Table of contents

Using the technique of asymptotic expansions for heat kernel type operators, it is shown how good qualitative measures of geometric/topological structure and complexity are naturally induced by the dynamics of a system.

A comparison is made between the Heisenberg equations of the quantum electron and the dynamical equations of the classical spinning and radiating electron.

On the basis of the method of generalized coherent states (GCS) of the SU(2) group we formulate the reduction procedure of the quantum lattice Heisenberg XYZ model to the continuum Landau-Lifshitz model. The choice of the GCS representation is determined (i) by their proximity to the corresponding classical states and (ii) by similarity of the geometric structure of the homogeneous spaces on which the SU(2) GCS and the vector of the magnetic moment of the corresponding Landau-Lifshitz model are defined. The present reduction procedure is allowed only in the case of weak anisotropy. Accounting for a weak one-ion anisotropy leads to the Landau-Lifshitz model with a renormalized anisotropy tensor. The contribution of such an anisotropy vanishes for the s = 1/2 case.

Models for "gaseous" spheres (i.e., the density ϱ vanishes at the outer boundary of the nonstatic sphere together with the pressure p) are investigated. A simple criterion which is sufficient for the pressure gradient to be negative is given. Several exact models for physically acceptable "gaseous" spheres are constructed.

Recently introduced conservation laws for volume expansion rates are used as a tool to investigate changes in the geometric and dynamical structure of strange attractors occurring, e.g., upon variation of a parameter. The appearance of edges in the Renyi dimension function D_q and metric entropy K_q is an indication of such transitions. A way to classify them by introducing two new indices j_q and j_q⁺ is discussed. Moreover, these critical points can be analyzed in terms of phase transitions, in the framework of the thermodynamic formalism for dynamical systems.

This paper is concerned with processes of self-organization which can take place both in the inanimate and animate world. In particular we study the question what physics can contribute to the understanding of these processes. Its traditional disciplines, namely thermodynamics and statistical mechanics which are concerned with the behavior of multi-component systems, require new ideas and concepts in order to cope with self-organizing systems. These concepts were elaborated in the new field of synergetics from the microscopic point of view. The present paper is mainly concerned with a macroscopic approach.

In Section 1 we briefly remind the reader of various concepts of entropy and information and we give brief definitions of structure and self-organization. At present there seems to be no satisfactory definition of complexity available. Section 2 provides two examples of self-organizing systems, namely the laser and slime mold. In Section 3 we briefly remind the reader of the microscopic approach used in synergetics. As a new result it is shown that the information of the total system close to instability points is essentially contained in the information in the order parameters for which the specific example of a single order parameter is then treated explicitly. Finally we show how adequate constraints can be found to formulate the maximum information entropy principle for self-organizing systems. Our approach allows one to deduce the order parameters and dominant spatial patterns of a system which undergoes a non-equilibrium phase transition by means of an algorithm rather than by guessing.

An analytically solvable model is used to study the barrier penetrability pattern for subbarrier fission and fusion of nuclei in the case when the pairing gap parameter Δ is treated as an additional dynamical variable whose behaviour in tunnelling is governed by the least action principle. It is found that, as compared to the standard (BCS) approach, the dynamical treatment of pairing correlations essentially modifies (considerably weakens) the dependence of the fission barrier penetrability on the intensity of pairing correlations in the initial state (Δ₀), on the barrier height, and on the energy of the initial state. On this basis, a more adequate explanation is proposed for typical order-of-magnitude values of the empirical hindrance factors associated with ground-state spontaneous fission of odd nuclei. It is also shown that a large enhancement of superfluidity in tunnelling - the inherent effect of the dynamical treatment of pairing correlations - strongly facilitates deeply subbarrier fusion of complex nuclei and results in increasing fusion cross sections by several orders of magnitude. Finally, an analysis is given for the probability of spontaneous fission decay from K-isomeric quasi-particle (q-p) states in even-even heavy nuclei. It is found that the relative change of the partial spontaneous fission half-life in going from the ground-state to a high-spin q-p isomeric state, T_sf*/T_sf, is strongly dependent on whether or not there takes place the dynamically induced enhancement of superfluidity in the tunnelling process. Measurements of T_sf*/T_sf provide thus a unique possibility of verifying theoretical predictions about the strong, inversesquare Δ dependence of the effective inertia associated with large-scale cold rearrangements of nuclei in fission and fusion.

