Matrix Model Calculations beyond the Spherical Limit

We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space.Comment: 44 page

Realistic interatomic potential for MD simulations

The coefficients of interatomic potential of simple form Exp-6 for neon are obtained. Repulsive part is calculated ab-initio in the Hartree-Fock approximation using the basis of atomic orbitals orthogonalized exactly on different lattice sites. Attractive part is determined empirically using single fitting parameter. The potential obtained describes well the equation of state and elastic moduli of neon crystal in wide range of interatomic distances and it is appropriate for molecular dynamic simulations of high temperature properties and phenomena in crystals and liquids.Comment: MikTex v.2.1 (AMS-TEX),11 pages, 3 EPS figure

Edge and waveguide THz surface plasmon modes in graphene micro-ribbons

Surface plasmon modes supported by graphene ribbon waveguides are studied and classified. The properties of both modes with the field concentration within the ribbon area (waveguiding modes) and on the edges (edge modes) are discussed. The waveguide and edge modes are shown to be separated from each other by a gap in wavenumbers. The even-parity hybridized edge mode results to be the fundamental electromagnetic mode of the ribbon, possessing also the lowest losses. All the plasmonic modes in the ribbons have an optimum frequency, at which the absorption losses are minimum, due to competition between the plasmon confinement and the frequency dependence of absorption in graphene.Comment: 4 pages, 4 figure

Separable Structure of Many-Body Ground-State Wave Function

We have investigated a general structure of the ground-state wave function for the Schr\"odinger equation for $N$ identical interacting particles (bosons or fermions) confined in a harmonic anisotropic trap in the limit of large $N$. It is shown that the ground-state wave function can be written in a separable form. As an example of its applications, this form is used to obtain the ground-state wave function describing collective dynamics for $N$ trapped bosons interacting via contact forces.Comment: J. Phys. B: At. Mol. Opt. Phys. 33 (2000) (accepted for publication