Table of contents

We study a mean-field Hamiltonian system whose potential energy V({q_i}_{i = 1...N}) is expressed as a sum of k-body interactions and we show that in the thermodynamic limit the presence and the energy position of first-order phase transitions can be inferred by the study of the topology of configuration space induced by V, without resorting to any statistical measure. The thermodynamics of our model is analytically solvable and—depending on the value of k—displays no transition (k = 1), second-order (k = 2) or first-order (k > 2) phase transition. This rich behaviour is quantitatively retrieved by the investigation of one of the topological invariants (the Euler characteristic χ(v)) of the subsets M_v defined by M_v = {(q₁,...,q_N)∣V({q_i})/N ⩽ v}.

We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the known expressions of the total, dynamical and geometrical phases for pure and mixed states evolving unitarily.

The delocalization phenomenon was discovered by Hatano et al. and Miller et al. for a class of non-Hermitian quantum-mechanical problems. We show that the delocalization is only one example of many possible critical phenomena which are associated with the self-orthogonality of an eigenstate of the non-Hermitian Hamiltonian. It is shown that in this class of problems the self-orthogonality occurs at the series of branch points in the complex energy plane that serve as gates for the "particle" to hop from one Bloch energy band to another one.

We present a dynamical description and analysis of non-equilibrium transitions in the noisy one-dimensional Ginzburg-Landau equation based on a canonical phase space formulation. The transition pathways are characterized by nucleation and subsequent propagation of domain walls or solitons. We also evaluate the Arrhenius factor in terms of an associated action and find good agreement with recent numerical optimization studies.

We analyze terrestrial topographic data from four Digital Elevation Models which collectively span the range 20000 km to 50 cm. We use power spectra and trace moment analysis techniques to show that topography is multifractal from planetary scales down to around 40 m, where the multiscaling is broken by trees. We show that over this range the topography is reasonably described by a global nonlinear moment scaling function, itself determined by three parameters. We argue that these isotropic analyses are insensitive to the anisotropies and are hence compatible with different geomorphologies.

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter α and for large time to the entropy nonextensivity parameter q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived from an extension of the Lévy central-limit theorem. They are in full agreement with the Jonscher universality principle. Moreover, our model gives a physical interpretation of the mathematical parameters of the Weron stochastic theory and opens new paths to understand the ubiquity of self-similarity and power laws in the relaxation of large classes of materials in terms of their fractal and nonextensive properties.

We argue that for complete wetting at a curved substrate (wall) the wall-fluid surface tension is non-analytic in R_i⁻¹, the curvature of the wall, and that the density profile of the fluid near the wall acquires a contribution proportional to the gas-liquid surface tension ×R_i⁻¹ plus higher-order contributions which are non-analytic in R_i⁻¹. These predictions are confirmed by results of density functional calculations for the square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder where complete wetting by gas (drying) occurs. The implications of our results for the solvation of big solvophobic particles are discussed.

We report measurements of the temporal fluctuations of the heat flux in Rayleigh-Bénard turbulent convection in various fluids and geometries. We observe that the rms fluctuations of the heat flux increase nearly proportionally to the temperature difference ΔT. The ratio of the rms fluctuations of the heat flux to their mean display a power law, Ra^−γ on two decades in Rayleigh number (2·10⁷ < Ra < 3·10⁹). We discuss this law as well as the non-Gaussian character of the probability density function of the heat flux.

At least up to Rayleigh numbers of the order 10¹³, a feature of turbulent convection in confined containers is a self-organized and coherent large-scale motion ("mean wind"). For aspect ratio unity, the mean wind is comparable in scale to the container size. Its magnitude is measured here using short-time temperature correlations in a cylindrical container of aspect ratio unity; the working fluid is cryogenic helium and the Rayleigh numbers span from 10⁶ to 10¹⁵. The self-organizing advection of "plumes" by the mean wind leads to periodic temperature oscillations near the sidewall. Comparisons of the observed oscillation frequency to the rotational rate of the mean wind, however, have differed by a factor of 2 in the recent literature. It is argued here that this apparent discrepancy is the result of the evolution of the shape of the mean wind, from a tilted and nearly elliptical shape at low Rayleigh numbers to a squarish shape at high Rayleigh numbers, thereby altering the effective path length from which the rotational rate of the mean wind is deduced.

