arXiv subjects

F. K. Diakonos

Publications and source records attributed to F. K. Diakonos.

101 records · Page 6Linked to original sources

arXiv1999

The helium atom in a strong magnetic field

We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonia n to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with res pect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue problem is solved numerically, providing in the present paper results for vanish ing magnetic quantum number M=0 and even or odd z-parity, each for both singlet and triplet spin symmetry. Total electronic energies of the ground state and the first few excitations in each su bspace as well as their one-electron ionization energies are presented as a function of the magnetic fie ld, and their behaviour is discussed. Energy values for electromagnetic transitions within the M=0 sub space are shown, and a complete table of wavelengths at all the detected stationary points with respect to their field dependence is given, thereby providing a basis for a comparison with observed ab sorption spectra of magnetic white dwarfs.

physics.atom-ph↗

arXiv1998

Fractals at T=Tc due to instanton-like configurations

We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point ($T=T_c$) we show that instanton-like configurations, corresponding to the minima of the effective action functional, build up clusters with fractal geometry characterizing locally the critical fluctuations. The connection between the corresponding (local) fractal dimension and the critical exponents is derived. Possible extension of the local geometry of the system to a global picture is also discussed.

hep-ph↗

arXiv1998

General theory and examples of the inverse Frobenius-Perron problem

The general solution of the inverse Frobenius-Perron problem considering the construction of a fully chaotic dynamical system with given invariant density is obtained within the class of one-dimensional unimodal maps. Some interesting connections between this solution and the approach via conjugation transformations are eluminated. The developed method is applied to obtain a wide class of maps having as invariant density the two-parametric beta-probability density function. Varying the parameters of the density a rich variety of dynamics is observed. Observables like autocorrelation functions, power spectra and Lyapunov exponents are calculated for representatives of this family of maps and some theoretical predictions concerning the decay of correlations are tested.

chao-dyn↗

arXiv1997

Analytical solutions to one-dimensional dissipative and discrete chaotic dynamics

Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time correlation function. We illustrate our solutions by means of a few examples for which conventional numerical trajectory calculations fail to predict the correct behaviour.

chao-dyn↗

arXiv1997

The hydrogen molecule in magnetic fields: The ground states of the Sigma manifold of the parallel configuration

The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the Sigma manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad regime of field strengths from B = 0 up to B = 100a.u. A variety of interesting phenomena can be observed. For the ^1Sigma_g state we found a monotonous decrease of the equilibrium distance and a simultaneously increase of the dissociation energy with growing magnetic field strength. The ^3Σ_g state is shown to develop an additional minimum which has no counterpart in field-free space. The ^1Σ_u state shows a monotonous increase in the dissociation energy with first increasing and than decreasing internuclear distance of the minimum. For this state the dissociation channel is H_2 to H^- + H^+ for magnetic-field strengths B greater than 20a.u. due to the existence of strongly bound H^- states in strong magnetic fields. The repulsive ^3Σ_u state possesses a very shallow van der Waals minimum for magnetic-field strengths smaller than 1.0a.u. within the numerical accuracy of our calculations. The ^1Σ_g and ^3Σ_u states cross as a function of B and the ^3Σ_u state, which is an unbound state, becomes the ground state of the hydrogen molecule in magnetic fields B greater than 0.2a.u. This is of particular interest for the existence of molecular hydrogen in the vicinity of white dwarfs. In superstrong fields the ground state is again a strongly bound state, the ^3Π_u state.

physics.chem-ph↗

arXiv1997

A general approach to the localization of unstable periodic orbits in chaotic dynamical systems

We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy. Based on a universal set of linear transformations the originally unstable periodic orbits are transformed into stable ones and can consequently be detected and analyzed easily. This method is applicable to dynamical systems of any dimension and requires no preknowledges with respect to the solutions of the original chaotic system. As an example of application of our method we investigate the Ikeda attractor in some detail.

chao-dyn↗

arXiv1997

A turning point analysis of the ergodic dynamics of iterative maps

The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a turning point which represents a local minimum or maximum of the trajectory. Following we investigate the highly organized and structured distribution of turning points. The turning point dynamics is discussed and the corresponding turning point map which possesses an appealing asymptotic scaling property is investigated. Strong correlations are shown to exist for the turning point trajectories which contain the information of the fixed points as well as the stability coefficients of the dynamical system. For the more specialized case of symmetric maps which possess a symmetric density we derive universal statistical properties of the corresponding turning point dynamics. Using the turning point concept we finally develop a method for the analysis of (one dimensional) time series.

chao-dyn↗

arXiv1995

Fractal Behaviour in the O(3) Model

We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.

hep-lat↗

arXiv1995

Nonperturbative treatment of the N-body system with dynamical mesons

The variational approach, used by Feynman in the study of the polaron problem, is generalized to treat a system of N non-relativistic particles interacting with scalar and vector mesons. After integrating out the meson fields in the path integral formulation we perform a variational calculation for the effective N-body two-time action to obtain the energy and the mass of the system. The interplay of self energies and exchange terms in attaining binding and saturation is examined. We estimate the size of the particles in the medium and give the mean number of mesons as a function of N.

nucl-th↗

arXiv1993

Criticality, Fractality and Intermittency in Strong Interactions

Assuming a second-order phase transition for the hadronization process, we attempt to associate intermittency patterns in high-energy hadronic collisions to fractal structures in configuration space and corresponding intermittency indices to the isothermal critical exponent at the transition temperature. In this approach, the most general multidimensional intermittency pattern, associated to a second-order phase transition of the strongly interacting system, is determined, and its relevance to present and future experiments is discussed.

hep-ph↗

arXiv1993

W + gamma + jet production as a test of the electromagnetic couplings of W at LHC and SSC

The reaction $pp \to W \ +\ γ +\ jet \ +\ X$ is considered at centre-of-mass energies $\sqrt{s} = 16$ and $40\;\tev$, including anomalous three-gauge-boson couplings $κ$ and $λ$. The possibility of obtaining limits on these quantities by comparison with the standard model is investigated. The radiation zero properties of the subprocess matrix elements are studied. CERN-TH.6753/92, DTP/92/92.

hep-ph↗