On Some Positivity Properties of the Interquark Potential in QCD

We prove that the Fourier transform of the exponential e^{-\b V(R)} of the {\bf static} interquark potential in QCD is positive. It has been shown by Eliott Lieb some time ago that this property allows in the same limit of static spin independent potential proving certain mass relation between baryons with different quark flavors.Comment: 6 pages, latex with one postscript figur

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Carbon nanotube quantum dots on hexagonal boron nitride

We report the fabrication details and low-temperature characteristics of the first carbon nanotube (CNT) quantum dots on flakes of hexagonal boron nitride (hBN) as substrate. We demonstrate that CNTs can be grown on hBN by standard chemical vapor deposition and that standard scanning electron microscopy imaging and lithography can be employed to fabricate nanoelectronic structures when using optimized parameters. This proof of concept paves the way to more complex devices on hBN, with more predictable and reproducible characteristics and electronic stability.Comment: 4 pages, 4 figure

A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Large time dynamics and aging of a polymer chain in a random potential

We study the out-of-equilibrium large time dynamics of a gaussian polymer chain in a quenched random potential. The dynamics studied is a simple Langevin dynamics commonly referred to as the Rouse model. The equations for the two-time correlation and response function are derived within the gaussian variational approximation. In order to implement this approximation faithfully, we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical action. For a short ranged correlated random potential the equations are solved analytically in the limit of large times using certain assumptions concerning the asymptotic behavior. Two possible dynamical behaviors are identified depending upon the time separation- a stationary regime and an aging regime. In the stationary regime time translation invariance holds and so is the fluctuation dissipation theorem. The aging regime which occurs for large time separations of the two-time correlation functions is characterized by history dependence and the breakdown of certain equilibrium relations. The large time limit of the equations yields equations among the order parameters that are similar to the equations obtained in the statics using replicas. In particular the aging solution corresponds to the broken replica solution. But there is a difference in one equation that leads to important consequences for the solution. The stationary regime corresponds to the motion of the polymer inside a local minimum of the random potential, whereas in the aging regime the polymer hops between different minima. As a byproduct we also solve exactly the dynamics of a chain in a random potential with quadratic correlations.Comment: 21 pages, RevTeX

Low-temperature and high magnetic field dynamic scanning capacitance microscope

We demonstrate a dynamic scanning capacitance microscope (DSCM) that operates at large bandwidths, cryogenic temperatures and high magnetic fields. The setup is based on a non-contact atomic force microscope (AFM) with a quartz tuning fork sensor with non-optical excitation and read-out for topography, force and dissipation measurements. The metallic AFM tip forms part of an rf resonator with a transmission characteristics modulated by the sample properties and the tip-sample capacitance. The tip motion gives rise to a modulation of the capacitance at the frequency of the AFM sensor and its harmonics, which can be recorded simultaneously with the AFM data. We use an intuitive model to describe and analyze the resonator transmission and show that for most experimental conditions it is proportional to the complex tip-sample conductance, which depends on both the tip-sample capacitance and the sample resistivity. We demonstrate the performance of the DSCM on metal disks buried under a polymer layer and we discuss images recorded on a two-dimensional electron gas in the quantum Hall effect regime, i.e. at cryogenic temperatures and high magnetic fields, where we directly image the formation of compressible stripes at the physical edge of the sample

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

Real-space imaging of quantum Hall effect edge strips

We use dynamic scanning capacitance microscopy (DSCM) to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, Gts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of Gts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample interior and the stripe observed in the imaginary part. The features are periodic in the inverse magnetic field and consistent with compressible and incompressible strips forming at the sample edge. For currents larger than the critical current of the QHE break-down the stripes vanish sharply and a homogeneous signal is recovered, similar to zero magnetic field. Our experiments directly illustrate the formation and a variety of properties of the conceptually important QHE edge states at the physical edge of a 2DEG.Comment: 7 page

A 23 GHz Survey of GRB Error Boxes

The Haystack 37-meter telescope was used in a pilot project in May 1995 to observe GRB error boxes at 23~GHz. Seven BATSE error boxes and two IPN arcs were scanned by driving the beam of the telescope rapidly across their area. For the BATSE error boxes, the radio observations took place two to eighteen days after the BATSE detection, and several boxes were observed more than once. Total power data were recorded continuously as the telescope was driven at a rate of 0.2~degrees/second, yielding Nyquist sampling of the beam with an integration time of 50~milliseconds, corresponding to a theoretical rms sensitivity of 0.5~Jy. Under conditions of good weather, this sensitivity was achieved. In a preliminary analysis of the data we detect only two sources, 3C273 and 0552+398, both catalogued sources that are known to be variable at 23~GHz. Neither had a flux density that was unusally high or low at the time of our observations.Comment: 5 pages, 1 postscript figure. To appear in Proceedings of the Third Huntsville Symposium on Gamma-Ray Bursts (eds. C. Kouveliotou, M. S. Briggs, and G. J. Fishman

Cyanoacrylic- and (1-cyanovinyl)phosphonic acid anchoring ligands for application in copper-based dye-sensitized solar cells

The syntheses and characterization of four new anchoring ligands (2–5) for copper(I) bis(diimine) dyes in dye-sensitized solar cells (DSCs) are reported. Ligands 2 and 3 contain a 6,6′-dimethyl-2,2′-bipyridine copper-binding unit, while 4 and 5 contain a 2,9-dimethyl-1,10-phenanthroline unit; 2 and 4 contain cyanoacrylic acid anchoring units, and 3 and 5 possess (1-cyanovinyl)phosphonic acid anchors. The performance of DSCs sensitized by [Cu(Lanchor)(Lancillary)]+ in which Lanchor is 2–5 and Lancillary is either 6,6′-dimethyl-2,2′-bipyridine (6) or 6-trifluoromethyl-2,2′-bipyridine (7) are compared with those of DSCs containing the dyes [Cu(1)(6)]+ or [Cu(1)(7)]+ where anchoring ligand 1 is the previously reported and well-performing ((6,6′-dimethyl-[2,2′-bipyridine]-4,4′-diyl)bis(4,1-phenylene))bis(phosphonic acid). Among dyes incorporating 2–5, the best performing dye contained anchor 3 (6,6′-Me2bpy/(1-cyanovinyl)phosphonic acid combination). The better performances of dyes containing the bpy-based 2 and 3 compared to the phen-based 4 and 5 are rationalized largely in terms of the greater flexibility of the bpy vs. phen unit, allowing dyes containing 2 and 3 to adopt a conformation that leads to better surface coverage on mesoporous TiO2. Replacing 1 by 3 leads to a small gain in the short-circuit current density (JSC), but dyes with anchor 1 (in place of 3) have enhanced open-circuit voltage (VOC). The results of electrochemical impedance spectroscopy (EIS) support the trends found from the J–V measurements. The EIS data for DSCs with dyes containing anchors 3 or 1 are compared; the latter has a higher recombination resistance and chemical capacitance although the former exhibits a lower transport resistance