From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

Biomechanical Evaluation of the Stabilizing Function of Three Atlantoaxial Implants Under Shear Loading: A Canine Cadaveric Study

OBJECTIVE: To compare the biomechanical properties of a ventral transarticular lag screw fixation technique, a new dorsal atlantoaxial instability (AAI) clamp, and a new ventral AAI hook plate under sagittal shear loading after transection of the ligaments of the atlantoaxial joint. STUDY DESIGN: Cadaveric biomechanical study. ANIMALS: Canine cadavers (n = 10). MATERIALS AND METHODS: The occipitoatlantoaxial region of Beagles euthanatized for reasons unrelated to the study was prepared leaving only ligamentous structures and the joint capsules between the first 2 cervical vertebrae (C1 and C2). The atlanto-occipital joints were stabilized with 2 transarticular diverging positive threaded K-wires. The occipital bone and the caudal end of C2 were embedded in polymethylmethacrylate and loaded in shear to a force of 50 Newtons. The range of motion (ROM) and neutral zone (NZ) of the atlantoaxial joint were determined after 3 loading cycles with atlantoaxial ligaments intact, after ligament transection, and after fixation with each implant. The testing order of implants was randomly assigned. The implants tested last were subjected to failure testing. RESULTS: All stabilization procedures decreased the ROM and NZ of the atlantoaxial joint compared to transected ligament specimens. Only stabilization with transarticular lag screws and ventral plates produced a significant reduction of ROM compare to intact specimens. CONCLUSION: Fixation with transarticular lag screws and a ventral hook plate was biomechanically similar and provided more rigidity compared to dorsal clamp fixation. Further load cycling to failure tests and clinical studies are required before making clinical recommendations.

Load Measurement on Foundations of Rockfall Protection Systems

Rockfall protection barriers are connected to the ground using steel cables fixed with anchors and foundations for the steel posts. It is common practice to measure the forces in the cables, while to date measurements of forces in the foundations have been inadequately resolved. An overview is presented of existing methods to measure the loads on the post foundations of rockfall protection barriers. Addressing some of the inadequacies of existing approaches, a novel sensor unit is presented that is able to capture the forces acting on post foundations in all six degrees of freedom. The sensor unit consists of four triaxial force sensors placed between two steel plates. To correctly convert the measurements into the directional forces acting on the foundation a special in-situ calibration procedure is proposed that delivers a corresponding conversion matrix.