Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Entanglement reciprocation between atomic qubits and entangled coherent state

Introducing classical fields, we can transfer entanglement completely from discrete qubits into entangled coherent state. The entanglement also can be retrieved from the continuous-variable state of the cavities to the atomic qubits. Via postselection measure, atomic entangled state and entangled coherent state can be mutual transformed fully.Comment: 5 pages, 3 fighres. accepted by J Phys

Neutron Density Distributions of Neutron-Rich Nuclei Studied with the Isobaric Yield Ratio Difference

The isobaric yield ratio difference (IBD) between two reactions of similar experimental setups is found to be sensitive to nuclear density differences between projectiles. In this article, the IBD probe is used to study the density variation in neutron-rich $^{48}$Ca. By adjusting diffuseness in the neutron density distribution, three different neutron density distributions of $^{48}$Ca are obtained. The yields of fragments in the 80$A$ MeV $^{40, 48}$Ca + $^{12}$C reactions are calculated by using a modified statistical abrasion-ablation model. It is found that the IBD results obtained from the prefragments are sensitive to the density distribution of the projectile, while the IBD results from the final fragments are less sensitive to the density distribution of the projectile.Comment: 3 figure