Recent Progress of Multiferroic Perovskite Manganites

Many multiferroic materials, with various chemical compositions and crystal structures, have been discovered in the past years. Among these multiferroics, some perovskite manganites with ferroelectricity driven by magnetic orders are of particular interest. In these multiferroic perovskite manganites, not only their multiferroic properties are quite prominent, but also the involved physical mechanisms are very plenty and representative. In this Brief Review, we will introduce some recent theoretical and experimental progress on multiferroic manganites.Comment: 24 pages, 17 figures. A brief revie

The spectral radius of minor free graphs

In this paper, we present a sharp upper bound for the spectral radius of an $n$-vertex graph without $F$-minor for sufficient large $n$, where $F$ is obtained from the complete graph $K_r$ by deleting disjointed paths. Furthermore, the graphs which achieved the sharp bound are characterized. This result may be regarded to be an extended revision of the number of edges in an $n$-vertex graph without $F$-minor.Comment: 18 pages, 1 figur

Quantum-memory-assisted entropic uncertainty relations

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.Comment: Review, 20 pages, published in Ann. Phys. (Berlin