Related papers: Mean field theory for a general class of short-ran…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
A dilute homogeneous 3D Fermi gas in the ground state is considered for the case of a repulsive pairwise interaction. The low-density (dilution) expansions for the kinetic and interaction energies of the system in question are calculated up…
We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean field models. The microscopic model is based on three…
We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology…
We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions,…
Optimization problems on probability measures in $\mathbb{R}^d$ are considered where the cost functional involves multi-marginal optimal transport. In a model of $N$ interacting particles, like in Density Functional Theory, the interaction…
The present paper is based on our graduate lectures in condensed-matter physics. We found that the mean-field solution of the Hubbard model is an excellent tool to stimulate students' reflections towards the treatment of realistic magnetic…
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in…
Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…
We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature,…
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation…
Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields…
Narrow resonances in systems with short-range interactions are discussed in an effective field theory (EFT) framework. An effective Lagrangian is formulated in the form of a combined expansion in powers of a momentum Q << Lambda--a…
We consider the mean-field limit of systems of particles with singular interactions of the type $-\log|x|$ or $|x|^{-s}$, with $0< s<d-2$, and with an additive noise in dimensions $d \geq 3$. We use a modulated-energy approach to prove a…
We study the interplay between repulsive interaction and an almost staggered on-site potential in one-dimension. Specifically, we address the Harper model for spinless fermions with nearest-neighbor repulsion, close to half-filling. Using…
We address the issue of determining an effective two-body interaction for mean-field calculations of energies of many-body systems. We show that the effective interaction is proportional to the phase shift, and demonstrate this result in…
The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with…
Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+\Delta H, where \Delta H is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a…