By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with ...By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction U moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes （potential parameter λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same λ that the interaction U always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.展开更多
In this article, the non-self dual extended Harper's model with a Liouville frequency is considered. It is shown that the corresponding integrated density of states is 1/2-Holder continuous. As an application, the...In this article, the non-self dual extended Harper's model with a Liouville frequency is considered. It is shown that the corresponding integrated density of states is 1/2-Holder continuous. As an application, the homogeneity of the spectrum is proven.展开更多
This study determined concentrations of iodine, consistent with WHO iodine fortification standards, in commercial edible salts mostly consumed in Harper. The following hypothesis was put forward in the research study;...This study determined concentrations of iodine, consistent with WHO iodine fortification standards, in commercial edible salts mostly consumed in Harper. The following hypothesis was put forward in the research study;H<sub>1</sub>: the iodine content of the two brands of iodized salts is different from the WHO iodine fortification levels;H<sub>0</sub>: the iodine content of the two brands of iodized salts is not different from the WHO iodine fortification levels. The hypothesis was tested in MS Excel 2010 and 2016 via the T-Test function giving p-value = 0.1476 and p-value = 0.0395 indicative of no significant difference in the iodine concentration of the salts compared with the lower limit of WHO standard 20 mg·Kg<sup>-1</sup> and huge contrast in the iodine concentration of the salts compared with the upper limit of WHO standard 40 mg·Kg<sup>-1</sup> respectively. The UV spectrophotometric method was used to analyze and measure the iodine concentration in the twelve (12) samples of two different brands bought from grocery stores in Harper city. Results indicated that all samples of the two (2) brands of iodized salts contained iodine of no significant difference relative to the lower limit of WHO standard but far below the upper limit of the WHO standard. The study therefore recommends monitoring of commercial iodized salts by appropriate authorities in Harper to ascertain the WHO iodization fortification standards before reaching consumers.展开更多
DURING the Han Dynasty, almost 2,000 years ago, the great King of Yutian asked the Chinese Emperor for silkworms. As silk was such a valuable commodity for trade with the Western world, the Emperor did not agree, and ...DURING the Han Dynasty, almost 2,000 years ago, the great King of Yutian asked the Chinese Emperor for silkworms. As silk was such a valuable commodity for trade with the Western world, the Emperor did not agree, and actually enlisted special展开更多
基金Project supported by the National Nature Science Foundation of China (Grant Nos 90203009,10175035 and 10674072)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20060319007)+1 种基金the Excellent Young Teacher Program of the Ministry of Education of Chinathe Nature Science Foundation of Jiangsu Province of China (GrantNo 06KJD140135)
文摘By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction U moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes （potential parameter λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same λ that the interaction U always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.
基金supported by China Postdoctoral Science Foundation(2018M641050)
文摘In this article, the non-self dual extended Harper's model with a Liouville frequency is considered. It is shown that the corresponding integrated density of states is 1/2-Holder continuous. As an application, the homogeneity of the spectrum is proven.
文摘This study determined concentrations of iodine, consistent with WHO iodine fortification standards, in commercial edible salts mostly consumed in Harper. The following hypothesis was put forward in the research study;H<sub>1</sub>: the iodine content of the two brands of iodized salts is different from the WHO iodine fortification levels;H<sub>0</sub>: the iodine content of the two brands of iodized salts is not different from the WHO iodine fortification levels. The hypothesis was tested in MS Excel 2010 and 2016 via the T-Test function giving p-value = 0.1476 and p-value = 0.0395 indicative of no significant difference in the iodine concentration of the salts compared with the lower limit of WHO standard 20 mg·Kg<sup>-1</sup> and huge contrast in the iodine concentration of the salts compared with the upper limit of WHO standard 40 mg·Kg<sup>-1</sup> respectively. The UV spectrophotometric method was used to analyze and measure the iodine concentration in the twelve (12) samples of two different brands bought from grocery stores in Harper city. Results indicated that all samples of the two (2) brands of iodized salts contained iodine of no significant difference relative to the lower limit of WHO standard but far below the upper limit of the WHO standard. The study therefore recommends monitoring of commercial iodized salts by appropriate authorities in Harper to ascertain the WHO iodization fortification standards before reaching consumers.
文摘DURING the Han Dynasty, almost 2,000 years ago, the great King of Yutian asked the Chinese Emperor for silkworms. As silk was such a valuable commodity for trade with the Western world, the Emperor did not agree, and actually enlisted special