The decompression stage of a relativistic heavy ion reaction is described within a Monte-Carlo-Time-Dependent-Hartree-Fock model suitable for quantum dynamical calculations. Temperature and compression effects lead to instabilities and nuclear disassembly. Low excited stable and high excited unstable fragments are generated. The model is based on a Monte-Carlo simulation. A statistical set of self-consistent Hartree calculations are performed. Systems with different particle number are studied. At critical break-up temperatures fragments are found in U-shaped spectra. Above the break-up threshold fast and small fragments are counted. Below the break-up threshold the excited matter shows vibrational modes. Density distributions are studied and evidence for volume dependent multifragmentation processes is obtained for most break-up temperatures. Mass spectra, multiplicities and momentum distributions are presented.

The optical spectrum of NiD has been reinvestigated. In the yellow-red wavelength region three sub-systems, A²Δ_5/2-X²Δ_5/2. ²Φ_7/2-X²Δ_5/2, and ²Δ_3/2-X²Δ_3/2, have been found. Four bands of these sub-systems were rotationally analysed. The analysis was also extended to the (3, 0) band of the earlier known B²Δ_5/2-X²Δ_5/2 sub-system. In addition, the (0, 0) band of the ²Δ_3/2-X²Δ_5/2 transition was analysed.

The results for NiD have been compared with those earlier obtained for NiH. Two term value calculations have been made, one for NiH and one for NiD. Since intercombination bands are known, all the term values could be calculated relative to each other. The term values are presented in a diagram.

The spectrum of Al I and Al II produced by a hollow-cathode discharge has been observed by the Fourier transform spectroscopy technique between 1800 and 9000 cm^-1. These observations have allowed an extension of the term systems of Al I and Al II. The results are also used for revising the identification of Al I lines in the solar photospheric spectrum.

An experimental and theoretical study has been made of the 3s-3p and 3p-3d transitions in Ni XIX. The method of beam-foil spectroscopy, using 30-64 MeV Ni ions from a tandem accelerator, has been combined with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) program.

Using the method of beam-foil spectroscopy we have measured the decay times of several n = 3 terms in Mg-like Ni XVII. By applying an effective method for correction of cascades (ANDC) we obtained reliable lifetimes for the terms 3s3p¹P, 3s3p³P, 3p²¹D and 3p²³P. The experimental data are in good agreement with recent theoretically predicted values.

The neon-like and sodium-like ions of medium Z elements, chromium and nickel are identified as abundant or strongly radiating species in the transport dominated region of the JET plasma. Also in plasma produced by laser ablation of multilayer targets stimulated emission has been identified from neon-like selenium. For both observations accurate theoretical electronic recombination rate coefficients contribute to spectral interpretation, to unambiguous separation of diffusive and atomic processes in impurity transport and to derivation of metal concentrations from VUV lines.

A new calculation is presented of recombination of fluorine-like, neon-like and sodium-like ions of chromium, iron, nickel and selenium. Radiative recombination and dielectronic recombination rates to angularly resolved energy levels of both low and high principal quantum number are determined using combination of multiconfiguration perturbation theory and Correspondence Principle techniques. The modifying effects of collisional redistribution in finite density plasma are evaluated and effective net recombination coefficients and effective recombination coefficients to excited levels leading to radiative emission obtained.

The theoretical radial distribution of nickel ions across the JET torus is obtained by combining the recombination results with a transport model.

