Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.Comment: 6 pages, 7 figure

Breathing mode for systems of interacting particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy allows us to tackle at once a wide range of power law interactions and interaction strengths, at linear and non linear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.Comment: 4 pages, 4 figure

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Ensemble inequivalence in systems with long-range interactions

Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.Comment: 12 pages, no figure

Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Large deviation techniques applied to systems with long-range interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with $0\leq\alpha<1$

Long-range gravitational-like interaction in a neutral atomic cold gas

A quasi-resonant laser induces a long-range attractive force within a cloud of cold atoms. We take advantage of this force to build in the laboratory a system of particles with a one-dimensional gravitational-like interaction, at a fluid level of modeling. We give experimental evidences of such an interaction in a cold Strontium gas, studying the density profile of the cloud, its size as a function of the number of atoms, and its breathing oscillations.Comment: 4 pages, 4 figures. Published in PRA 87, 013401 (2013

Improved optical phenotyping of the grape berry surface using light-separation and automated RGB image analysis

Grape resilience towards Botrytis cinerea (B. cinerea) infections (Botrytis bunch rot) is an important concern of breeders and growers. Beside grape bunch architecture, berry surface characteristics like berry bloom (epicuticular wax) as well as thickness and permeability of the berry cuticle represent further promising physical barriers to increase resilience towards Botrytis bunch rot. In previous studies, two efficient sensor-based phenotyping methods were developed to evaluate both berry surface traits fast and objectively: (1) light-separated RGB (red-green-blue) image analysis to determine the distribution of epicuticular wax on the berry surface; and (2) electrical impedance characteristics of the grape berry cuticle based on point measurements. The present proof-of-concept study aiming at the evaluation of light-separated RGB images for both phenotyping applications, phenotyping wax distribution pattern and berry cuticle impedance values. Within the selected grapevine varieties like 'Riesling', 'Sauvignon Blanc' or 'Calardis Blanc' five contributions were achieved: (1) Both phenotyping approaches were fused into one prototypic unified phenotyping method achieving a wax detection accuracy of 98.6 % and a prediction of electrical impedance with an accuracy of 95 %. (2) Both traits are derived using only light-separated images of the grapevine berries. (3) The improved method allows the detection and quantification of additional surface traits of the grape berry surface such as lenticels (punctual lignification) and the berry stem that are also known as being able to affect the grape susceptibility towards Botrytis. (4) The improved image analysis tools are further integrated into a comprehensive workbench allowing end-users, like breeders to combine phenotyping experiments with transparent data management offering valuable services like visualizations, indexing, etc. (5) Annotation work is supported by a sophisticated annotation tool of the image analysis workbench. The usage of light-separated images enables fast and non-invasive phenotyping of different optical berry surface characteristics, which saves time-consuming labor and additionally allows the reuse of the berry samples for subsequent investigations, e.g. Botrytis infection studies

Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators

The largest Lyapunov exponent of a system composed by a heavy impurity embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators is numerically computed for various values of the impurity mass $M$. A crossover between weak and strong chaos is obtained at the same value $\epsilon_{_T}$ of the energy density $\epsilon$ (energy per degree of freedom) for all the considered values of the impurity mass $M$. The threshold \epsi lon_{_T} coincides with the value of the energy density $\epsilon$ at which a change of scaling of the relaxation time of the momentum autocorrelation function of the impurity ocurrs and that was obtained in a previous work ~[M. Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete Lyapunov spectrum does not depend significantly on the impurity mass $M$. These results suggest that the impurity does not contribute significantly to the dynamical instability (chaos) of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. Finally, it is shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak to strong chaos at the same value of the energy density that the crossover value $\epsilon_{_T}$ of largest Lyapunov exponent. Implications of this result are discussed.Comment: 6 pages, 5 figures, revtex4 styl

First and second order clustering transitions for a system with infinite-range attractive interaction

We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in a unique cluster. At higher energy it exhibits a transition towards a homogenous phase. For sufficiently strong coupling $A$ an intermediate phase characterized by two clusters appears. Depending on the value of $A$ the observed transitions can be either second or first order in the canonical ensemble. In the latter case microcanonical results differ dramatically from canonical ones. However, a canonical analysis, extended to metastable and unstable states, is able to describe the microcanonical equilibrium phase. In particular, a microcanonical negative specific heat regime is observed in the proximity of the transition whenever it is canonically discontinuous. In this regime, {\it microcanonically stable} states are shown to correspond to {\it saddles} of the Helmholtz free energy, located inside the spinodal region.Comment: 4 pages, Latex - 3 EPS Figs - Submitted to Phys. Rev.