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.

Ernst Simons Bialik-Monographie [Rezension]

Emanuel Bin-Gorion

Granulometry of two sediment cores from Maxwell Bay, South Shetland Islands, West Antarctica

The climate evolution of the South Shetland Islands during the last c. 2000 years is inferred from the multiproxy analyses of a long (928 cm) sediment core retrieved from Maxwell Bay off King George Island. The vertical sediment flux at the core location is controlled by summer melting processes that cause sediment-laden meltwater plumes to form. These leave a characteristic signature in the sediments of NE Maxwell Bay. We use this signature to distinguish summer and winter-dominated periods. During the Medieval Warm Period, sediments are generally finer which indicates summer-type conditions. In contrast, during the Little Ice Age (LIA) sediments are generally coarser and are indicative of winter-dominated conditions. Comparison with Northern and Southern Hemisphere, Antarctic, and global temperature reconstructions reveals that the mean grain-size curve from Maxwell Bay closely resembles the curve of the global temperature reconstruction. We show that the medieval warming occurred earlier in the Southern than in the Northern Hemisphere, which might indicate that the warming was driven by processes occurring in the south. The beginning of the LIA appears to be almost synchronous in both hemispheres. The warming after the LIA closely resembles the Northern Hemisphere record which might indicate this phase of cooling was driven by processes occurring in the north. Although the recent rapid regional warming is clearly visible, the Maxwell Bay record does not show the dominance of summer-type sediments until the 1970s. Continued warming in this area will likely affect the marine ecosystem through meltwater induced turbidity of the surface waters as well as an extension of the vegetation period due to the predicted decrease of sea ice in this area.

John Maxwell Coetzee. Costas extrañas; ensayos, 1986-1999. Trad. de Pedro Tena. Buenos Aires, Debate, 2005

Fil: Colombi, Pablo Darío.