Related papers: Modulated Free Energy and Mean Field Limit

This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…

In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels…

This note extends the modulated entropy and free energy methods for proving mean-field limits/propagation of chaos to the whole space without any confining potential, in contrast to previous work limited to the torus or requiring…

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…

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…

The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting…

In models of $N$ interacting particles in $\R^d$ as in Density Functional Theory or crowd motion, the repulsive cost is usually described by a two-point function $c_\e(x,y) =\ell\Big(\frac{|x-y|}{\e}\Big)$ where $\ell: \R_+ \to [0,\infty]$…

We provide a proof of mean-field convergence of first-order dissipative or conservative dynamics of particles with Riesz-type singular interaction (the model interaction is an inverse power $s$ of the distance for any $0<s<d$) when assuming…

The cluster-based Mean Field method (cMF) and it's second order perturbative correction[1], was introduced by Jim\'enez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small…

Jarzynski's equality [1] allows us to investigate free energy landscapes (FELs) by constructing distributions of work performed on a system from an initial ensemble of states to final states. This work is experimentally measured by…

In recent years the shperical wave expansion method has been widely applied to the theory and calculation of electromagnetic fields. But the inner product exist in reference[1] is defined on the Banach space[2]. Through redefining the inner…

This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and…

The perturbative expansion introduced by Zwanzig [R. W. Zwanzig, J. Chem. Phys. {\bf 22}, 1420 (1954)] expresses the difference in Helmholtz free energy between a system of interest and that of a reference system as series of cumulants…

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…

Laser manipulation plays a critical role in precisely tailoring relativistic electron beams through energy modulation, enabling the generation of coherent, intense, and ultrashort radiation in accelerator-based light sources such as…

Here we present a fundamental comprehension of the microscopic mechanisms leading to the emergence of inverse melting transitions by considering a thorough mean-field analysis of a variety of minimal models with different competing…

In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…