Table of contents

A semi-classical time-dependent Green's function for the hyperbolic wave equation is constructed using a summation over quasi-recurrent classical ray trajectories. The finite resolution of the wave problem associated to the smallest wavelength introduces a natural coarse graining which allows us to partition the classical rays into bundles. Our parametrization introduces precursor contributions in the sum, which allow for a very good agreement with the direct numerical integration of the wave equation in integrable as well as chaotic two-dimensional (2D) billiards. These precursors give a new insight in the role of focal points in semi-classical wave dynamics.

Light-front quantization of the Chern-Simons theory coupled to complex scalars is performed in the local light-cone gauge following the Dirac procedure. The light-front Hamiltonian turns out to a simple one and the framework may be useful to construct a renormalized field theory of anyons. The theory is shown to be relativistic in spite of the unconventional transformations of the matter and the gauge field, in the non-covariant gauge adopted, under space rotations.

We study the problem of pattern and velocity selection of morphologically stable two-dimensional fronts propagating in a spatially modulated medium. The generic system is governed by a local equation and evolves towards a non-trivial steady state with a spatial structure which arises from non-local competition effects and does not necessarily mimic the local structure externally fixed by the modulation. The dynamical process leading to this steady state is studied both analytically and numerically.

We discuss a non-local modification of the lattice Boltzmann BGK model. The modification involves the mixing of particle configurations over a range of distances. We show that at large distances and large times the modified BGK model entails the presence of an effective viscosity, and is thus similar to the usual closure approximation to the Navier-Stokes equation. We discuss the case of turbulent channel flow.

Sintering of Si₃N₄nanoclusters is investigated with the molecular-dynamics approach. At 2000 K thermally rough nanocrystals develop an asymmetric neck in 100 picoseconds. The neck contains more fourfold than threefold coordinated Si atoms. Amorphous nanoclusters develop a symmetric neck which has nearly equal number of threefold and fourfold coordinated Si atoms. In both cases, sintering is driven by surface diffusion of Si and N atoms. The diffusion is much more rapid in the neck joining amorphous nanoclusters than in the neck region of nanocrystals.

We report results of calculations that explain in the itinerant electron picture weak ferromagnetism in hematite, α-Fe₂O₃. We use the local approximation to spin-density functional theory and the ASW method incorporating spin-orbit coupling (SOC) and non-collinear moment arrangements. By a detailed symmetry analysis we show how the relativistic effect of SOC and the particular crystal symmetry of α-Fe₂O₃ cooperate to lead to a non-collinear magnetic structure and thus to weak ferromagnetism.

We show that the analytic single-particle density of states and the optical conductivity for the half-filled Hubbard model on the Bethe lattice with infinite connectivity describe quantitatively the behaviour of the gap and the kinetic-energy ratio of the correlated insulator V₂O₃. The form of the optical conductivity shows ω^3/2 rising and is quite similar to the experimental data, and the density of states shows ω^1/2 behaviour near low-frequency band edges.

We study numerically the time evolution of the coupled system of an electron, described by a tight-binding model exhibiting metal-insulator transition, interacting with vibrational degrees of freedom. Depending on the initial energy of the electron, E_e(0), its effective mass, m*, on how close to the mobility edge it is and the strength of the electron-phonon coupling, different types of localized and extended states are formed. We find, that, in general, an increase of E_e(0) decreases the ability of the system to form localized states, a large m* does not always favor localization and polaron formation is facilitated near the mobility edge.

We propose an information-theoretic model to describe the common features of typical chaotic scattering processes by including two time scales, a prompt and an equilibrated component. The model, introduced in nuclear physics, uses the average value of the scattering matrix to describe the prompt processes, and satisfies flux conservation, causality, and ergodicity. We show that the model successfully describes electronic transport through a much larger class of chaotic quantum dots than previously considered. The predicted distribution of the conductance may differ dramatically from that of previous models.

The magnetoresistance in the variable-range hopping regime due to Zeeman spin-splitting and intra-impurity interactions is calculated analytically and shown to be a universal function of μH/kT log R. Good agreement with numerical calculations in one and two dimensions is observed. With the inclusion of quantum interference effects, excellent agreement with recent experiments is obtained.

We have investigated the effect of an electromagnetic field on the tunnelling current bistability through a double-barrier structure. The main effect of an external electromagnetic field applied to the sample is to modify the amount of charge stored in the well due to the induced photon absorption and emission processes, specially for bias in the range corresponding to the bistability region. Therefore, the current density is modified with respect to the case where the light is not present, and the bistability region is reduced. Another interesting effect due to the light is the appearance of new bistability regions for certain values of barriers and well widths and intensity and frequency of the light.

Andreev-reflection spectra of superconducting-normal contacts with HoNi₂B₂C show a continuous increase of the superconducting order parameter at the antiferromagnetic phase transition T_N = 5 K without re-entrant behaviour below the superconducting critical temperature T_c = 9 K. A change is found in the superconducting ground state at T_c* = 6.5 K (zero magnetic field), and the magnetic-field–temperature phase diagram corresponding to the two superconducting states is reconstructed.

We identify two distinct regimes in the high-frequency response of the insulating, Ising spin-glass, LiHo_0.167Y_0.833F₄. The asymptotic high-frequency behavior of the imaginary part of the magnetic susceptibility becomes frequency independent as the spin-glass transition is approached: the shortest and the longest measured time scales both contain information about the actual phase transition. We compare our results to corresponding data on supercooled liquids.