Belousov-Zhabotinsky droplet mixing on-chip for chemical computing applications

Without an imposed physical structure, even the most complex chemistries are limited in their ability to process information. For example, the Belousov-Zhabotinsky (BZ) oscillating reaction has been shown to have information procession potential, but only if structure is imposed e.g. using physical barriers or light-sensitive catalysts. Recently, separated BZ droplets in oil have been investigated. Another option for aqueous/oil systems is to add lipid into the oil, which self-assembles into a monolayer at the phase boundary. If the lipid-stabilised droplets are brought into contact, a bilayer is formed, separating the BZ droplets into compartments. This technique is more flexible than other methods of imparting structure, allowing for the creation of droplet arrays inspired by biological neuronal networks

Multichannel Anomaly of the Resonance Pole Parameters Resolved

Inspired by anomalies which the standard scattering matrix pole-extraction procedures have produced in a mathematically well defined coupled-channel model, we have developed a new method based solely on the assumption of partial-wave analyticity. The new method is simple and applicable not only to theoretical predictions but to the empirical partial-wave data as well. Since the standard pole-extraction procedures turn out to be the lowest-order term of the proposed method the anomalies are understood and resolved.Comment: 5 page

On the connection between mutually unbiased bases and orthogonal Latin squares

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200

The detailed mechanism of the eta production in pp scattering up to the Tlab = 4.5 GeV

Contrary to very early beliefs, the experimental cross section data for the eta production in proton-proton scattering are well described if pi and only eta meson exchange diagrams are used to calculate the Born term. The inclusion of initial and final state interactions is done in the factorization approximation by using the inverse square of the Jost function. The two body Jost functions are obtained from the S matrices in the low energy effective range approximation. The danger of double counting in the p-eta final state interaction is discussed. It is shown that higher partial waves in meson-nucleon amplitudes do not contribute significantly bellow excess energy of Q=100 MeV. Known difficulties of reducing the multi resonance model to a single resonance one are illustrated.Comment: 10 pages, 5 figures, corrected typos in relation (3), changed content (added section with differential cross sections

Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

We present a modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems. We restrict the calculation to a window moving along with a signal, which by the Lieb-Robinson bound is contained within a light cone. Signal fronts can be studied unperturbed and with high precision for much longer times than on finite systems. Entanglement inside the window is naturally small, greatly lowering computational effort. We investigate the time evolution of the transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in their symmetry broken phases after several different local quantum quenches. In both models, we observe distinct magnetization plateaus at the signal front for very large times, resembling those previously observed for the particle density of tight binding (TB) fermions. We show that the normalized difference to the magnetization of the ground state exhibits similar scaling behaviour as the density of TB fermions. In the XXZ model there is an additional internal structure of the signal front due to pairing, and wider plateaus with tight binding scaling exponents for the normalized excess magnetization. We also observe parameter dependent interaction effects between individual plateaus, resulting in a slight spatial compression of the plateau widths. In the TFI model, we additionally find that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalized excess longitudinal magnetization agrees exactly with the particle density of TB fermions.Comment: 10 pages with 5 figures. Appendix with 23 pages, 13 figures and 4 tables. Largely extended and improved versio

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber