Search

International audience; We study the rate-independent decohesion process for a chain linked to a substrate through a series of breakable elements with a softening mechanism. Such an assumption describes the realistic case when connecting links can undergo softening transitions before breaking. For instance, this is a diffuse mechanism observed both in fracture of soft materials and biological adhesion. The analysis of this model is developed in the framework of equilibrium statistical mechanics. In order to describe mechanically induced detachment of the chain from the substrate both in the cases of hard devices (prescribed extension) or soft devices (applied force), we consider both Helmholtz and Gibbs ensembles. In any case, the model can be exactly solved and is characterized by a phase transition at a given critical temperature, corresponding to the complete detachment of the chain even without mechanical actions. Interestingly, according to the 'size' of the softened region, we observe two different regimes. In one case (fragile regime) during the decohesion the measure of the softened region is negligible, whereas in the other case (ductile regime) we obtain a finite measure of the softened region that is constant, giving a temperature dependent analytic measure of the process zone.

The class of quantum operations known as Local Operations and Classical Communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to the unitarily invariant measure) of the set of LOCC-convertible bipartite pure states, where the ordering is characterised by an algebraic relation known as majorization. The numerical results, which exploit a tridiagonal model of random matrices, provide quantitative evidence that the proportion of LOCC-convertible pairs vanishes in the limit of large dimension, and therefore support a previous conjecture by Nielsen. In particular, we show that the problem is equivalent to the persistence of a non-Markovian stochastic process and the proportion of LOCC-convertible pairs decays algebraically with a nontrivial persistence exponent. We extend this analysis by investigating the distribution of the maximal success probability of LOCC-conversions. We show a dichotomy in behaviour between balanced and unbalanced bipartitions. In the latter case the asymptotics is somehow surprising: in the limit of large dimensions, for the overwhelming majority of pairs of states a perfect LOCC-conversion is not possible; nevertheless, for most states there exist local strategies that succeed in achieving the conversion with a probability arbitrarily close to one. We present strong evidences of a universal scaling limit for the maximal probability of successful LOCC-conversions and we suggest a connection with the typical fluctuations of the smallest eigenvalue of Wishart random matrices., 29 pages, 8 figures