Automatic groups and amalgams

AbstractThe objectives of this paper are twofold. The first is to provide a self-contained introduction to the theory of automatic and asynchronously automatic groups, which were invented a few years ago by J.W. Cannon, D.B.A. Epstein, D.F. Holt, M.S. Paterson and W.P. Thurston. The second objective is to prove a number of new results about the construction of new automatic and asynchronously automatic groups from old ones by means of amalgamated products

Soft-core meson-baryon interactions. I. One-hadron-exchange potentials

The Nijmegen soft-core model for the pseudoscalar-meson baryon interaction is derived, analogous to the Nijmegen NN and YN models. The interaction Hamiltonians are defined and the resulting amplitudes for one-meson-exchange and one-baryon-exchange in momentum space are given for the general mass case. The partial wave projection is carried through and explicit expressions for the momentum space partial wave meson-baryon potentials are presented.Comment: 25 pages, 2 PostScript figures, revtex4, submitted to Phys. Rev.

Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces

Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In this approach, the Maxwell equations are solved exactly on the background of static cosmological Einstein model, parameterized by special cylindrical coordinates and realized as a Riemann space of constant positive curvature. A discrete frequency spectrum for electromagnetic modes depending on the curvature radius of space and three parameters is found, and corresponding basis electromagnetic solutions have been constructed explicitly. In the case of elliptical model a part of the constructed solutions should be rejected by continuity considerations. Similar treatment is given for Maxwell equations in hyperbolic Lobachevsky model, the complete basis of electromagnetic solutions in corresponding cylindrical coordinates has been constructed as well, no quantization of frequencies of electromagnetic modes arises.Comment: 39 page

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Abelian subgroups of Garside groups

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.Comment: This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/060258

On Surface Plasmon Damping in Metallic Nanoparticles

Two possible mechanisms of surface plasmon (SP) oscillations damping in metallic nanoparticles (MNPs), not connected with electron-phonon interaction are investigated theoretically: a) the radiation damping of SP, b) resonant coupling of SP oscillations with electronic transitions in matrix. It is shown that the radiation damping rate is proportional to the number of electrons in MNP and therefore this channel of energy outflow from MNP becomes essential for relatively large particles. The investigation of second mechanism shows that the rate of SP oscillations energy leakage from MNP dos not depend on particle size and is fully determined by the optical characteristics of the matrix. It is demonstrated that for very small MNPs of 3-5 nm size, where the strong 3D size quantization effect suppresses the electron-phonon interaction, the resonance coupling in certain cases provides an effective energy outflow.Comment: 6 pages; E-mail address: [email protected]

Electron correlation vs. stabilization: A two-electron model atom in an intense laser pulse

We study numerically stabilization against ionization of a fully correlated two-electron model atom in an intense laser pulse. We concentrate on two frequency regimes: very high frequency, where the photon energy exceeds both, the ionization potential of the outer {\em and} the inner electron, and an intermediate frequency where, from a ``single active electron''-point of view the outer electron is expected to stabilize but the inner one is not. Our results reveal that correlation reduces stabilization when compared to results from single active electron-calculations. However, despite this destabilizing effect of electron correlation we still observe a decreasing ionization probability within a certain intensity domain in the high-frequency case. We compare our results from the fully correlated simulations with those from simpler, approximate models. This is useful for future work on ``real'' more-than-one electron atoms, not yet accessible to numerical {\em ab initio} methods.Comment: 8 pages, 8 figures in an extra ps-file, submitted to Phys. Rev. A, updated references and shortened introductio

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan