Capelli identity on multiparameter quantum linear groups

A quantum Capelli identity is given on the multiparameter quantum general linear group based on the $(p_{ij}, u)$-condition. The multiparameter quantum Pfaffian of the $(p_{ij}, u)$-quantum group is also introduced and the transformation under the congruent action is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also investigated.Comment: 22 pages. Accepted for publication in SCIENCE CHINA Mathematics. Part of the paper (eg transformation formula for multiparameter Pfaffians) was contained in arXiv:1701.07458, which will be either withdrewn or update

Probing Gravitational Dark Matter

So far all evidences of dark matter (DM) come from astrophysical and cosmological observations, due to gravitational interactions of the DM. It is possible that the true DM particle in the universe joins gravitational interactions only, but nothing else. Such a Gravitational DM (GDM) acts as a weakly interacting massive particle (WIMP), which is conceptually simple and attractive. In this work, we explore this direction by constructing the simplest scalar GDM particle $\chi_s$. It is a $Z_2$ odd singlet under the standard model (SM) gauge group, and naturally joins the unique dimension-4 interaction with Ricci curvature, $\xi_s \chi_s^2 R$, where $\xi_s$ is the dimensionless nonminimal coupling. We demonstrate that this gravitational interaction $\xi_s \chi_s^2 R$, together with Higgs-curvature nonminimal coupling term $\xi_h H^\dag H R$, induces effective couplings between $\chi_s^2$ and SM fields which can account for the observed DM thermal relic abundance. We analyze the annihilation cross sections of GDM particles and derive the viable parameter space for realizing the DM thermal relic density. We further study the direct/indirect detections and the collider signatures of such a scalar GDM. These turn out to be highly predictive and testable.Comment: 33pp, JCAP Final Version. Only minor rewordings, references adde

Optimal entanglement generation in cavity QED with dissipation

We investigate a two-level atom coupled to a cavity with a strong classical driving field in a dissipative environment and find an analytical expression of the time evolution density matrix for the system. The analytical density operator is then used to study the entanglement between the atom and cavity by considering the competing process between the atom-field interactions and the field-environment interactions. It is shown that there is an optimal interaction time for generating atom-cavity entanglement.Comment: 9 pages, 7 figure