L. Reatto

Liquid state theories and critical phenomena

The description of the critical behaviour within liquid state theories is reviewed with emphasis on both the universal and the non-universal properties. Simple lattice and continuous models, such as the Ising model and the Lennard-Jones fluid, are examined by the use of several techniques, ranging from the integral equation method to the renormalization group analysis. A self-contained derivation of the hierarchical reference theory (HRT) of fluids is given together with a detailed discussion of the universal properties within a simple approximation to the exact HRT equations. Applications to simple models and comparisons with the results of other investigations are presented. HRT is then generalized to binary fluids, allowing for a complete description of the possible critical behaviours in these systems. The problems of a microscopic definition of the order parameter in mixtures and of the origin of strong crossover phenomena in binary fluids are also addressed.

Modulational instability and complex dynamics of confined matter-wave solitons.

We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.

Structural Arrest in Dense Star-Polymer Solutions

The dynamics of star polymers is investigated via extensive molecular and Brownian dynamics simulations for a large range of functionality f and packing fraction eta. The calculated isodiffusivity curves display both minima and maxima as a function of eta and minima as a function of f. Simulation results are compared with theoretical predictions based on different approximations for the structure factor. In particular, the ideal glass transition line predicted by mode-coupling theory is shown to exactly track the isodiffusivity curves, offering a theoretical understanding for the observation of disordered arrested states in star-polymer solutions.

Microphase separation in two-dimensional systems with competing interactions

The formation of clusters in condition of thermodynamic equilibrium can be easily observed both in two and three dimensions. In two dimensions relevant cases include pattern formation in Langmuir monolayers and ferrofluids, while in three dimensions cluster phases have been observed in colloids and in protein solutions. We have analyzed the problem within the scenario of competing interactions: typically, a short-range attractive interaction against a long-range repulsive one. This simplified approach is suggested by the fact that the forces, governing self-organization, act on a length scale which is larger than the molecular size; as a consequence many specific details of the molecules of interest are not necessary for studying the general features of microphases. We have tackled the microphase formation by simulations in bidimensional fluids, exploiting the parallel tempering scheme. In particular, we have analyzed the density range in which the particles arrange in circular domains (droplets), and the temperature range in which the system goes from microphases to the homogeneous fluid phase. As the density increases, the droplet size increases as well, but above a certain density the morphology changes and stripes are formed. Moreover at low density, we observe the formation of a liquidlike phase of disordered droplets; at higher densities, instead, the droplets tend to arrange onto a triangular superlattice. Such a change affects the features of the static structure factor, which gives well defined signatures of the microphase morphology. In each case, the specific heat exhibits a peak close to the transition from microphases to the homogeneous fluid phase, which is due to the breaking up of the clusters. The saturation of the height of the specific heat peak, with the increasing of the system size, suggests the possibility of a Kosterlitz-Thouless transition.

A bidimensional fluid system with competing interactions: spontaneous and induced pattern formation

In this paper we present a study of pattern formation in bidimensional systems with competing short-range attractive and long-range repulsive interactions. The interaction parameters are chosen in such a way as to allow us to analyse two different situations: the spontaneous pattern formation due to the presence of strong competing interactions on different length scales and the pattern formation as a response to an external modulating potential when the system is close to its Lifshitz point. We compare different Monte Carlo techniques showing that the parallel tempering technique represents a promising approach for the study of such systems and we present detailed results for the specific heat and the structural properties. We also present random phase approximation predictions concerning spontaneous pattern formation (or microphase separation), as well as linear response theory predictions concerning the induced pattern formation due to the presence of an external modulating field. In particular we observe that the response of our systems to external fields is much stronger than the response of a Lennard-Jones fluid.

Model colloidal fluid with competing interactions: Bulk and interfacial properties

Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter sigma, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, whereby the ultimate decay of correlation functions changes from monotonic to long wavelength damped oscillatory decay on crossing certain lines in the phase diagram or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters the authors find, within the DFT, a lambda line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a lambda line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>>sigma) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the lambda line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby lambda transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface.

Theory for the phase behaviour of a colloidal fluid with competing interactions

We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gas–liquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behaviour. The amplitude of the density modulations is the order parameter in our theory. The theory predicts that the phase transition from the uniform to the modulated fluid phase can be either first order or second order (continuous). The phase diagram exhibits two tricritical points, joined to each other by the line of second order transitions.

Condensate bright solitons under transverse confinement

Istituto Nazionale per la Fisica della Materia, Unit`a di ComoDipartimento di Scienze Fisiche, Universit`a dell’Insubria,Via Valeggio 11, 23100 Como, ItalyWe investigate the dynamics of Bose-condensed bright solitons made of alkali-metal atoms withnegative scattering length and under harmonic confinement in the transverse direction. Contrary tothe 1D case, the 3D bright soliton exists only below a critical attractive interaction which dependson the extent of confinement. Such a behavior is also found in multi-soliton condensates with boxboundary conditions. We obtain numerical and analytical estimates of the critical strength beyondwhich the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr¨odinger equa-tion (NPSE), which accurately takes into account the transverse dynamics of cigar-like condensates,we numerically simulate the dynamics of the ”soliton train” reported in a recent experiment (Nature417 150 (2002)). Then, analyzing the macroscopic quantum tunneling of the bright soliton on aGaussian barrier we find that its interference in the tunneling region is strongly suppressed withrespect to non-solitonic case; moreover, the tunneling through a barrier breaks the solitonic natureof the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering onthe barrier or by the collision with another matter wave when the density reaches a critical value,for which we derive an accurate analytical formula.03.75.Fi; 32.80.Pj; 42.50.VkI. INTRODUCTION

STRUCTURE AND STABILITY OF BOSONIC CLOUDS : ALKALI-METAL ATOMS WITH NEGATIVE SCATTERING LENGTH

We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low-density metastable solution, a different branch of Bose condensate appears at higher density when nonlocality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number

Non-simple magnetic order for simple Hamiltonians

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