相关论文: Dynamics of trap models
We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed $p$-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
We report some results on the quenched disordered Spherical multi-$p$-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the…
Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition…
We follow the dynamic evolution of a cluster of Ising spins pointing up surrounded by other spins pointing down, on a lattice. The cluster represents a liquid drop. Under a microscopic point of view, the short range ferromagnetic coupling…
In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac…
We report on the stochastic dynamics of a few sodium atoms immersed in a cold potassium cloud. The studies are realized in a dual-species magneto-optical trap by continuously monitoring the emitted fluorescence of the two atomic species. We…
We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the…
This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…
We study the behavior of classical dimer coverings of the square lattice - a paradigmatic model for systems subject to constraints - evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We…
Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state…
We study the dynamics of a glassy model with infinite range interactions externally driven by an oscillatory force. We find a well-defined transition in the (Temperature-Amplitude-Frequency) phase diagram between (i) a `glassy' state…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…