Sudden braking and turning in the single/multi-stream inflation: primordial black hole formation

We study a two-field inflation model with a Gaussian bump on the potential, also known as the multi-stream inflation, which can give rise to multiply inflationary trajectories with various interesting phenomena. With a shifted Gaussian bump, the multiply streams are approximately reduced to a single stream. We find that when inflaton rounds the Gaussian potential, its speed is easily slowed down, and thus the slow-roll parameter can be largely reduced. Consequently, the original decaying modes of comoving curvature perturbations during the slow-roll phase start growing, and lead to enhanced small-scale density perturbations which can produce amounts of primordial black holes (PBHs) and associated scalar-induced gravitational waves. In addition, inflaton also undergoes sudden turnings at the encounter of the Gaussian potential, which is insignificant to the overall curvature power spectrum since their durations are quite short. Our work gives a simple example of the extension of a bump-like potential for PBH formation in a single-field inflation to a two-field case, which can relax the fine-tuning of initial conditions to some extent.Comment: 25 pages, 6 figure

Theoretical Exploration on the Magnetic Properties of Ferromagnetic Metallic Glass: An Ising Model on Random Recursive Lattice

The ferromagnetic Ising spins are modeled on a recursive lattice constructed from random-angled rhombus units with stochastic configurations, to study the magnetic properties of the bulk Fe-based metallic glass. The integration of spins on the structural glass model well represents the magnetic moments in the glassy metal. The model is exactly solved by the recursive calculation technique. The magnetization of the amorphous Ising spins, i.e. the glassy metallic magnet is investigated by our modeling and calculation on a theoretical base. The results show that the glassy metallic magnets has a lower Curie temperature, weaker magnetization, and higher entropy comparing to the regular ferromagnet in crystal form. These findings can be understood with the randomness of the amorphous system, and agrees well with others' experimental observations.Comment: 11 pages, 5 figure

Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states

We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho\otimes\varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid \textit{et al.} [Phys. Rev. Lett. \textbf{101}, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experimental unknown state.Comment: 8 pages, 5 figure