Long-Range Forces of QCD

We consider the scattering of two color dipoles (e.g., heavy quarkonium states) at low energy - a QCD analog of Van der Waals interaction. Even though the couplings of the dipoles to the gluon field can be described in perturbation theory, which leads to the potential proportional to (N_c^2-1)/R^{7}, at large distances R the interaction becomes totally non-perturbative. Low-energy QCD theorems are used to evaluate the leading long-distance contribution \sim (N_f^2-1)/(11N_c - 2N_f)^2 R^{-5/2} exp(-2 \mu R) (\mu is the Goldstone boson mass), which is shown to arise from the correlated two-boson exchange. The sum rule which relates the overall strength of the interaction to the energy density of QCD vacuum is derived. Surprisingly, we find that when the size of the dipoles shrinks to zero (the heavy quark limit in the case of quarkonia), the non-perturbative part of the interaction vanishes more slowly than the perturbative part as a consequence of scale anomaly. As an application, we evaluate elastic \pi J/\psi and \pi J/\psi \to \pi \psi' cross sections.Comment: 16pages, 9 eps figures; discussion extended, 2 new references added, to appear in Phys.Rev.

Long range laser traversing system

The relative azimuth bearing between first and second spaced terrestrial points which may be obscured from each other by intervening terrain is measured by placing at one of the points a laser source for projecting a collimated beam upwardly in the vertical plane. The collimated laser beam is detected at the second point by positioning the optical axis of a receiving instrument for the laser beam in such a manner that the beam intercepts the optical axis. In response to the optical axis intercepting the beam, the beam is deflected into two different ray paths by a beam splitter having an apex located on the optical axis. The energy in the ray paths is detected by separate photoresponsive elements that drive logic networks for proving indications of: (1) the optical axis intercepting the beam; (2) the beam being on the left of the optical axis and (3) the beam being on the right side of the optical axis

Long-Range Superharmonic Josephson Current

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an \textit{odd} number of Cooper pairs cannot have a long-range propagation when there is \textit{only one} spin-active region. When temperature is much lower than the Thouless energy, the coherent transport of \textit{two} Cooper pairs becomes dominant process and the \textit{superharmonic} current-phase relation is obtained ($I\propto\sin2\phi$).Comment: 4 pages, 3 figure

Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.Comment: 18 pages, 3 figures. Replaces earlier version, submission 1204.3439, major updat