Related papers: Mean Field Theory for Lossy Nonlinear Composites
In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…
We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [1], the three minima of these potentials form a small…
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…
A mean-field theory based on Gibbs-Bogoliubov inequality is constructed to study the interactions between two like-charged polyions. It is shown that contrary to the previously established paradigm, a properly constructed mean-field theory…
We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…
Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep…
We study the predictions of three mean-field theoretical approaches in the description of the ground state properties of some spherical nuclei far from the stability line. We compare binding energies, single particle spectra, density…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
In this Review article, a brief description of the stochastic mean-field theory (SMF) for describing reaction dynamics in low-energy heavy-ion collisions at bombarding energies in the vicinity of the Coulomb barrier is presented. In these…
A generalized supersymmetric representation of the Hubbard operator algebra is considered. This representation is applied to the infinite-U Hubbard model. A mean-field theory which takes into account both on-site and inter-site virtual…
Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et. al. that the mean-field theory is exact for spin systems with non-additive long-range interactions. This is called…
Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…
Using the technique of mean field theory applied to the lattice boundary Ising and tricritical Ising models we provide a qualitative description of their boundary phase diagrams. We will show this is in agreement with the known picture from…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the…
We compare two widespread formulations of the mean-field approximation, based on minimizing an appropriately built mean-field free energy. We use the example of the antiferromagnetic Ising model to show that one of these formulations does…
We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method…
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…
A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…
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…