Termination of a continent-margin upwelling system at the Permian-Triassic boundary (Opal Creek, Alberta, Canada)

Models of mass extinctions caused by greenhouse warming depend on the ability of warming to affect the oxygenation of the ocean, either through slowing circulation or changes in biological productivity and the organic carbon budget. Opal Creek, Alberta, Canada is a biostratigraphically continuous Permian–Triassic Boundary (PTB) section deposited in deep water on an outer shelf setting in the vast and understudied Panthalassic Ocean, along the western margin of Pangaea. The latest-Permian extinction is here represented as the disappearance of the previously dominant benthic fauna (siliceous sponges). On the basis of nitrogen and reduced sulfur isotopes as well as productivity-sensitive trace elements, the Middle Permian at Opal Creek is interpreted as a highly productive coastal upwelling zone where vigorous denitrification and sulfate reduction occurred in a mid-water oxygen minimum. Similar conditions appear to have continued into the latest Permian until the onset of a euxinic episode represented by a discrete pyrite bed and several trace element indicators of high productivity. This euxinic pulse is followed by the extinction of benthic fauna and a shift in nitrogen and sulfur isotopes to more normal marine values, suggesting the cessation of coastal upwelling and the consequent weakening of the mid-water oxygen minimum. The Lower Triassic appears to be a dysoxic, relatively unproductive environment with a bottom water oxygen minimum. Rhenium–osmium isotope systematics show a minimum of radiogenic Os near the main extinction event, which may be due to volcanic input, and increasingly radiogenic values approaching the PTB, possibly due to increased continental erosion. The Opal Creek system demonstrates that, while the biogeochemical crisis in the latest Permian was capable of impacting the coastal upwelling modality of ocean circulation, a transient increase in productivity likely drove the system toward euxinia and, ultimately, extinction

Canonically conjugate pairs and phase operators

For quantum mechanics on a lattice the position (``particle number'') operator and the quasi-momentum (``phase'') operator obey canonical commutation relations (CCR) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in simple potentials on the lattice with the expectations, when the CCR are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions this leads to reasonable results. In the long time limit the use of the CCR can lead to a qualitativel wrong dynamics even if the initial state is in the dense set.Comment: 4 pages, 5 figures. Phys. Rev. A, in pres