Related papers: Recent Applications of Dynamical Mean-Field Method…
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time…
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local…
The recent successes of deep learning and deep reinforcement learning have firmly established their statuses as state-of-the-art artificial learning techniques. However, longstanding drawbacks of these approaches, such as their poor sample…
Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme…
I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished:…
The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
We show that a family of disordered systems with non-relaxational dynamics may exhibit ``glassy'' behavior at nonzero temperature, although such a behavior appears to be ruled out by a face-value application of mean-field theory.…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of…
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for…
We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in…
An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium…
We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an…
There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived,…