In order to understand the atomistic origin of the inverse piezoelectric effect, the changes of integrated intensities of selected Bragg reflection of α-SiO₂ and α-GaPO₄ were studied, which were induced by an external high electric field of up to E = ±8 kV/mm. Because the model of the field-induced displacement of ionic sublattices against each other fails for the interpretation of experimental data, we propose a model of the inverse piezoelectric effect, which considers the strong covalent bond between Si and O atoms in α-SiO₂. Here the main effect of screening the external electric field is a change in the Si-O-Si bonding angles, i.e. the rotations of rigid SiO₄ tetrahedra. The same model holds for α-GaPO₄, which is an isostructural compound to α-SiO₂. For the first time a similar experiment was performed at low temperatures. Between 50 K ⩽ T⩽300 K the piezoelectric coefficient d₁₁₁ of both substances behaves nearly temperature independent. On the other hand, the field-induced change of the intensities increases for decreasing temperature. This can be interpreted by the rotation of tetrahedra, which is partially originated by the temperature decrease and by the external electric field, respectively, accompanied by a field-induced deformation of tetrahedra.

The complexation of oppositely charged colloidal objects is considered in this paper as a thermodynamic micellization process where each kind of object needs the others to micellize. This requirement gives rise to quantitatively different behaviors than the so-called mixed-micellization where each species can micellize separately. A simple model of the grand potential for micelles is proposed to corroborate the predictions of this general approach.

The dynamics of polymer collapse with a fixed distance between endpoints is studied analytically and numerically by the Nosé-Hoover algorithm. We find that at the pearling stage of the collapse the number of pearls decays as t^−1/2 leading to anomalously long collapse time. To understand the effect of Stokes drag we reduced the problem of long-polymer-chain collapse to the one-dimensional diffusion-limited coalescence of particles with the mass-dependent mobility. In this case the number of pearls decays slower, as t^−3/7.

A chemical pattern on a substrate is transposed into thin films of a ternary polymer blend during spin-casting from a common solvent. One of the blend components intercalates at interfaces between the other two phases to reduce their interfacial energy. As a result, an extensive substructure is formed, in addition to domains with pattern periodicity λ. Morphologies with well-ordered lateral domains are created not only when the inherent scale of the phase domains R is comparable to λ (as observed previously) but also for R ∼ λ/2, extending pattern transposition to smaller length scales.

By means of large-scale atomistic simulations we investigate the recrystallization features of an interface between boron-doped amorphous silicon and crystalline silicon. Present simulations are both consistent with available experimental information and predictive as far as the relevant elementary mechanisms occurring during solid-phase epitaxy. In particular, we prove that the experimentally observed solubility limit for electrically active boron is due to sizeable boron ripening phenomena, occurring in the amorphous-silicon region, as well as during recrystallization.

We have computed the time-dependent susceptibility for the finite-size mean-field random orthogonal model (ROM). We find that for temperatures above the mode-coupling temperature, the imaginary part of the susceptibility χ''(ν) obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of χ'' decreases, following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature T_c, where the configurational entropy vanishes.

We study theoretically the adhesion between two approaching surfaces, one containing tethered ligands and the other receptors. Using the reaction-diffusion formalism, we show that the range of adhesion ℓ_r is generally determined by a combination of tether dynamics, ligand-receptor affinity and experimental speed of approach v. Contrary to previous studies, we fully account for back reactions and are thus able to describe the crossover between irreversible adhesion at large affinities or high speed v and reversible adhesion at small affinities or low speed. We also briefly discuss the case of rupture and show that in the limit of irreversible adhesion the rupture occurs always at a larger distance than ℓ_r determined for approaching surfaces.

Tunneling spectroscopy of epitaxial (100) oriented YBa₂Cu₃O_{7 − δ} films was performed using an STM at 4.2 K. On atomically smooth areas, tunneling spectra revealing clear U-shaped gaps with relatively low zero bias conductance were measured. These spectra can be well fitted to the tunneling theory into a d-wave superconductor only when introducing a strong dependence of the tunneling probability on the wave vector k. Possible origins for this k-selectivity in STM measurements will be discussed. On other areas, V-shaped gaps as well as zero bias conductance peaks are observed, indicating relaxation of k-selectivity and the effect of nanofaceting, respectively.

We study via renormalization group (RG) and large N methods the problem of continuum SU(N) quantum Heisenberg ferromagnets (QHF) coupled to gapless electrons. We establish the phase diagram of the dissipative problem and investigate the changes in the Curie temperature, magnetization, and magnetic correlation length due to dissipation and both thermal and quantum fluctuations. We show that the interplay between the topological term (Berry's phase) and dissipation leads to non-trivial effects for the finite temperature critical behavior.

The large shape distortions that occur during the drying of sessile drops of polymer solution are shown to be related to a buckling instability. As solvent evaporates, polymers accumulate near the vapor/drop interface and, depending on the experimental conditions, can form a glassy skin which bends as the volume it encloses decreases. A comparison of the times that characterize drying kinetics and glassy skin formation enables us to predict instability occurrence. Good agreement is found with measurements performed at different polymer concentrations, drop volumes and drying rates.

We show that a recent letter claiming to present exact cosmological solutions in Brans-Dicke theory actually uses a flawed set of equations as the starting point for their analysis. The results presented in the letter are therefore not valid.