Related papers: Mean-Field Coupled Systems and Self-Consistent Tra…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we…
We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross-effects, in the framework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a…
The circuit theory of mesoscopic transport provides a unified framework to describe spin-dependent or superconductivity-related phenomena. We extend this theory to hybrid systems of normal metals, ferromagnets and superconductors. Our main…
A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…
We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced…
We consider the relationship between the temperature at which averaged energy landscape properties change sharply ($T_{o}$), and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution…
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple…
The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems, as found in mathematical physics, neuroscience, economics, power systems and neural…
This article aims at quantifying the long time behavior of solutions of mean field PDE systems arising in the theory of Mean Field Games and McKean-Vlasov control. Our main contribution is to show well-posedness of the ergodic problem and…
The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given…
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular,…
We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic…
When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harvesters as competing rational agents, we are led to a…
We study the transition from a many-body localized phase to an ergodic phase in spin chain with correlated random magnetic fields. Using multiple statistical measures like gap statistics and extremal entanglement spectrum distributions, we…
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active…
We investigate the monitored dynamics of many-body quantum systems in which projective measurements of extensive operators are alternated with unitary evolution. Focusing on mean-field models characterized by all-to-all interactions, we…