Table of contents

A new mechanism for spatial 1/f power spectra is proposed for a type of open dynamical system. This mechanism has two competing ingredients. One tends to preserve the long-range correlations while the other tends to destroy it. A specific model with this mechanism based on a class of extremely simple context-free grammars is analyzed. In this model replication and transposition are repeated applied to a string of discrete elements. Computer experiments show that for a wide range of parameter values, the model yields spatial power spectra of the form 1/f^α with α close to 1. The frequency range spanned by the 1/f^α form as well as the exponent α depend on the probability with which replication and transposition operations are applied.

Two methods for the exact calculation of optimal manifolds in random media are presented. The first method is an extension of a transfer operator (TO) technique to nondirected manifolds ("returning paths"). The method is applied to the percolation problems in two dimensions. In the second approach the calculation is mapped onto a random resistor network (RRN) problem. The RRN formulation allows us to find optimal manifolds by the solution of a boundary value problem. Whereas the TO technique is very powerful for the calculation of 1D manifolds the RRN formalism has more potential for higher-dimensional applications.

In the framework of the third quantization of a simple minisuperspace model with Λ-term, the vacuum quantum state for Friedmann-like universes is shown to be a two-mode squeezed state for De Sitter-like universes. The parameter of this two-mode squeezed state is calculated.

Qualitative changes in the rotational structure of a finite particle quantum system are studied. The crossover phenomenon is explained from the point of view of consecutive quantum bifurcations. The generic organization of bifurcations is related to the stratification of the space of dynamical variables imposed by the invariance group of the Hamiltonian.

The initial quantum state of gravitons in the expanding universe is shown to be transformed into a squeezed state. The squeeze parameter for high-frequency fluctuations is calculated in the framework of a spatially closed model.

We have determined a generalized majority rule which optimizes the error reduction for the retrieval of noisy input patterns in Boolean networks for associative memory and have evaluated the consequential storage capacity, which is very robust against training noise disruption, when compared with previously proposed stepwise algorithms. We have indicated how the rule can be implemented using a multi-state algorithm. We compare such Boolean and conventional networks, whose respective short- and long-ranged retrieval behaviour are associated with low and high training noises, and also demonstrate that Hebb rule minimizes the output error for extremely noisy conventional networks.

Dynamical properties of a network model composed of N continuous elements with randomly chosen asymmetrical couplings and reduced connectivity are studied numerically. Depending on the connectivity and the strength of the nonlinearity we find stable, quasi-periodic and chaotic solutions. The chaotic state exhibits the typical sensitive dependence on the initial conditions. The line of transition from stationary to time-dependent solutions turns out to be almost independent of N in a wide range of network sizes.

It is shown that the lattice Boltzmann equation (LBE) for a lattice gas provides a viable numerical method for the study of three-dimensional flows in complex geometries. Numerical results for low Reynolds number flows in a three-dimensional random medium are reported. The Darcy's law is recovered and a preliminary estimation of the permeability presented.

The effective potential of open or toroidal bosonic p-branes in the 1/d approximation or one-loop approximation is investigated. The effective potential of 3-branes is analysed in detail. We find that there is a critical radius R₀ below which the toroidal 3-brane develops tachyons (in 1/d approximation). Such tachyonic instability does not take place in open 3-brane.

Recent experiments on superfluorescence from O₂^- centres in KCl host crystals, with quasi-one-dimensional active volumes, have shown identically shaped and perfectly synchronized forward and backward pulses in each run. This is in blatant contrast to previous experiments on atomic beams and gases in which no forward-backward correlation beyond energy conservation had been found. We argue that a linear coupling due to backscattering from the bulk or the surface of the active volume, a phenomenon much weaker in gases than in solids, is responsible for the effect.

Rayleigh-Bénard convection in the presence of a horizontal throughflow perpendicular to the convective roll chain is investigated with a 1d amplitude equation and with a 2d numerical simulation of the basic hydrodynamic equations. Results agree very well with each other. The flow leads to propagating convective patterns in the form of travelling wave states which for increasing flow are localized further and further downstream. Unique wave number selection is observed. Related experiments are discussed.

All acoustic and the lowest optic branches in three main symmetry directions have been determined by inelastic neutron scattering at room temperature using a double isotope monocrystal ¹⁵⁴Sm¹¹B₆. In comparison with the integer valence system LaB₆ the phonons are softer, and the LA branches exhibit remarkable anomalies. These features are interpreted on the basis of a specific coupling of the lattice vibrations with the dipole (f-d) and monopole (f-f) excitations of the Sm shells, the latter being characteristic for the mixed valence semiconductor. A weak broad signal has been observed in the energy gap between acoustic and optic modes, which can be ascribed to an additional mode appearing due to the nonadiabatic interaction of phonons with valence fluctuations.

Neural network models of associative memory with uniform inhibition are studied. It is shown that for sufficiently strong inhibition the system orders only partially even at low temperatures. A fraction of the neurons freezes in a quiescent state while the activities of the rest of the neurons fluctuate in time around an average level that is small compared to the saturation level. These models may help understanding the origin of the low neuronal firing rates observed in cortical recordings.

The ionic conductivity of β-AgI has been measured at frequencies from 1 kHz to 2.6 GHz, at different temperatures. A marked increase of the conductivity is observed at about 1 MHz. The spectra are interpreted in terms of localized hopping processes of the silver ions, performed between neighbouring tetrahedral sites. From the spectra it is concluded that these processes are largely cooperative in character.

We present measurements of the magnetic spin lattice relaxation time of degenerate normal liquid ³He down to 3 mK. The results were obtained using the rapid melting technique to produce polarized liquid ³He. The measurements indicate an effective linear dependence of (T₁)⁻¹ on temperature in the intrinsic region, and are consistent with a T²-dependence in the diffusion limited wall relaxation region at the lowest temperatures. At higher temperatures good agreement is obtained with theory.

Recently, a tiling derived from the well-known 2D quasi-periodic octagonal tiling has been introduced. In this letter, we show that in the framework of a tight-binding model, the electronic spectrum of this nontrivial tiling can be derived. The integrated density of state is singular and can be a devil staircase, there can be a finite or infinite number of gaps, whereas the measure of the spectrum can be zero or not, all these properties depending on the hopping parameters. This transition is explained with a very simple model.

Magnetotransport measurements on two-dimensional systems show that the experimentally determined resistivity ρ_xx may depend on the length and the width of the device. This result is explained on the basis of a combination of edge and bulk currents if a non-equilibrium exists between the one-dimensional edge currents. The experiments demonstrate that such a nonequilibrium between adjacent edge channels may be present not only if quantum point contacts are used for a selective population of edge currents but also in standard resistivity measurements with ohmic contacts.

The fusion rates for the reactions pd, dd and pp in a solid-state environment are determined under the assumption that the fusion process is mediated by bound states of the reactant pair. An effective binding potential which accounts for lattice, electronic and pair interactions is envisaged to model plausible equilibrium and nonequilibrium conditions. Our estimates for the upper-bound fusion rates in condensed matter lie well below the actual experimental limits.

The relaxation of electronic birefringence has been measured in a polydisperse solution of rodlike ionic micelles of cetylpyridinium chloride. The asymptotic behaviour of the relaxation is found to be characterized by a stretched-exponential: R(t) ≈ exp [−(t/τ)^α]. The value of the exponent α is 0.25 in the dilute regime. As the concentration of rods exceeds the critical concentration for entanglement c*, α grows progressively reaching the value 0.5. A simple theoretical model is presented to explain the dilute-regime results.