First principle simulations of the surface diffusion of Si and Me adatoms on the Si(111)3×3-Me surface,Me= Al,Ga, In,Pb

The intriguing but yet still unexplained experimental results of Hibino and Ogino [Phys. Rev. B 54, 5763 (1996); Surf. Sci. 328, L547 (1995)], who have observed single defect movement on an Me induced Si(111)$\sqrt{3}\times \sqrt{3}$ surface, have been revived and theoretically analysed. Using Nudged Elastic Band (NEB) optimization, the minimal energy path for an Si adatom moving on the ideal and vacancy defected surfaces has been obtained and the most probable mechanism of the vacancy mediated single defect diffusion has been established. This mechanism is shown to be responsible for the experimentally observed Si adatom movement and predicts a far easier movement of the Me adatom on vacancy defected Me induced Si(111)$\sqrt{3}\times \sqrt{3}$ surfaces.     

Noteworthy fractal features and transport properties of Cantor tartans

This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan $d_s$ is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if $D>1.5$. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if $D>\sqrt{3}$, or sub-diffusion, if $1.5<D<\sqrt{3}$.     

Enhancing entanglement of entangled coherent states by single-mode coherent superposition of photon subtraction and addition

We introduce a new entangled quantum state generated by applying single-mode coherent superposition of photon subtraction and addition (a^† cos θ + a sin θ)^m to the entangled coherent state |Ψ_±(α,0)〉$|{\Psi }_{\pm }\left(\alpha ,0\right)〉$, and then investigate the entanglement properties affected by coherent superposition operation. It is shown that this operation can be applied to enhance the entanglement of the state |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$. In addition, the effects of the coherent operation is better to improve the entanglement than that of the creation operation (a^†m) for |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$ in a small-amplitude regime and for |Ψ₋(α,0)〉$|{\Psi }_{-}\left(\alpha ,0\right)〉$ in any regime.     

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as , where k equals the number of used moduli. The time complexity is modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.