Related papers: Mean field approximation for the dense charged dro…
We propose a method to extract nuclear charge distributions from elastic electron scattering data based upon a mean field approach. The nuclear charge distributions are generated by solving the Schroedinger equation with a mean-field…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…
Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis,…
This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
The mean field approximation is numerically validated in the bosonic case by considering the time evolution of quantum states and their associated reduced density matrices by many-body Schr\"odinger dynamics. The model phase-space is…
We develop an approximation scheme for our worldsheet model of the sum of planar diagrams based on mean field theory. At finite coupling the mean field equations show a weak coupling solution that resembles the perturbative diagrams and a…
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
We consider a test charged particle falling onto a Schwarzschild black hole and evaluate its electromagnetic field. The Regge-Wheeler equation is solved analytically by approximating the potential barrier with Dirac delta function and…
We describe a mean field technique for quantum string (or dimer) models. Unlike traditional mean field approaches, the method is general enough to include string condensed phases in addition to the usual symmetry breaking phases. Thus, it…
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are…
We present analytic expressions for the scattering of light by an extended atomic cloud. We obtain the solution for the mean-field excitation of different atomic spherical distributions driven by an uniform laser, including the initial…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schr\"odinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a…
We use the mean-field approximation to simplify the master equation for sympathetic cooling of Bosons. For the mean single-particle occupation numbers, this approach yields the same equations as the factorization assumption introduced in an…
We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…