Comparative study of the two-phonon Raman bands of silicene and graphene

We present a computational study of the two-phonon Raman spectra of silicene and graphene within a density-functional non-orthogonal tight-binding model. Due to the presence of linear bands close to the Fermi energy in the electronic structure of both structures, the Raman scattering by phonons is resonant. We find that the Raman spectra exhibit a crossover behavior for laser excitation close to the \pi-plasmon energy. This phenomenon is explained by the disappearance of certain paths for resonant Raman scattering and the appearance of other paths beyond this energy. Besides that, the electronic joint density of states is divergent at this energy, which is reflected on the behavior of the Raman bands of the two structures in a qualitatively different way. Additionally, a number of Raman bands, originating from divergent phonon density of states at the M point and at points, inside the Brillouin zone, is also predicted. The calculated spectra for graphene are in excellent agreement with available experimental data. The obtained Raman bands can be used for structural characterization of silicene and graphene samples by Raman spectroscopy

Theoretical Raman fingerprints of α\alpha-, β\beta-, and γ\gamma-graphyne

The novel graphene allotropes $\alpha$-, $\beta$-, and $\gamma$-graphyne derive from graphene by insertion of acetylenic groups. The three graphynes are the only members of the graphyne family with the same hexagonal symmetry as graphene itself, which has as a consequence similarity in their electronic and vibrational properties. Here, we study the electronic band structure, phonon dispersion, and Raman spectra of these graphynes within an \textit{ab-initio}-based non-orthogonal tight-binding model. In particular, the predicted Raman spectra exhibit a few intense resonant Raman lines, which can be used for identification of the three graphynes by their Raman spectra for future applications in nanoelectronics

On moments of twisted LL-functions

We study the average of the product of the central values of two $L$-functions of modular forms $f$ and $g$ twisted by Dirichlet characters to a large prime modulus $q$. As our principal tools, we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of $q$, and we use the theory of Deligne and Katz to estimate certain complete exponential sums in several variables and prove new bounds on bilinear forms in Kloosterman sums with power savings when both variables are near the square root of $q$. When at least one of the forms $f$ and $g$ is non-cuspidal, we obtain an asymptotic formula for the mixed second moment of twisted $L$-functions with a power saving error term. In particular, when both are non-cuspidal, this gives a significant improvement on M.~Young's asymptotic evaluation of the fourth moment of Dirichlet $L$-functions. In the general case, the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in Kloosterman sums.Comment: final version; to appear in American Journal of Mat

Asian competition in the clock & [and] watch sector: what threats tp the Swiss industry ?

The Swiss clock & watch industry has been the indisputable leader worldwide during many decades in terms of excellence and notoriety. Many challengers such as Japanese or American companies, tried to compete at the same level without dazzling success thus far. However, three main competitions had significant impacts on the Swiss industry over the years. The first was the new production process of American companies that forced Swiss companies to shift from an artisanal production to a mass production factory system in the late 19th century. The second came the Japanese watches quartz innovation that obliged Switzerland to differentiate its products with a “Swiss Made” label for protection. The last and current competition is coming from Mainland China which is omnipresent in the low-end segment, having the largest production of watches in terms of volume, and that is willing to upgrade its production to high-end segments. Under this third competitor, the Swiss clock & watch industry is once more challenged. This paper focuses on the understanding of the competition that the Swiss industry is currently facing and identifying the levels of threat on the different steps of the value chain. Comparing the previous Japanese competition with the current Chinese competition will lead us to the identification of the imperfections of the Swiss industry in which competitors found a failure or an opportunity in order to contest some market shares. In the first part of the analysis, different threats are distinctly identified at different stages of the value chain. For example, Chinese firms bring a serious menace in the upstream stages of the value chain in raw material production, intermediary manufacturing, and assembling. Whereas there is a lack of know-how when it comes to market and communicating the brand to the end consumers. Moreover, the help of the local government is non-negligible for the future growth of Chinese watch brands. In the second part, several similarities and differences between the previous and current competitions are determined. It comes as no surprise that the low-end segment is the most vulnerable. The Swiss industry was strongly challenged in this segment by Japan as well as by China. In addition to that, Switzerland has not been protecting enough its products and is still struggling to improve it. Last but not least, technological innovation is and will always be a factor that could call into question the industry, talking about the quartz revolution in the past and the possible smartwatch revolution nowadays, which could not be measured for the moment

Matrix Product State description of the Halperin States

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the Halperin states. These latest can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wavefunction symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation length which are compared to plasma analogy arguments.Comment: 23 pages, 16 figure

Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Let B be a positive quaternion algebra, and let be an Eichler order. There is associated, in a natural way, a variety the connected components of which are indexed by the ideal classes of and are isomorphic to spheres. This variety is naturally equipped with a Laplace operator and a large family of Hecke operators. For a joint eigenfunction φ of the Hecke algebra and of the Laplace operator with eigenvalue λ, the hybrid sup norm bound for any is shown, where t=(1+λ)1/2 an

Hybrid bounds for automorphic forms on ellipsoids over number fields

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds $X$ of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are $d$ -fold products of $2$ -spheres or $3$ -spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (‘Weyl-type') saving of $\mathrm{vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon }