Structure of the σ\sigma-meson and diamagnetism of the nucleon

The structure of the $\sigma$ meson and the diamagnetism of the nucleon are shown to be topics which are closely related to each other. Arguments are found that the $\sigma$ meson couples to two photons via its non-strange $q\bar{q}$ structure component. This ansatz leads to a quantitative explanation of the $t$-channel component of the difference of electromagnetic polarizabilities, (\alpha-\beta)^t$, containing the diamagnetism of the nucleon. The prediction is$(\alpha-\beta)^t_{p,n}=(5\alpha_e g_{\pi MM})/(6\pi^2 m^2_\sigma f_\pi)=15.3$in units of$10^{-4}{\rm fm}^3$to be compared with the experimental value$(\alpha-\beta)^t_p=15.1\pm 1.3$for the proton and$(\alpha-\beta)^t_n=14.8\pm 2.7$for the neutron. The equivalent approach to exploit the$\pi\pi$structure component of the$\sigma$meson via the BEFT sum rule leads to$(\alpha-\beta)^t_{p,n}=14\pm 2$, what also is in agreement with the experimental results.Comment: Contribution made by Martin Schumacher to the International Workshop on the Physics of Excited Baryons, 12 - 15 Oct. 2005, Tallahasse, Florida US

Quantum privacy and quantum coherence

We derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography.Comment: 6 pages RevTex; two short comments added 7 October 199

Relativistic corrections to the electromagnetic polarizabilities of compound systems

The low-energy amplitude of Compton scattering on the bound state of two charged particles of arbitrary masses, charges and spins is calculated. A case in which the bound state exists due to electromagnetic interaction (QED) is considered. The term, proportional to $\omega^2$, is obtained taking into account the first relativistic correction. It is shown that the complete result for this correction differs essentially from the commonly used term $\Delta\alpha$, proportional to the r.m.s. charge radius of the system. We propose that the same situation can take place in the more complicated case of hadrons.Comment: 19 pages, LaTe

Surface roughness and interfacial slip boundary condition for quartz crystal microbalances

The response of a quartz crystal microbalance (QCM) is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first order effect of slip is only present in the frequency response. Importantly, in this approximation the frequency response satisfies an additivity relation with a net response equal to a Kanazawa liquid term plus an additional Sauerbrey "rigid" liquid mass. For the slip length to result in an enhanced frequency decrease compared to a no-slip boundary condition, it is shown that the slip length must be negative so that the slip plane is located on the liquid side of the interface. It is argued that the physical application of such a negative slip length could be to the liquid phase response of a QCM with a completely wetted rough surface. Effectively, the model recovers the starting assumption of additivity used in the trapped mass model for the liquid phase response of a QCM having a rough surface. When applying the slip boundary condition to the rough surface problem, slip is not at a molecular level, but is a formal hydrodynamic boundary condition which relates the response of the QCM to that expected from a QCM with a smooth surface. Finally, possible interpretations of the results in terms of acoustic reflectivity are developed and the potential limitations of the additivity result should vapour trapping occur are discussed

Poly(arylene Ether Sulfone)s with Ammonium Groups Located on Pendent Phenyl Sulfonyl Moieties for Anionic Exchange Membranes

A series of poly(aryl ether sulfone)s with varying percentages of ammonium groups, located on truly pendent positions, was prepared and characterized. The initial polymers were prepared by nucleophilic aromatic substitution (NAS) polycondensation reactions of varying ratios of 3,5-difluoro-4\u27-methyldiphenylsulfone and 4,4\u27-difluorodiphenylsulfone, with bisphenol-A as the nucleophilic reaction partner. The tolyl groups in the resulting polymers were subjected to radical bromination with N-bromosuccinimide, followed by amination with three different amines: trimethylamine, dimethylhexadecylamine, and N-methylimidazole. The polymers were characterized by 1H and 13C NMR spectroscopy, thermogravimetric analysis, and differential scanning calorimetry. With the exception of the 100% functionalized polymers, tough films were observed after casting from solutions in dimethylformamide. The films were evaluated for potential use as alkaline exchange membranes (AEM) by determining their water uptake and ion exchange capacity values

Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity

Let $J \in C(\mathbb{R})$, $J\ge 0$, \int_{\tiny\mathbb{R}} J = 1 and consider the nonlocal diffusion operator $\mathcal{M}[u] = J \star u - u$. We study the equation $\mathcal{M} u + f(x,u) = 0$, $u \ge 0$, in $\mathbb{R}$, where $f$ is a KPP-type nonlinearity, periodic in $x$. We show that the principal eigenvalue of the linearization around zero is well defined and that a nontrivial solution of the nonlinear problem exists if and only if this eigenvalue is negative. We prove that if, additionally, $J$ is symmetric, then the nontrivial solution is unique