A short proof of stability of topological order under local perturbations

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed Hamiltonian $H_0$ can be written as a sum of local pairwise commuting projectors on a $D$-dimensional lattice. We consider a perturbed Hamiltonian $H=H_0+V$ involving a generic perturbation $V$ that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of $V$ is below a constant threshold value then $H$ has well-defined spectral bands originating from the low-lying eigenvalues of $H_0$. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of $H_0$ decays faster than any power of the lattice size.Comment: 15 page

Transnational environmental crime threatens sustainable development

Transnational environmental crime has become the largest financial driver of social conflict, with severe implications for peace and security. Sustainable-development frameworks need to overtly recognize and mitigate the risks posed by transnational environmental crime to environmental security

Rock snot and lake mud: exploring the history of recent blooms of didymosphenia geminata using information contained in lake sediments

Ecosystem managers have often considered the nuisance diatom species, Didymosphenia gemi¬nata (didymo) as being introduced to the natural environment through human activities; however, observations from early 20th-century surveys challenge this characterization. We use diatoms pre¬served in lake sediment cores to investigate the history of didymo blooms from Gaspésie, Quebec. Relative abundances of diatoms were examined from the dated sediments of Lac Humqui and Lac au Saumon (a lake with an inflowing river currently supporting blooms). Didymo was observed throughout the Lac au Saumon core, demonstrating that it has been present in the region well before the first reports of blooms in 2006. Lac Humqui diatom assemblages experienced a shift in composition with declines in benthic taxa (attached to substrates) and increases in planktonic (free floating) diatoms that began ~1970. Strong relationships between this diatom shift, and increases in regional air temperatures and earlier river ice-out dates were consistent with the expected effects of climate warming on aquatic systems. Our paleolimnological evidence shows that climate warming, rather than human introduction, likely plays an important role in triggering didymo blooms