Multichannel charge Kondo effect and non-Fermi liquid fixed points in conventional and topological superconductor islands

We study multiterminal Majorana and conventional superconducting islands in the vicinity of the charge degeneracy point using bosonization and numerical renormalization group. Both models map to the multichannel charge Kondo problem, but for noninteracting normal leads they flow to different non-Fermi liquid fixed points at low temperatures. We compare and contrast both cases by numerically obtaining the full crossover to the low temperature regime and predict distinctive transport signatures. We attribute the differences between both types of islands to a crucial distinction of charge-$2e$ and charge-$e$ transfer in the conventional and topological case, respectively. In the conventional case, our results establish s-wave islands as a new platform to study the intermediate multichannel Kondo fixed point. In the topological setup the crossover temperature to non-Fermi liquid behavior is relatively high as it is proportional to level broadening and the transport results are not sensitive to channel coupling anisotropy, moving away from the charge degeneracy point or including a small Majorana hybridization, which makes our proposal experimentally feasible.Comment: 14 pages, 10 figure

A Model for Donation Verification

In this paper, we introduce a model for donation verification. A randomized algorithm is developed to check if the money claimed being received by the collector is $(1-\epsilon)$-approximation to the total amount money contributed by the donors. We also derive some negative results that show it is impossible to verify the donations under some circumstances

Integrated HI emission in galaxy groups and clusters

The integrated HI emission from hierarchical structures such as groups and clusters of galaxies can be detected by FAST at intermediate redshifts. Here we propose to use FAST to study the evolution of the global HI content of clusters and groups over cosmic time by measuring their integrated HI emissions. We use the Virgo cluster as an example to estimate the detection limit of FAST, and have estimated the integration time to detect a Virgo type cluster at different redshifts (from z=0.1 to z=1.5). We have also employed a semi-analytic model (SAM) to simulate the evolution of HI contents in galaxy clusters. Our simulations suggest that the HI mass of a Virgo-like cluster could be 2-3 times higher and the physical size could be more than 50\% smaller when redshift increases from z=0.3 to z=1. Thus the integration time could be reduced significantly and gas rich clusters at intermediate redshifts can be detected by FAST in less than 2 hour of integration time. For the local universe, we have also used SAM simulations to create mock catalogs of clusters to predict the outcomes from FAST all sky surveys. Comparing with the optically selected catalogs derived by cross matching the galaxy catalogs from the SDSS survey and the ALFALFA survey, we find that the HI mass distribution of the mock catalog with 20 second of integration time agrees well with that of observations. However, the mock catalog with 120 second integration time predicts much more groups and clusters that contains a population of low mass HI galaxies not detected by the ALFALFA survey. Future deep HI blind sky survey with FAST would be able to test such prediction and set constraints to the numerical simulation models. Observational strategy and sample selections for the future FAST observations of galaxy clusters at high redshifts are also discussed.Comment: 18 pages,5 figure