Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold

In this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of superintegrable systems. Analytic formulas for the involved integrals are calculated in all the cases. All the known superintegrable systems are classified as special cases of these six general classes.Comment: LaTeX, 72 pages. Extended version of the published version in JM

Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation

By using conformal Killing-Yano tensors, and their generalisations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors, symmetry operators that map any solution to another.Comment: 35 pages, plain Te

Statistical Estimation of Quantum Tomography Protocols Quality

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a-priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography

Local estimates for entropy densities in coupled map lattices

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding. This embedding allows us to identify the local character of the equations of motion. Based on this method we present an approximate estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

Families of classical subgroup separable superintegrable systems

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.Comment: 9 page

N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane

The family of Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit a ${\cal N} = 2$ supersymmetric extension of the same kind as that introduced by Freedman and Mende for the Calogero problem and based on an ${\rm osp}(2/2, \R) \sim {\rm su}(1,1/1)$ superalgebra. The irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion $X_k$ of $H_k$. Bases for them are explicitly constructed. The ground state of each supersymmetrized Hamiltonian is shown to belong to an atypical lowest-weight state irreducible representation.Comment: 18 pages, no figur

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

Electronic structure and the minimum conductance of a graphene layer on SiO2 from density-functional methods.

The effect of the SiO$_2$ substrate on a graphene film is investigated using realistic but computationally convenient energy-optimized models of the substrate supporting a layer of graphene. The electronic bands are calculated using density-functional methods for several model substrates. This provides an estimate of the substrate-charge effects on the behaviour of the bands near $E_F$, as well as a variation of the equilibrium distance of the graphene sheet. A model of a wavy graphene layer is examined as a possible candidate for understanding the nature of the minimally conducting states in graphene.Comment: 6 pages, 5 figure

Evolution of PAHs in protoplanetary disks

Depending on whom you ask, PAHs are either the smallest dust particles or the largest gas-phase molecules in space. Whether referred to as gas or dust, these PAHs can contain up to 20% of the total cosmic carbon abundance and as such also play an important role in the carbon chemistry of protoplanetary disks. The interpretation of PAH bands is often a complex procedure involving not only gas physics to determine their ionization stage and temperature, but also radiative transfer effects that can bury these bands in a strong thermal continuum from a population of larger dust particles. PAHs are most readily seen in the spectral energy distributions (SEDs) of disks around Herbig AeBe stars where they are photoprocessed by the stellar radiation field. Resolved images taken in the PAH bands confirm their origin in the flaring surfaces of circumstellar disks: if the SED is consistent with a flat disk structure (less illuminated), there is little or no evidence of PAH emission. The very low detection rates in the disks around T Tauri stars often require an overall lower abundance of PAHs in these disk surface as compared to that in molecular clouds. In this review, I will adress three aspects of PAHs in protoplanetary disks: (1) Do PAHs form in protoplanetary disks or do they originate from the precursor molecular cloud? (2) Is the presence of PAH features in SEDs a consequence of the disk structure or do PAHs in fact shape the disk structure? (3) How can we use PAHs as tracers of processes in protoplanetary disks?Comment: 13 pages, 3 figures, invited review at the conference "PAHs and the Universe", C. Joblin and A.G.G.M Tielens Eds, EAS Publications Series vol. 46, 201