Destruction of invariant circles for Gevrey area-preserving twist maps

In this paper, we show that for exact area-preserving twist maps on annulus, the invariant circles with a given rotation number can be destroyed by arbitrarily small Gevrey-$\alpha$ perturbations of the integrable generating function in the $C^r$ topology with $r1$.Comment: to appear in Journal of Dynamics and Differential Equations (JDDE). arXiv admin note: text overlap with arXiv:1208.2840, arXiv:1106.613

Intrinsic Defects and Electronic Conductivity of TaON: First-Principles Insights

As a compound in between the tantalum oxide and nitride, the tantalum oxynitride TaON is expected to combine their advantages and act as an efficient visible-light-driven photocatalyst. In this letter, using hybrid functional calculations we show that TaON has different defect properties from the binary tantalum oxide and nitride: (i) instead of O or N vacancies or Ta interstitials, the $O_N$ antisite is the dominant defect, which determines its intrinsic n-type conductivity and the p-type doping difficulty; (ii) the $O_N$ antisite has a shallower donor level than O or N vacancies, with a delocalized distribution composed mainly of the Ta $5d$ orbitals, which gives rise to better electronic conductivity in the oxynitride than in the oxide and nitride. The phase stability analysis reveals that the easy oxidation of TaON is inevitable under O rich conditions, and a relatively O poor condition is required to synthesize stoichiometric TaON samples

Thermodynamic Oxidation and Reduction Potentials of Photocatalytic Semiconductors in Aqueous Solution

We introduce an approach to calculate the thermodynamic oxidation and reduction potentials of semiconductors in aqueous solution. By combining a newly-developed ab initio calculation for compound formation energy and band alignment with electrochemistry experimental data, this approach can be used to predict the stability of almost any compound semiconductor in aqueous solution. 30 photocatalytic semiconductors have been studied, and a graph (a simplified Pourbaix diagram) showing their valence/conduction band levels and oxidation/reduction potentials is produced. Based on this graph, we have studied the stabilities and trends against the oxidative and reductive photocorrosion for compound semiconductors. We found that, only metal oxides can be thermodynamically stable when used as the n-type photoanodes. All the non-oxides are unstable due to easy oxidation by the photogenerated holes, but they can be resistant to the reduction by electrons, thus stable as the p-type photocathodes

Quantum Transport Calculations Using Periodic Boundary Conditions

An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculation, thus it makes accurate quantum transport calculations for large systems possible.Comment: 9 pages, 6 figure