Real-space recipes for general topological crystalline states

Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively studied in band theory and have been experimentally discovered, the classification and diagnosis of their strongly interacting counterparts are relatively less well understood. Here we present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space "building blocks" and "connectors". Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are "glue" that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the "no-open-edge condition" and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology.Comment: 17+44 pages, 7+1 figures, 0+2 tables. The content is the same as the published version, but arranged differentl

Large-field CO(1--0) observations toward the Galactic historical supernova remnants: a large cavity around Tycho's supernova remnant

The investigation of the interaction between the supernova remnants (SNRs) and interstellar gas is not only necessary to improve our knowledge of SNRs, but also to understand the nature of the progenitor systems. As a part of the Milky Way Imaging Scroll Painting CO line survey (MWISP), we study the interstellar gas surrounding the Galactic historical SNRs, using the PMO 13.7-meter telescope. In this work, we present large-field (3$^\circ$$\times$2$^\circ$) and high-sensitivity CO(1-0) molecular line observations toward Tycho's SNR. The CO observations reveal, from the outside in, large molecular clouds, stream-like structures, and an inner rim around Tycho's SNR. We derived the basic properties (column density, mass, and kinematics) of these objects based on the CO observations. The large molecular clouds individually show an arc toward the remnant center, outlining a large cavity with radii of $\sim$0.3$^\circ$$\times$0.6$^\circ$ (or 13 pc $\times$27 pc at a distance of 2.5 kpc) around the remnant. The CO line broadenings and asymmetries detected in the surrounding clouds, the observed expansion of the cavity, in concert with enhanced $^{12}$CO(2-1)/(1-0) intensity ratio detected in previous studies, suggest the interaction of the large cavity with a wind in the region. After excluding the scenario of a large bubble produced by bright massive stars, we suggest that the large cavity could be explained by accretion wind from the progenitor system of Tycho's supernova. Nevertheless, the possibility of the random distribution of a large cavity around Tycho's SNR cannot be ruled out thus far. Further observations are needed to confirm the physical association of the large cavity with Tycho's SNR.Comment: 15 pages, 9 figures, updated according to the A&A proo

Performance of multiple-input multiple-output wireless communications systems using distributed antennas

In this contribution we propose and investigate a multiple-input multiple-output (MIMO) wireless communications system, where multiple receive antennas are distributed in the area covered by a cellular cell and connected with the base-station (BS). We first analyze the total received power by the BS through the distributed antennas, when assuming that the mobile's signal is transmitted over lognormal shadowed Rayleigh fading channels. Then, the outage probability of the distributed antenna MIMO systems is investigated, when considering various antenna distribution patterns. Furthermore, space-time coding at the mobile transmitter is considered for enhancing the outage performance of the distributed antenna MIMO system. Our study and simulation results show that the outage performance of a distributed antenna MIMO system can be significantly improved, when either increasing the number of distributed receive antennas or increasing the number of mobile transmit antennas

Density Operator Description of Atomic Ordered Spatial Modes in Cavity QED

We present a quantum Monte-Carlo simulation for a pumped atom in a strong coupling cavity with dissipation, where two ordered spatial modes are formed for the atomic probability density, with the peaks distributed either only in the odd sites or only in the even ones of the lattice formed by the cavity field. A mixed state density operator model, which describes the coupling between different atomic spatial modes and the corresponding cavity field components, is proposed, which goes beyond the pure state interpretation. We develop a new decomposition treatment to derive the atomic spatial modes as well as the cavity field statistics from the simulation results for the steady state. With this treatment, we also investigate the dynamical process for the probabilities of the atomic spatial modes in the adiabatic limit. According to the analysis of the fitting error between the simulation results and the density operator model, the latter is a good description for the system