A note on bounds for the cop number using tree decompositions

In this short note, we supply a new upper bound on the cop number in terms of tree decompositions. Our results in some cases extend a previously derived bound on the cop number using treewidth

Enhanced Pairing of Quantum Critical Metals Near d=3+1

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies > Lambda_{BCS}, Lambda_{CDW}.Comment: 34 pages, 4 figures, submitted to PR

Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces

We propose an interferometric method for statistically discriminating between nonorthogonal states in high dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases

Energy-resolved neutron imaging for reconstruction of strain introduced by cold working

Energy-resolved neutron transmission imaging is used to reconstruct maps of residual strains in drilled and cold-expanded holes in 5-mm and 6.4-mm-thick aluminum plates. The possibility of measuring the positions of Bragg edges in the transmission spectrum in each 55 × 55 µm2 pixel is utilized in the reconstruction of the strain distribution within the entire imaged area of the sample, all from a single measurement. Although the reconstructed strain is averaged through the sample thickness, this technique reveals strain asymmetries within the sample and thus provides information complementary to other well-established non-destructive testing methods

System configuration and executive requirements specifications for reusable shuttle and space station/base

System configuration and executive requirements specifications for reusable shuttle and space station/bas