Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

In this paper, we focus on Sobolev inequality in the context of Sharma-Mittal entropy. Using this new inequality, generalized entropic uncertainty relation in accordance with Sharma-Mittal entropy is derived and the pseudoadditivity relation has been obtained. This new entropic uncertainty relation has then been applied to physical examples such as one dimensional harmonic oscillator and Posch-Teller potential. Finally, it has been shown that for certain values of the parameters of Sharma-Mittal measure, the present results reduce to the corresponding results of Shannon, Renyi and Tsallis measures

Modification of electronic structure, magnetic structure, and topological phase of bismuthene by point defects

Akturk, Ethem/0000-0002-1615-7841; Demirci, Salih/0000-0002-1272-9603WOS: 000418655400016This paper reveals how the electronic structure, magnetic structure, and topological phase of two-dimensional (2D), single-layer structures of bismuth are modified by point defects. We first showed that a free-standing, single-layer, hexagonal structure of bismuth, named h-bismuthene, exhibits nontrivial band topology. We then investigated interactions between single foreign adatoms and bismuthene structures, which comprise stability, bonding, electronic structure, and magnetic structures. Localized states in diverse locations of the band gap and resonant states in band continua of bismuthene are induced upon the adsorption of different adatoms, which modify electronic and magnetic properties. Specific adatoms result in reconstruction around the adsorption site. Single vacancies and divacancies can form readily in bismuthene structures and remain stable at high temperatures. Through rebondings, Stone-Whales-type defects are constructed by divacancies, which transform into a large hole at high temperature. Like adsorbed adatoms, vacancies induce also localized gap states, which can be eliminated through rebondings in divacancies. We also showed that not only the optical and magnetic properties, but also the topological features of pristine h-bismuthene can be modified by point defects. The modification of the topological features depends on the energies of localized states and also on the strength of coupling between point defects.TUBA, Turkish Academy of Sciences (Turkey); Research Fund of Adnan Menderes University (Turkey) [MF-16004]The computational resources are provided by TUBITAK ULAKBIM, High Performance and Grid Computing Center (TR-Grid e-Infrastructure). S.C. acknowledge financial support from TUBA, Turkish Academy of Sciences (Turkey). This research was supported by Research Fund of Adnan Menderes University (Turkey), Project No. MF-16004. We thank Dominik Gresch for helpful discussions on operating Z2-PACK