Table of contents

An analytic expression for the Green function of the one-dimensional periodic Helmholtz operator is used to analyze the behaviour of the local density of states (LDOS). We provide numerical evidence that in the n-th band the LDOS has at least n minima and maxima. Near the band edge ω_c, the LDOS exhibits strong fluctuations, with its mimima approaching zero and the maxima diverging to infinity. For the lowest band, the ratio of the maximum to the minimum of the LDOS is shown to diverge as (ω_c − ω)⁻¹ as ω approaches the band edge. Since, in the case of electromagnetic waves, the LDOS governs the spontaneous emission of light of embedded atoms and molecules, this may have profound implications for technology using photonic crystals.

A method is proposed for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S. It uses the cumulant technique and a coherent-state representation of the partition function . The expansion of in terms of cumulants yields an effective classical Hamiltonian with temperature-dependent quantum corrections. For the Heisenberg quantum Hamiltonian, they have a non-Heisenberg form. The effective Hamiltonian can be solved by methods familiar for classical systems.

A generalised master equation is constructed from a non-homogeneous random walk scheme. It is shown how fractional Fokker-Planck equations for the description of anomalous diffusion in external fields, recently proposed in the literature, can be derived from this framework. Long-tailed waiting time distributions which cause slowly decaying memory effects, are demonstrated to give rise to a time-fractional Fokker-Planck equation that describes systems close to thermal equilibrium. An extension to include also Lévy flights leads to a generalised Laplacian in the corresponding fractional Fokker-Planck equation.

We investigate chaotic maps as generators of noise in bistable systems. The chaotic force generates complicated non-Gaussian behaviour, reflected in asymmetric stationary probability densities and escape times. We study how this non-Gaussian behaviour depends on the deterministic map we use to generate the chaotic force. For all such maps we find Langevin-like behaviour in the limit of vanishing time scale parameter.

We study the texture of surfaces imaged by scanning tunneling microscopy (STM) under different control conditions in the feedback loop of the STMs control unit. The surface texture parameters such as the rms-roughness, the average wavelength and the fractal character have a strong dependence on the values of the parameters used in the feedback loop even when the visual quality of the images is the same. The reliability of the images can be described quantitatively by giving the values of two nondimensional parameters that described the measurement conditions.

An original model of nuclear fusion mechanism in metal crystal structures at low energies is developed. It uses a new approach for the estimation of electron screening in metals which is based on the dynamic account of the outer metal electronic shells deformation during counter motion of two deuterons near their sites boundary. Computer simulation of deuterium behaviour in the palladium deuteride crystal structure has shown that the calculated rate of nuclear reactions agrees in order of magnitude with the values deduced from experimental data on excess heat output. A reaction rate sharply (10⁵ − 10⁶ times) increases in conditions of high mobility of deuterons in crystal structures. Crucial factors for fusion feasibility are indicated.

Oppositely charged macro-ions—one of which is flexible and carries a larger total charge than the other—are expected on an energetic basis to assemble into neutral complexes which can aggregate due to attractive (e.g., van der Waals) interactions. We treat in this paper the counter-intuitive appearance of spontaneous overcharging in polyelectrolyte-colloid complexes, a phenomenon which has been observed in experiments and simulations involving flexible chains adsorbing on oppositely charged cores. We show that this overcharging can be accounted for in the Poisson-Boltzmann approximation; within this theory, overcharging is an entropic effect associated with release of the counterions of the highly charged polyelectrolyte chain as it "overwinds" onto the rigid colloidal particle. Increasing the rigidity of the polyelectrolyte chain leads eventually to undercharging of the complex.

We consider a degenerate and transversally extended optical parametric oscillator, and predict the presence of a "spatial EPR paradox" that arises from the entanglement of the photon pairs emitted in the parametric down-conversion process. The effect emerges for reasonable values of the frequency spacing among adjacent transverse modes and of the waist of the pump beam.

