Spiral model, jamming percolation and glass-jamming transitions

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to an underlying jamming percolation transition which has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law, leading to a Vogel-Fulcher-like divergence of the relaxation time. Here we present a detailed physical analysis of SM, see [5] for rigorous proofs. We also show that our arguments for SM does not need any modification contrary to recent claims of Jeng and Schwarz [10].Comment: 9 pages, 7 figures, proceedings for StatPhys2

On the study of jamming percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property

The transition from a coherent optical vortex to a Rankine vortex: beam contrast dependence on topological charge

Spatially coherent helically phased light beams carry orbital angular momentum (OAM) and contain phase singularities at their centre. Destructive interference at the position of the phase singularity means the intensity at this point is necessarily zero, which results in a high contrast between the centre and the surrounding annular intensity distribution. Beams of reduced spatial coherence yet still carrying OAM have previously been referred to as Rankine vortices. Such beams no longer possess zero intensity at their centre, exhibiting a contrast that decreases as their spatial coherence is reduced. In this work, we study the contrast of a vortex beam as a function of its spatial coherence and topological charge. We show that beams carrying higher values of topological charge display a radial intensity contrast that is more resilient to a reduction in spatial coherence of the source

Sub-shot-noise shadow sensing with quantum correlations

The quantised nature of the electromagnetic field sets the classical limit to the sensitivity of position measurements. However, techniques based on the properties of quantum states can be exploited to accurately measure the relative displacement of a physical object beyond this classical limit. In this work, we use a simple scheme based on the split-detection of quantum correlations to measure the position of a shadow at the single-photon light level, with a precision that exceeds the shot-noise limit. This result is obtained by analysing the correlated signals of bi-photon pairs, created in parametric downconversion and detected by an electron multiplying CCD (EMCCD) camera employed as a split-detector. By comparing the measured statistics of spatially anticorrelated and uncorrelated photons we were able to observe a significant noise reduction corresponding to an improvement in position sensitivity of up to 17% (0.8dB). Our straightforward approach to sub-shot-noise position measurement is compatible with conventional shadow-sensing techniques based on the split-detection of light-fields, and yields an improvement that scales favourably with the detector’s quantum efficiency

Fractional moment bounds and disorder relevance for pinning models

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For \alpha<1/2 it is known that disorder is irrelevant: quenched and annealed critical points coincide for small disorder, as well as quenched and annealed critical exponents. The same has been proven also for \alpha=1/2, but under the assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant. Here we prove that, if 1/21, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is known to be smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered by Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To appear on Commun. Math. Phy

Replica bounds for diluted non-Poissonian spin systems

In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an interpolation procedure that stresses the relation between interpolation methods and the cavity method. As a byproduct we obtain self-averaging identities that generalize the Ghirlanda-Guerra ones to the multi-overlap case.Comment: Latex file, 15 pages, 2 eps figures; Weak point revised and corrected; Misprints correcte

Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page

Finite size effects in the dynamics of glass-forming liquids

We present a comprehensive theoretical study of finite size effects in the relaxation dynamics of glass-forming liquids. Our analysis is motivated by recent theoretical progress regarding the understanding of relevant correlation length scales in liquids approaching the glass transition. We obtain predictions both from general theoretical arguments and from a variety of specific perspectives: mode-coupling theory, kinetically constrained and defect models, and random first order transition theory. In the latter approach, we predict in particular a non-monotonic evolution of finite size effects across the mode-coupling crossover due to the competition between mode-coupling and activated relaxation. We study the role of competing relaxation mechanisms in giving rise to non-monotonic finite size effects by devising a kinetically constrained model where the proximity to the mode-coupling singularity can be continuously tuned by changing the lattice topology. We use our theoretical findings to interpret the results of extensive molecular dynamics studies of four model liquids with distinct structures and kinetic fragilities. While the less fragile model only displays modest finite size effects, we find a more significant size dependence evolving with temperature for more fragile models, such as Lennard-Jones particles and soft spheres. Finally, for a binary mixture of harmonic spheres we observe the predicted non-monotonic temperature evolution of finite size effects near the fitted mode-coupling singularity, suggesting that the crossover from mode-coupling to activated dynamics is more pronounced for this model. Finally, we discuss the close connection between our results and the recent report of a non-monotonic temperature evolution of a dynamic length scale near the mode-coupling crossover in harmonic spheres.Comment: 19 pages, 10 figures. V2: response to referees + refs added (close to published version

Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics

We show that facilitated spin models of cooperative dynamics introduced by Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar to the one predicted by the mode-coupling theory of supercooled liquids and the dynamical theory of mean-field disordered systems. At low temperature such cooperative models show a two-step relaxation and their equilibration time diverges at a finite temperature according to a power-law. The geometric nature of the dynamical arrest corresponds to a bootstrap percolation process which leads to a phase space organization similar to the one of mean-field disordered systems. The relaxation dynamics after a subcritical quench exhibits aging and converges asymptotically to the threshold states that appear at the bootstrap percolation transition.Comment: 7 pages, 6 figures, minor changes, final version to appear in Europhys. Let