Elastic Spin Hall effect in Mechanical Graphene

We show that spin-orbit interaction and elastic spin-Hall effect can exist in a classical mechanical system consisting of a two-dimensional honeycomb lattice of masses and springs. The band structure shows the presence of splitting at K point induced by the difference of longitudinal and transverse elastic constant, and this splitting can be regarded as an effective Dresselhaus-type spin-orbit coupling. Interestingly, as an initial displacement away from the equilibrium is applied, the time evolution simulation shows that waves of different spin polarization propagates along different directions at the Gamma and K point, which is characteristic of spin-Hall effect. Several cases for spin-Hall effect are also discussed.Comment: 15 pages, 5 figures, and 3395 word

Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

We explore two different geometric quantum discords defined respectively via the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite systems. A rigorous hierarchy relation is revealed for the two GQDs in a class of symmetric two-qubit $X$-shape states. For multiqubit pure states, it is found that both GQDs are related to the entanglement concurrence, with the hierarchy relation being saturated. Furthermore, we look into a four-partite dynamical system consisting of two cavities interacting with independent reservoirs. It is found that the GQD-2 can exhibit various sudden change behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs exhibiting different monogamous properties.Comment: 5 pages, 3 figure

The sizes of BLRs and BH masses of double-peaked broad low-ionization emission line objects

In this paper, the sizes of the BLRs and BH masses of DouBle-Peaked broad low-ionization emission line emitters (dbp emitters) are compared using different methods: virial BH masses vs BH masses from stellar velocity dispersions, the size of BLRs from the continuum luminosity vs the size of BLRs from the accretion disk model. First, the virial BH masses of dbp emitters estimated by the continumm luminosity and line width of broad H$\beta$ are about six times (a much larger value, if including another dbp emitters, of which the stellar velocity dispersions are traced by the line widths of narrow emission lines) larger than the BH masses estimated from the relation $M_{BH} - \sigma$ which is a more accurate relation to estimate BH masses. Second, the sizes of the BLRs of dbp emitters estimated by the empirical relation of $R_{BLR} - L_{5100\AA}$ are about three times (a much larger value, if including another dbp emitters, of which the stellar velocity dispersions are traced by the line widths of narrow emission lines) larger than the mean flux-weighted sizes of BLRs of dbp emitters estimated by the accretion disk model. The higher electron density of BLRs of dbp emitters would be the main reason which leads to smaller size of BLRs than the predicted value from the continuum luminosity.Comment: 7 pages, two figures and one table. Accepted by MNRA