We consider the tunnelling of acoustic waves between two slender tubes through a monomode structure. We give in closed form the conditions for selective transfer of a single propagating state from one tube to the other, leaving all other neighbor states unaffected. We illustrate the results of this analysis by analytical solutions for a simple structure made out of pieces of slender tubes.

Nanocomposites have been made by mixing soft particles (polymer latex) with hard particles (silica) in aqueous dispersions and extracting water to produce a dense film. Segregation between the two kinds of particles can be controlled, and even suppressed. The elongational modulus is strongly increased by such fillers at low deformations, and remains important at large deformations, which the samples can stand without breaking. Since the silica particles are small (200 Å), we can follow their relative displacements under stretching, by Small-Angle Neutron Scattering, through analysis and simulation of the anisotropic patterns. The latter show a crossover from affine displacements to a set of shear displacements that let the particles avoid each other at large deformations. The shear could release the localized stresses (due to polymer confinement) and dissipate more energy. In this way it may contribute to the toughness of the composite against crack propagation.

We investigate the strain evolution in low strained gratings before and after embedding in the substrate material by high-resolution grazing incidence X-ray diffraction and elasticity theory. For the experiments, we use a non-coplanar multiple crystal arrangement. A suitable selection of reflections allows us to characterise the grating shape independently of the strain state. Depth selective measurements give evidence for a non-uniform strain relaxation in the surface grating and a complete planarization of the sample surface by the burying process. In the buried grating a counteraction of the embedding material is found. The counteraction only leads to a partial restraining of the grating. There remains a laterally periodic strain modulation in the grating, which extends into the non-patterned material below and above the grating and reaches the free surface of the embedding material. The experimental findings are confirmed by calculations of the strain field based on elasticity theory. The subsequent simulations of the diffraction patterns show a good quantitative agreement with experiment.

We report a neutron scattering study of multilamellar membranes supported on solid substrates. In contrast to previous work, the high degree of orientational alignment allows for a clear distinction between specular and nonspecular reflectivity contributions. In particular, we demonstrate that by using the specific advantages of neutron optics the nonspecular scattering can be mapped over a wide range of reciprocal space. Several orders of magnitude in scattering signal and parallel momentum transfer can easily be recorded in multilamellar stacks of lipid membranes. This opens up the possibility to study fluctuations, and more generally lateral structure parameters of membrane on length scales between a few Å up to several μm. The first results obtained for a system of partially hydrated 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) indicate strong deviations from the predictions of the standard Caillé model.

We consider the electrostatic interaction between a spherical macroion of charge Qq and an oppositely, highly charged polyelectrolyte of charge − Nq (N,Q > 0). For N ⩽ Q the polyelectrolyte fully collapses on the macroion, while for N > Q only a partial collapse (up to neutralization of the macroion) is expected. We show, however, that for N > Q, the amount of collapsed polyelectrolyte can be bigger than that required to neutralize the macroion, i.e. the macroion can be overcharged. The overcharging increases with the diameter of the macroion (continuously or through multiple first-order transitions), until a total collapse of the polyelectrolyte takes place. The predictions of this model are then compared with Monte Carlo simulations and a possible mechanism is suggested for the overcharging of the octameric histone in the nucleosome.

We have observed an excess specific heat in bcc solid ³He at low temperatures and at pressures between the melting pressure and 46 bar. The excess specific heat is nearly independent of temperature. In the solid just above the melting pressure, the magnitude of the anomaly is about 2.5 times larger than that at high pressures. Except for the solid near the melting pressure, the magnitude is constant with pressure and is nearly the same as that in liquid ³He in Vycor. This anomaly of the specific heat in solid ³He is explained in terms of the amorphous surface solid on a disordered substrate.

The kinetics of irreversible adsorption of colloidal particles is analyzed through a statistical description of the transport process. Our approach describes in a consistent way both the transport from the bulk and the interaction with previously adsorbed particles. A surface density expansion for the adsorption rate is obtained. The coefficients of this expansion are obtained from the analysis of situations with only 1,2, ... , n pre-adsorbed particles. Also, a mean-field approach allows us to obtain an effective transport equation which is valid near the jamming limit. The formalism is explicitly applied to the adsorption of diffusing hard spheres, obtaining good agreement with non-sequential computer simulations.

