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Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…
Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise…
The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this…
A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
The LSW model with encounters has been suggested by Lifshitz and Slyozov as a regularization of their classical mean-field model for domain coarsening to obtain universal self-similar long-time behavior. We rigorously establish that an…
We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The…
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…
We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one…
We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…
Glassiness occurs when disorder and frustration cause local degrees of freedom to freeze despite the lack of long-range order. In systems of interacting bosons, such glassiness may involve a purely quantum degree of…
The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple…
The exact mean-field theory for the simplest glass-forming system - the dense assembly of hard spheres in the large dimensional limit - predicts the existence of a Gardner phase. This transition is characterized by full replica symmetry…