe Synthetic Biology and its aspects

Ad-hoc-Ausschuss beim Bundesminister fuer Forschung und Technologie: Solare Wasserstoffenergiewirtschaft Gutachten und wissenschaftliche Beitraege

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Superuidity and BEC in a Model of Interacting Bosons in a Random Potential

We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential

Triterpenoic Acids from Apple Pomace Enhance the Activity of the Endothelial Nitric Oxide Synthase (eNOS)

Pomace is an easy-accessible raw material for the isolation of fruit-derived compounds. Fruit consumption is associated with health-promoting effects, such as the prevention of cardiovascular disease. Increased vascular nitric oxide (NO) bioavailability, for example, due to an enhanced endothelial nitric oxide synthase (eNOS) activity, could be one molecular mechanism mediating this effect. To identify compounds from apple (Malus domestica Borkh.) pomace that have the potential to amplify NO bioavailability via eNOS activation, a bioassay-guided fractionation of the methanol/water (70:30) extract has been performed using the ¹⁴C-l-arginine to ¹⁴C-l-citrulline conversion assay (ACCA) in the human endothelium-derived cell line EA.hy926. Phytochemical characterization of the active fractions was performed using the spectrophotometric assessment of the total phenolic content, as well as TLC, HPLC-DAD-ELSD, and HPLC-MS analyses. Eleven triterpenoic acids, of which one is a newly discovered compound, were identified as the main constituents in the most active fraction, accompanied by only minor contents of phenolic compounds. When tested individually, none of the tested compounds exhibited significant eNOS activation. Nevertheless, cell stimulation with the reconstituted compound mixture restored eNOS activation, validating the potential of apple pomace as a source of bioactive components