arXiv subjects
Publications and source records attributed to Betti Hartmann.
We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of MNLS as well as spinning generalisations.
Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In the SU(2) case, we recover the equations studied in great detail previously, while for the SU(N) (N > 2) case we find new solutions. In the SU(3) case we see that our expressions are the gravitating analogues of the solutions obtained through the SO(3) embedding into SU(2).
We study a modified non-linear Schroedinger equation on a 2 dimensional sphere with radius R aiming to describe electron-phonon interactions on fullerenes and fullerides. These electron-phonon interactions are known to be important for the explanation of the high transition temperature of superconducting fullerides. Like in the $R\to \infty$ limit, we are able to construct non-spinning as well as spinning solutions which are characterised by the number of nodes of the wave function. These solutions are closely related to the spherical harmonic functions. For small R, we discover specific branches of the solutions. Some of the branches survive in the $R\to\infty$ limit and the solutions obtained on the plane ($R=\infty$) are recovered.
We consider a Froehlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. We study the existence of solitons in this model using both analytical and numerical methods. We find exact solutions of our equations and discuss some of their properties.
We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the "units" of a biophysical system. The mechanical degrees of freedom of these chains are coupled to the internal degrees of freedom through position dependent excitation transfer functions. We reconsider the case of the one chain model discussed by Mingaleev et al. and present new results concerning the soliton sector of this model. We also give new (preliminary) results in the two chain model in which case we have introduced an interaction potential inspired by the Morse potential.
We consider an Einstein-Yang-Mills Lagrangian in a five dimensional space-time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional Einstein-Yang-Mills-Higgs-dilaton model where the cosmological constant induces a Liouville potential in the dilaton field. We construct spherically symmetric solutions analytically in specific limits and study the generic solutions for vanishing dilaton coupling numerically. We find that in this latter case the solutions bifurcate with the branch of (Anti-) de Sitter-Reissner-Nordstrom ((A)dSRN) solutions.
We consider global monopoles in asymptotic de Sitter/ Anti- de Sitter space-time. We present the by our numerical analysis confirmed asymptotic behaviour of the metric and Goldstone field functions. We find that the appearance of horizons in this model depends strongly on the sign and value of the cosmological constant as well as on the value of the gravitational coupling. In Anti-de Sitter (AdS) space, we find that for a fixed value of the cosmological constant, global monopoles without horizons exist only up to a critical value of the gravitational coupling. Moreover, we observe (in contrast to another recent study) that the introduction of a cosmological constant can NOT render a positive mass of the global monopole.
We review three examples of quasi exactly solvable (QES) Hamitonians which possess multiple algebraisations. This includes the most prominent example, the Lame equation, as well as recently studied many-body Hamiltonians with Weierstrass interaction potential and finally, a 2x2 coupled channel Hamiltonian.
We study both global as well as local (Nielsen-Olesen) strings in de Sitter space. While these type of topological defects have been studied in the background of a de Sitter metric previously, we study here the full set of coupled equations. We find only ``closed'' solutions. The behaviour of the metric tensor of these solutions resembles that of ``supermassive'' strings with a curvature singularity at the cosmological horizon. For global strings (and the composite defect) we are able to construct solutions which are regular on the interval from the origin to the cosmological horizon if the global string core lies completely inside the horizon.
We construct globally regular as well as non-abelian black hole solutions of a higher order curvature Einstein-Yang-Mills (EYM) model in $d=5$ dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO(d)$ Yang--Mills hierarchy.
Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close relation to the algebraic properties of the elliptic functions. Accordingly, series of new algebraic eigenfunctions can be constructed.
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. An example of a Hamiltonian possessing such a hidden algebra is analyzed.
We construct spherically and axially symmetric monopoles in SU(5) Yang-Mills-Higgs theory both in flat and curved space as well as spherical and axial non-abelian, ''hairy'' black holes. We find that in analogy to the SU(2) case, the flat space monopoles are either non-interacting (in the BPS limit) or repelling. In curved space, however, gravity is able to overcome the repulsion for suitable choices of the Higgs coupling constants and the gravitational coupling. In addition, we confirm that indeed all qualitative features of (gravitating) SU(2) monopoles are found as well in the SU(5) case. For the non-abelian black holes, we compare the behaviour of the solutions in the BPS limit with that for non-vanishing Higgs self-coupling constants.
Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to the scalar dilaton nor to dilaton-gravity leads to bound multimonopole states.
We study the direct interaction between global and local monopoles. While in two previous papers, the coupling between the two sectors was only indirect through the coupling to gravity, we here introduce a new term in the potential that couples the Goldstone field and the Higgs field directly. We investigate the influence of this term in curved space and compare it to the results obtained previously.
We present a numerical study of critical phenomena (including the Lue-Weinberg phenomenon) arising for gravitating monopoles in a global monopole spacetime. The equations of this model have been recently studied by Spinelly et al. in a domain of parameter space away from the critical points.
We consider axially symmetric SU(2) Yang-Mills-Higgs (YMH) multimonopoles in Brans-Dicke theory for winding number n > 1. In analogy to the spherically symmetric n=1 solutions, we find that the axially symmetric solutions exist for higher values of the gravitational coupling than in the pure Einstein gravity case. For large values of the gravitational coupling, the solutions collapse to form a black hole which outside the horizon can be described by an extremal Reissner-Nordstrom solution. Similarly as in the pure Einstein gravity case, like-charged monopoles reside in an attractive phase in a limited domain of parameter space. However, we find that the strength of attraction is decreasing for decreasing Brans-Dicke parameter.
We consider the Abelian Higgs model as well as the SU(2) Georgi-Glashow model in which the gauge field action is replaced by a non linear Born-Infeld action. We study soliton solutions arising in these models, namely the vortex and monopole solutions, respectively. We construct formulas which provide good approximations for the mass of the Born-Infeld deformed solitons using only the data of the undeformed solutions. The results obtained indicate that in the self-dual limit, the Born-Infeld interaction leads to bound vortices, while for monopoles it gives rise to repulsion.