Related papers: Mean field limit for many-particle interactions
Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter is proportional to…
We study the time evolution in system of $N$ bosons with a relativistic dispersion law interacting through an attractive Coulomb potential with coupling constant $G$. We consider the mean field scaling where $N$ tends to infinity, $G$ tends…
We study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
In our previous work \cite{GMM1},\cite{GMM2} we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
This paper proves the validity of the joint mean-field and classical limit of the quantum $N$-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure.…
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic…
We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean…
We consider a mean-field model to describe the dynamics of $N_1$ bosons of species one and $N_2$ bosons of species two in the limit as $N_1$ and $N_2$ go to infinity. We embed this model into Fock space and use it to describe the time…
We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the…
In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of $N$ $d$-dimensional bosons for large $N$. The…
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…
We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance $\rho>0$ from the initial BEC, the…
We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are…
We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and…
The mathematically exact solution of a one-dimensional (1D) quantum N-identical-boson system with zero-range pair interaction has been well known. We find that this solution is non-physical, since there exists a paradox of its energy…
We consider a stochastic $N$-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when $N\to \infty$. For any time $T>0$ we bound the distance between the empirical…