Applying the techniques of resonant and off-resonant Doppler-free 2-photon laser spectroscopy, we have studied a number of transitions in the group IIIa elements Al, Ga and Tl with the thermionic diode. In order to check the accuracy of the experimental set-up and the spectroscopic method applied, the hfs of the intermediate state 3d²D_3/2,5/2 of ²⁷Al has been determined from the spectra of the 3p²P_J-3d²D_J-nf²F_J or -np²P_J transitions and compared with more precise values by other authors from atomic beam magnetic resonance measurements. From 4p²P_1/2-nf²F_J and 4p²P_J-4d²D_J-nf²F_J or -np²P_J transitions in ^69,71Ga, we have deduced the hfs and the residual isotope shifts (RLIS) of the intermediate states (4d²D_3/2,5/2) and the RLIS of the 4p²P_1/2,3/2 ground states. In Tl, we have measured the 6p²P_1/2-nf²F_5/2 (n = 6-9) and -10p²P_3/2 lines. From the experimental results we have determined the residual level isotope shift (^205,203Tl) of the 6p²P_1/2 state and the hfs of the 10p²P_3/2 level.

Carbon-contaminated mirrors and gratings have been cleaned by a d.c. glow discharge in oxygen. The reflectance of mirrors and the efficiency of gratings were measured in situ before and after cleaning in the photon-energy range 4 ∼ 40 eV or 100 ∼ 1000 eV using reflectrometers which incorporated a discharge electrode. Angle-resolved scattering of mirrors and diffraction patterns of gratings were also measured. The mirror reflectance was restored to that of original mirror materials and the scattering level was reduced rather than increased by the discharge cleaning. The grating efficiency of the inside first order was drastically improved by cleaning, even by nearly an order of magnitude in some energy regions. Furthermore, the effect of a blaze was shown to be recovered by examining changes in the efficiencies of other orders as well.

The analytic solution of the multiple scattering m-nth moment equation with different wave numbers and different position is given in the small angle scattering approximation for optical wave propagated through such a random medium that the material parameter fluctuates inhomogeneously in the direction of propagation and homogeneously in the direction transverse to the propagation path. The applications of the solution to the problems related with the optical beam propagation is discussed.

The constructive interference between the two oppositely propagating lasers can produce a forced stationary electron density ripple. The latter can reflect the incident laser light from an expanding plasma in the underdense region. The effects of the laser intensity, the laser wavelength, and the plasma temperature on the total reflectivity are investigated. Application of our results in laser-fusion plasma is discussed.

Irradiated metals and alloys represent open dissipative systems able to undergo structural phase transitions under certain conditions. Below, we analyse the experimentally observed process of periodic decomposition of some concentrated binary alloys. The defect production rate K is considered as a control parameter and must be large enough to cause spatial instability. Both the threshold value of K and the largest wavelength of growing fluctuations are presented. Such spatial instability is expected to initiate the self-organization process in alloys considered.

If the life time of the vibrational states of adsorbates is large compared to their vibrational period a quantum theory for inelastic scattering, sticking and desorption of gas molecules at surfaces can be developed. The Schrödinger equation is used for short times to calculate the relaxation rates of a kinetic equation describing the transitions between the vibrational states of adsorbed particles. The long time behavior of the kinetic equation then yields sticking coefficients, accommodation coefficients, desorption rates and angular and energy distributions of desorbing particles. Some results of such a theory are reviewed.

Sharply defined multilayered structure have been grown from a variety of semiconducting materials. In these thin-film structures the accumulation of interfaces gives rise to new excitation modes that can be found both in the phonon and plasmon energy ranges. The detailed polariton structure of a general stratified material, with either a finite or an infinite number of layers, can conveniently be assessed in terms of an exact continued-fraction expansion of its relevant response functions, which can be used to quantitatively account for reflectance measurements and attenuated total reflection (ATR). Calculations of the infrared polariton structure, reflectivity and ATR spectra of typical superlattices made of polar materials are presented. The formation of Bloch-like continua of modes and isolated surface or interface states are discussed.

