Table of contents

We consider overdamped Brownian particles in anisotropic, periodic structures (ratchets) that are rocked periodically. Together with the periodic forcing, white thermal noise can generate a non-zero, macroscopic velocity. By tuning the parameters, the direction of the current can be reversed. Additionally, the current as a function of the driving amplitude exhibits several local maxima at finite driving frequencies. For zero thermal noise, the deterministic current assumes an intriguing structure, reflecting the complex dynamics of particle excursions along the ratchet.

We study the ground state of a classical X-Y model with p ⩾ 3-fold spin anisotropy D in a uniform external field, H. An interface is introduced into the system by a suitable choice of boundary conditions. For large D, as H → 0, we show using an expansion in D^-1 that the interface unbinds from the surface through an infinite series of layering transitions. Numerical work shows that the transitions end in a sequence of critical end points.

The infrared behaviour of the one-loop tachyon self-energy is described at any finite temperature in the D = 26 closed-bosonic-thermal-string theory based upon the thermofield dynamics.

We use velocity-selective Raman pulses generated by two diode lasers to cool cesium atoms in 1 dimension to an r.m.s. of 1.2 mm/s. This is about 1/3 of the single-photon recoil velocity v_rec = ℏk/M, where ℏk is the photon momentum and M the atom's mass. The corresponding effective temperature is a factor of 9 below the single-photon recoil temperature given by k_BT_rec/2 = 1/2Mv_rec². Because of the high cesium mass, this temperature is only (23 ± 5) nanokelvin, the lowest 1D kinetic temperature reported to date.

Mercury vapour depolarized-light scattering spectra have been measured at various densities and temperatures up to 1070 K for the first time. Absolute-intensity calibration has been done. Comparisons of the zeroth and second spectral moments with theoretical calculations using various available pair potentials and the dipole-induced-dipole approximation for the pair polarizability anisotropy have been performed. The large disagreement between experimental values and theoretical calculations is attributed to the breakdown of the classical point dipole approximation.

Small-angle neutron scattering was employed to study the effect of shear flow on the nematic (N) and lamellar (L_α) phases in aqueous solutions of cesium perfluoro-octanoate. Shear rates as high as ∼ 4000 s^-1 were used. The N phase was found to align with the director in the direction of the gradient velocity. The L_α phase oriented with lamellae parallel to the shear plane. This change in equilibrium orientation is attributed, primarily, to changes in the value of the Ericksen viscosity parameter α₂. Subtle shear-rate-dependent director reorientations were also observed in the proximity of the N-to-L_α phase transition.

We study the stability and shapes of domains in mixed-fluid films and membranes. These domains can result from the inclusion of an impurity in a fluid membrane, or from phase separation within the membrane. We show that for small but finite line and surface tensions and for finite spontaneous curvatures, an equilibrium phase of protruding circular domains is obtained at low impurity concentrations. However, at higher concentrations we predict a transition from circular domains to stripes. In both cases, we calculate the shapes of these domains within the Monge representation for the membrane shape.

We present investigations of the optical properties of quantum wire arrays grown on vicinal surfaces with lateral periods between 8 nm and 32 nm. Because of the decreasing tunnelling between adjacent wires when the lateral periodicity gets larger, the dimensionality changes from two to one. This has been evidenced, experimentally and theoretically, by a red-shift of the photoluminescence and by the appearance of spectral polarization oscillations which are indicative of one-dimensional subbands.

The magnetic-exciton modes in singlet ground-state systems exhibit soft-mode-type anomalies close to an induced magnetic instability. A bosonized description of these modes shows that an attraction between excitons exists which may, for a quasi-two-dimensional dispersion, lead to the formation of a magnetic-biexciton bound state. The binding energy, dispersion and signature in the dynamical susceptibility of these bound states are calculated and discussed.

A recent method for treating colloid-polymer mixtures is extended to study the phase behaviour of hard-sphere mixtures. It is shown that, for small size ratios ξ r₂/r₁, the addition of small spheres (radius r₂) to a system of large spheres (radius r₁) induces bulk phase separation into coexisting crystal and fluid phases. Moreover, prior to inducing bulk crystallization, the small spheres cause crystallization of the large spheres next to a hard wall. The positions of the wall and bulk crystallization phase boundaries calculated for a size ratio of 0.14 compare favourably with a set of recent experimental results.

When a sufficient density of permanent random crosslinks is incorporated into a system of macromolecules, the system undergoes a continuous equilibrium phase transition from a liquid to an amorphous solid state. In this solid state, a certain fraction of monomers are entirely delocalised. The remaining fraction (i.e. the gel-fraction) are localised about random mean positions, and have random r.m.s. displacements (i.e. localisation lengths). A microscopic mean-field theory of this so-called vulcanisation transition is presented, in which the gel-fraction and statistical distribution of localisation lengths are determined self-consistently. A scaling form for the distribution of localisation lengths, valid for all near-critical crosslink densities, is obtained, and it is found that both the fraction of localised monomers and the typical inverse localisation length vanish continuously at the transition.

We study on-line learning of a linearly separable rule with a simple perceptron. Training utilizes a sequence of uncorrelated, randomly drawn N-dimensional input examples. In the thermodynamic limit the generalization error after training such examples with P can be calculated exactly. For the standard perceptron algorithm it decrease like (N/P)^1/3 for large P/N, in contrast to the faster (N/P)^1/2-behaviour of the so-called Hebbian learning. Furthermore, we show that a specific parameter-free on-line scheme, the AdaTron algorithm, gives an asymptotic (N/P)-decay of the generalization error. This coincides (up to a constant factor) with the bound for any training process based on random examples, including off-line learning. Simulations confirm our results.

The generalization ability of a spherical perceptron with non-monotonous activation function serving as a toy model for multilayer networks is investigated. With increasing size of the training set there is in replica symmetry a discontinuous transition from a poorly to a well-generalizing phase. The replica-symmetric saddle-point is tested for its local and global stability. The results indicate that for multilayer nets the equilibrium properties of the generalization problem are correctly described in replica symmetry whereas the study of metastable states necessitates replica symmetry breaking.