A Common Generalization of the Theorems of ErdH{o}s-Ko-Rado and Hilton-Milner

Let $m$, $n$, and $k$ be integers satisfying $0 < k leq n < 2k leq m$. A family of sets $mathcal{F}$ is called an $(m,n,k)$-intersecting family if $binom{[n]}{k} subseteq mathcal{F} subseteq binom{[m]}{k}$ and any pair of members of $mathcal{F}$ have nonempty intersection. Maximum $(m,k,k)$- and $(m,k+1,k)$-intersecting families are determined by the theorems of ErdH{o}s-Ko-Rado and Hilton-Milner, respectively. We determine the maximum families for the cases $n = 2k-1, 2k-2, 2k-3$, and $m$ sufficiently large.

The sudden birth and sudden death of thermal fidelity in a two-qubit XY model

We study the energy level crossings of the states and thermal fidelity for a two-qubit system in the presence of a transverse and inhomogeneous magnetic field. It is shown clearly the effects of the anisotropic factor of the magnetic field through the contour figures of energy level crossing in two subspaces, the isotropy subspace and anisotropy subspace. We calculate the quantum fidelity between the ground state and the state of the system at temperature $T$, and the results show the strong effect of the anisotropic factor again. In addition, by making use of the transition of Yangian generators in the tensor product space, we study the evolution of the thermal fidelity after the transition. The potential applications of Yangian algebra, as a switch to turn on or off the fidelity, are proposed.

Compensation-dependence of magnetic and electrical properties in Ga1-xMnxP

We demonstrate the control of the hole concentration in Ga1-xMnxP over a wide range by introducing compensating vacancies. The resulting evolution of the Curie temperature from 51 K to 7.5 K is remarkably similar to that observed in Ga1-xMnxAs despite the dramatically different character of hole transport between the two material systems. The highly localized nature of holes in Ga1-xMnxP is reflected in the accompanying increase in resistivity by many orders of magnitude. Based on variable-temperature resistivity data we present a general picture for hole conduction in which variable-range hopping is the dominant transport mechanism in the presence of compensation.

Entanglement of Two-Superconducting-Qubit System Coupled with a Fixed Capacitor

We study thermal entanglement in a two-superconducting-qubit system in two cases, either identical or distinct. By calculating the concurrence of system, we find that the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits, and our result is in a good agreement with the experimental data.

Controlled aggregation of magnetic ions in a semiconductor. Experimental demonstration

The control on the distribution of magnetic ions into a semiconducting host is crucial for the functionality of magnetically doped semiconductors. Through a structural analysis at the nanoscale, we give experimental evidence that the aggregation of Fe ions in (Ga,Fe)N and consequently the magnetic response of the material are affected by growth rate and co-doping with shallow impurities.