Large Angular Momentum States in a Graphene Film

At energy lower than 2 eV, the dispersion law of the electrons in a graphene sheet presents a linear dependence of the energy on the kinetic momentum, which is typical of photons and permits the description of the electrons as massless particles by means of the Dirac equation and the study of massless particles acted upon by forces. We analytically solve the Dirac equation of an electron in a graphene disk with radius of 10,000 atomic units pierced by a magnetic field and find the eigenenergies and eigenstates of the particles for spin up and down. The magnetic field ranges within three orders of magnitude and is found to confine the electron in the disk. States with a relatively large total angular momentum exist and can be considered in a vorticose condition; these states are seen to peak at different distances from the disk centre and can be used to store few bit of information

Bound on the multiplicity of almost complete intersections

Let $R$ be a polynomial ring over a field of characteristic zero and let $I \subset R$ be a graded ideal of height $N$ which is minimally generated by $N+1$ homogeneous polynomials. If $I=(f_1,...,f_{N+1})$ where $f_i$ has degree $d_i$ and $(f_1,...,f_N)$ has height $N$, then the multiplicity of $R/I$ is bounded above by $\prod_{i=1}^N d_i - \max\{1, \sum_{i=1}^N (d_i-1) - (d_{N+1}-1) \}$.Comment: 7 pages; to appear in Communications in Algebr

High-order density-matrix perturbation theory

We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows a simple derivation for the expression for the high order derivatives of the density matrix; (ii) in extended insulators, the treatment of uniform-electric-field perturbations and of the polarization derivatives is straightforward.Comment: 4 page

How to fill a narrow 27 KM long tube with a huge number of accelerator components?

As in large scale industrial projects, research projects, such as giant and complex particle accelerators, require intensive spatial integration studies using 3D CAD models, from the design to the installation phases. The future management of the LHC machine configuration during its operation will rely on the quality of the information, produced during these studies. This paper presents the powerful data-processing tools used in the project to ensure the spatial integration of several thousand different components in the limited space available. It describes how the documentation and information generated have been made available to a great number of users through a dedicated Web site and how installation nonconformities were handled

Lower Semi-frames, Frames, and Metric Operators

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense. The study is done also with the help of the generalized frame operator associated with a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed, if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Random Graph-Homomorphisms and Logarithmic Degree

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the infinite line Z. It is shown that if the maximal degree of G is `sub-logarithmic', then the range of such a homomorphism is super-constant. Furthermore, some examples are provided, suggesting that perhaps for graphs with super-logarithmic degree, the range of a typical homomorphism is bounded. In particular, a sharp transition is shown for a specific family of graphs C_{n,k} (which is the tensor product of the n-cycle and a complete graph, with self-loops, of size k). That is, given any function psi(n) tending to infinity, the range of a typical homomorphism of C_{n,k} is super-constant for k = 2 log(n) - psi(n), and is 3 for k = 2 log(n) + psi(n)