Thermal effects on bipartite and multipartite correlations in fiber coupled cavity arrays

We investigate the thermal influence of fibers on the dynamics of bipartite and multipartite correlations in fiber coupled cavity arrays where each cavity is resonantly coupled to a two-level atom. The atom-cavity systems connected by fibers can be considered as polaritonic qubits. We first derive a master equation to describe the evolution of the atom-cavity systems. The bipartite (multipartite) correlations is measured by concurrence and discord (spin squeezing). Then, we solve the master equation numerically and study the thermal effects on the concurrence, discord, and spin squeezing of qubits. On the one hand, at zero temperature, there are steady-state bipartite and multipartite correlations. One the other hand, the thermal fluctuations of a fiber may blockade the generation of entanglement of two qubits connected directly by the fiber while the discord can be generated and stored for a long time. This thermal-induced blockade effects of bipartite correlations may be useful for quantum information processing. The bipartite correlations of a longer chain of qubits is more robust than a shorter one in the presence of thermal fluctuations

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

The Multi-shop Ski Rental Problem

We consider the {\em multi-shop ski rental} problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a \emph{consumer} has to make decisions on when and where to buy. We are interested in the {\em optimal online (competitive-ratio minimizing) mixed strategy} from the consumer's perspective. For our problem in its basic form, we obtain exciting closed-form solutions and a linear time algorithm for computing them. We further demonstrate the generality of our approach by investigating three extensions of our basic problem, namely ones that consider costs incurred by entering a shop or switching to another shop. Our solutions to these problems suggest that the consumer must assign positive probability in \emph{exactly one} shop at any buying time. Our results apply to many real-world applications, ranging from cost management in \texttt{IaaS} cloud to scheduling in distributed computing