Classical and quantum interference in multiband optical Bloch oscillations

Classical and quantum interference of light propagating in arrays of coupled waveguides and undergoing multiband optical Bloch oscillations (BOs) with negligible Zener tunneling is theoretically investigated. In particular, it is shown that Mach-Zehnder-like interference effects spontaneously arise in multiband BOs owing to beam splitting and subsequent beam recombination occurring in one BO cycle. As a noteworthy example of quantum interference, we discuss the doubling of interference fringes in photon counting rates for a correlated photon pair undergoing two-band BOs, a phenomenon analogous to the manifestation of the de Broglie wavelength of an entangled biphoton state observed in quantum Mach-Zehnder interferometry.Comment: 11 pages, 4 figure

Reverse and dual Loomis-Whitney-type inequalities

Various results are proved giving lower bounds for the $m$th intrinsic volume $V_m(K)$, $m=1,\dots,n-1$, of a compact convex set $K$ in ${\mathbb{R}}^n$, in terms of the $m$th intrinsic volumes of its projections on the coordinate hyperplanes (or its intersections with the coordinate hyperplanes). The bounds are sharp when $m=1$ and $m=n-1$. These are reverse (or dual, respectively) forms of the Loomis-Whitney inequality and versions of it that apply to intrinsic volumes. For the intrinsic volume $V_1(K)$, which corresponds to mean width, the inequality obtained confirms a conjecture of Betke and McMullen made in 1983

The constrained E6SSM

We discuss the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), with a universal high energy soft scalar mass, soft trilinear coupling and soft gaugino mass. The spectrum includes a light gluino, a light wino-like neutralino and chargino pair and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. We also discuss scenarios with an extra light exotic colour triplet of fermions and scalars and a TeV scale Z', which lead to early exotic physics signals at the LHC.Comment: To appear in proceedings of The 2009 Europhysics Conference on High Energy Physics, 16-22 July 2009 Krakow, Poland; 4 page