Related papers: Continuum approximations to systems of correlated …
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
We consider the motion of interacting particles governed by a coupled system of ODEs with random initial conditions. Direct computations for such systems are prohibitively expensive due to a very large number of particles and randomness…
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…
The tight-coupling approximation (TCA) used to describe the early dynamics of the baryons-photons system is systematically built to higher orders in the inverse of the interaction rate. This expansion can be either used to grasp the…
Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier…
In this work, which is based on our previously derived theoretical framework [1], we apply the truncated Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for ultracold bosonic systems with a fixed number of particles to two…
We present the algorithmic details of the dynamical cluster approximation (DCA) algorithm. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA). The DCA is…
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase space methods…
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality)…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
This paper develops a non-asymptotic, local approach to quantitative propagation of chaos for a wide class of mean field diffusive dynamics. For a system of $n$ interacting particles, the relative entropy between the marginal law of $k$…
We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for…
Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and…
We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued…
Many machine learning and optimization algorithms can be cast as instances of stochastic approximation (SA). The convergence rate of these algorithms is known to be slow, with the optimal mean squared error (MSE) of order $O(n^{-1})$. In…
We discuss a general treatment based on the mean field plus random phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method,…
The mean spherical approximation (MSA) is a closure relation for pair correlation functions (two-point functions) in statistical physics. It can be applied to a wide range of systems, is computationally fairly inexpensive, and when properly…
The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity…