Exact order-parameter distribution for critical mean-field percolation and critical aggregation

We show that the order-parameter distribution for the mean-field percolation at the critical point is the Kolmogorov-Smirnov distribution and that it coincides with the corresponding distribution for a mean-field aggregation process at the critical time. Both processes are known to belong to the same universality class in the sense that they share the same set of critical exponents, but percolation is at the equilibrium while the aggregation is a dynamical critical process. This shows that, in this case, the probability density for order-parameter fluctuations is universal at the critical point of the infinite lattice, independent of the hypothesis of thermodynamic equilibrium.     

Universal fluctuations in heavy-ion collisions in the Fermi energy domain

We discuss the scaling laws of both the charged fragments multiplicity n fluctuations and the charge of the largest fragment Z(max) fluctuations for Xe + Sn collisions in the range of bombarding energies between 25A MeV and 50A MeV. We show at E(lab) > or similar to 32 MeV/A the transition in the fluctuation regime of Z(max) which is compatible with the transition from the ordered to disordered phase of excited nuclear matter. The size (charge) of the largest fragment is closely related to the order parameter characterizing this process.     

Dynamics of spinor condensates and stochastic approach

The dynamics of the collective spin for Bose-Einstein condensates with nonlinear interactions, is studied within the framework of the two-component spinor. We discuss the spin resonance when the system is submitted to a periodically-modulated magnetic field at the zero temperature. In this case, the nonlinearity parameter controls the critical change between a localized and a homogeneous spin state. When the temperature is finite – or a random magnetic field is considered – the movement of the collective spin is governed by the Landau-Lifshitz-Gilbert equation, from which the complete Fokker-Planck equation is derived. This equation is the essential tool to describe the time-evolution of the probability distribution function for the collective spin. The functional integral approach is used to solve analytically examples of BEC spin behavior in a static magnetic field at finite temperature. We show how such a method can lead effectively to the complete solution of the Fokker-Planck equation for this kind of problems.     

Fractal aggregates of particles

Recent work to understand aggregation of particles using the concept of fractal is reviewed. We introduce all the tools issued from the theory of fractals, and which are useful for our study. Then we define and detail the two main models: the particle-cluster process where individual particles come to stick on large clusters, and the cluster-cluster process where clusters diffuse and stick when they collide. The important parameters of these models are varied and their influence on the resulting geometrical disordered structure is discussed. All along the paper, the connections with existing experiments are given.     

Moment Scaling at the Sol-Gel Transition

Two standard models of sol-gel transition are revisited here from the point of view of their fluctuations in various moments of both the mass-distribution and the gel-mass. Bond-percolation model is an at-equilibrium system and undergoes a static second-order phase transition, while Monte-Carlo Smoluchowski model is an off-equilibrium one and shows a dynamical critical phenomenon. We show that the macroscopic quantities can be splitted into the three classes with different scaling properties of their fluctuations, depending on whether they correspond to: (i) noncritical quantities, (ii) critical quantities or to (iii) an order parameter. All these three scaling properties correspond to a single form: M P(M) = ((M – M)/ M), with the values of respectively: = 1/2 (regime (i)), 1/2 and 1 (regime (ii)), and = 1 (regime (iii)). These new scalings are very robust and, in particular, they do not depend on the precise form of an Hamiltonian.