RESUMO
Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker-the Chern number expressed in terms of the Fourier transformed Chern character-is an easily applicable local marker in even dimensions, but there are no analogous expressions for odd dimensions. We provide general analytic expressions for local markers for free-fermion topological states in odd dimensions protected by local symmetries: a Chiral marker, a local Z marker which in case of translation invariance is equivalent to the chiral winding number, and a Chern-Simons marker, a local Z_{2} marker characterizing all nonchiral phases in odd dimensions. We achieve this by introducing a one-parameter family P_{Ï} of single-particle density matrices interpolating between a trivial state and the state of interest. By interpreting the parameter Ï as an additional dimension, we calculate the Chern marker for the family P_{Ï}. We demonstrate the practical use of these markers by characterizing the topological phases of two amorphous Hamiltonians in three dimensions: a topological superconductor (Z classification) and a topological insulator (Z_{2} classification).
RESUMO
BackgroundThe role of pre-school children as a source and distributor of SARS-CoV-2 infections is still unclear. Daycare facilities that care particularly for young children with limited hygiene measures may contribute to the infection dynamics during the pandemic. The aim of this study was to implement and evaluate a voluntary SARS-CoV-2 screening program in daycare facilities. MethodsThe study was conducted over a period of 4 weeks, from June 10th to July 7th 2020. The aim was to screen a representative group of 5000 individuals (children and staff at a ratio 3:1) attending daycare facilities in Dusseldorf, North Rhine-Westphalia. Tests were performed twice per week with oral rinsing water as sample material for the detection of SARS-CoV-2-RNA by molecular pool testing. ResultsA total number of 5210 participants (75.9% children and 24.1% staff) from 115 day care centers participated in the study. Of a total of 34,068 returned samples (81.7%) during the study period, only one SARS-CoV-2 infection of a child was detected in the study cohort with one likely secondary infection within the daycare facility. Of note, during the study phase, no increase of SARS- CoV-2 infections was observed in daycare center compared to the overall incidence in Dusseldorf. ConclusionsA voluntary screening program for SARS-CoV-2 infections could successfully be implemented in daycare facilities. Although the low overall incidence during the study period precludes firm conclusions, there was no evidence for increased transmission in children attending daycare facilities compared to the general population of Dusseldorf. SummarySARS-CoV-2 screening programs in daycare facilities may help to detect asymptomatic infections at an early stage and thereby support containment. Here, a large screening study was evaluated suggesting similar infection rates in daycare facilities compared to the general population.