Using optical microscopy, we followed the evolution of thin and initially smooth liquid polymer films on wettable solid substrates for different surrounding media. For thicknesses between 30 and 110 nm, we observed an instability of the film, eventually leading to the formation of nanodroplets on a remaining wetting layer. Exchanging the surrounding medium allowed to reverse the process and to re-establish a smooth film. Our results are in accordance with theoretical considerations and computer simulations. Weak but long-ranged dispersion forces may have drastic consequences concerning the morphology of thin liquid films even if short-range interactions force the film to stay on the substrate.

By including the contribution of a bound electron to the potential to be screened, it is shown that the screening cloud around a Coulomb charge is repelled so as to enable the formation of a persistent localized state. This result is obtained either with Thomas-Fermi or Lindhard screening, and is applied to the determination of Mott's critical density.

We consider tunneling of electromagnetic waves through a polariton band gap of a 1-D chain of atoms. We analytically demonstrate that a defect embedded in the structure gives rise to the resonance transmission at the frequency of a local polariton state associated with the defect.

Unlike rigid uniformly charged particles, vesicles bearing transmembrane inclusions undergo, under electrophoretic motion, a redistribution of their surface charges. We study how this internal response of the vesicle affects its electrophoretic mobility, which is shown to depend on the vesicle size, on the average inclusion concentration and on the field intensity. The surface reorganization of the inclusions may cause the mobility to change sign as the field is increased. From our analysis, free-flow fractionation methods can be envisaged.

We study the influence of hydrodynamic interactions on the self-diffusion of super-paramagnetic colloidal particles suspended in water. The colloids interact via repulsive dipolar forces due to an applied magnetic field, and their motion is effectively confined to two dimensions. By comparing experimental data with the results from extensive computer simulations, where the water flow fields are treated at the Rotne-Prager level, we show that the diffusivity is enhanced at all times due to hydrodynamic interactions. The enhancement effect becomes stronger with increasing particle density, but is almost unaffected by the temperature.

Shear banding of wormlike micelle solution has been studied in the context of constitutive instability of the Johnson-Segalman (JS) model plus Newtonian stress. We have incorporated a higher-order gradient term of the deformation-rate tensor into the JS model for investigating the dynamics of a mechanical interface in shear-banded flow. Two-dimensional modelling of the new model has been carried out by a general Lagrangian-Eulerian scheme. Within the unstable region, our results show that the new term plays an important role in selecting steady-state shear stress and the selected stress is independent of the nominal shear rate. The transit period of reaching the steady state can be much longer than the intrinsic relaxation time of the JS fluid. We have verified the experimental evidence on the existence of mechanical metastable regime, over which hysteresis in flow curve might occur. The model captures many features of experimental results on shear banded flow.

The first non-centrosymmetric lamellar systems were reported recently by Stadler et al. They were obtained from ABC triblock and AC diblock copolymers when they arrange in the sequence "ABCCAABCCA...". We give a tentative theoretical explanation for such a superlattice arrangement and obtain predictions for the phase diagram of such systems in terms of the molecular parameters.

Addendumi of Europhys. Lett.35 (9), pp. 114-117 (1999)

For technical reasons the above paper has not been published in its final version. The following concluding paragraph has been omitted.

Moreover, the CBM properties discussed above can be only one of the manifestations of a much deeper link with the fundamental physical laws, namely, negatively curved space - mixing - complexity - second law of thermodynamics - arrow of time. Thus, we observe the time asymmetry and the second law because we live in a Universe with negative curvature, and those laws may not be the same in flat or positively curved spaces. We plan to discuss curvature/second-law conjecture, including the relations between thermodynamic, cosmological and other arrows of time, in a separate paper.

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I am thankful to W. Zurek and my collaborator A. Allahverdyan for valuable discussions and the referee for helpful comments.

We apologize to the author for the unpleasant inconvenience.