This paper is devoted to the spectroscopy of long-wavelength vibrations in an arbitrary stratified medium made of polar semiconductors. The classical, electrodynamic theory of phonon-polaritons is such a medium is reviewed. From a unified theory of the relevant response functions, three spectroscopic techniques of current interest are considered: electron-energy-loss spectroscopy in the reflection geometry, infrared reflectivity measurement and attenuated total reflection. It is shown that the response functions of a plane-stratified medium are easily expressed in term of an exact continued-fraction expansion of a dimensionless surface impedance. Throughout the paper, illustrations are given for a GaAs-AlAs superlattice.

The screening properties of metal surfaces from an important element in the description of phenomena under investigation in surface physics. The purpose of these notes is to review the basic features of the response of metal electrons to static and dynamic external fields which can be generated by probes such as electrons, atoms, photons, etc. The density functional approach and its time-dependent extension will be used to calculate the screening cloud. Various examples will be given that illustrate the behavior of the density induced at the surface as a function of frequency and momentum and the connection to several observable quantities will be discussed.

The calculated total magnetic moment including orbital and spin contributions in a fully relativistic Dirac theory for solids is presented. Non-self-consistent, fully relativistic, spin-polarized calculations were performed for γ-Ce and fcc-Pu. The agreement with the experimental magnetic moments is not satisfactory. The orbital moment is calculated using the Greens function of the spin-polarized Kohn-Sham-Dirac equations.

Three aspects of the interaction of a low energy electron beam with surface excitations are described. The long range dipolar scattering concentrates the inelastic electrons in a narrow lobe close to the specular reflection. The resulting spectra are quantitatively interpreted by the macroscopic dielectric theory in order to retrieve the infrared dielectric response of the target. Dipolar HREEL spectra of adsorbates obey the metal surface selection rule. Short range impact scattering disperses the inelastic electrons in a broad isotropic distribution. It allows the observation of short wavelength excitations and cancels the dipolar selection rule. Resonance scattering is a particular scattering mechanism which is observed for certain conditions of electron beam energy.

General concepts for the quantitative description of the dynamics of social processes are introduced. They allow for embedding social science into the conceptual framework of synergetics. Equations of motion for the socioconfiguration are derived on the stochastic and quasideterministic level. As an application the migration of interacting human populations is treated. The solutions of the nonlinear migratory equations include limit cycles and strange attractors. The empiric evaluation of interregional migratory dynamics is exemplified in the case of Germany.

Quantitative information-theoretical measures for structure are defined, and the connection to statistical mechanics concepts such as exergy (available work) is pointed out. Several information quantities, called `contrasts', are decomposed with respect to correlation order, structure size and position in space. The concepts are applied to the evolution of structure in a model of a chemical self-organizing system.

A short introduction to models of spin glasses and neural networks is given. Some recent results are outlined.

The kinetic equations of polynucleotide replication can be brought into fairly simple form provided certain environmental conditions are fulfilled. Two flow reactors, the continuously stirred tank reactor (CSTR) and a special dialysis reactor are particularly suitable for the analysis of replication kinetics. An experimental setup to study the chemical reaction network of RNA synthesis was derived from the bacteriophage Qβ. It consists of a virus specific RNA polymerase, Qβ replicase, the activated ribonucleosides GTP, ATP, CTP and UTP as well as a template suitable for replication.

The ordinary differential equations for replication and mutation under the conditions of the flow reactors were analysed by the qualitative methods of bifurcation theory as well as by numerical integration.

The various kinetic equations are classified according to their dynamical properties: we distinguish "quasilinear systems" which have uniquely stable point attractors and "nonlinear systems" with inherent nonlinearities which lead to multiple steady states, Hopf bifuractions, Feigenbaum-like sequences and chaotic dynamics for certain parameter ranges. Some examples which are relevant in molecular evolution and population genetics are discussed in detail.