相关论文: Second order corrections to mean field evolution f…

We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of…

In this paper, we investigate the dynamics of a system of $N$ weakly interacting bosons with singular three-body interactions in three dimensions. By assuming factorized initial data $\Psi_{N,0}=\varphi_{0}^{\otimes N}$ and triple…

Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a…

This note shows that, with a little modification, the results in arXiv:0904.0158 hold in the 3-body interactions case.

We consider the evolution of N bosons, where N is large, with two-body interactions of the form $N^{3\beta}v(N^\beta \cdot)$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of interactions. We compare the exact evolution…

We provide an error bound for approximating the time evolution of N bosons by a generalized nonlinear Hartree equation. The bosons are assumed to interact via permutation symmetric bounded many-particle potentials and the initial…

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…

We consider the dynamics of a large number N of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to describe the fluctuations around the mean field Hartree…

We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3\beta-1} w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and large $N$, we obtain a norm approximation to…

The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a…

We present a systematic derivation of the Heisenberg evolution of a trilinear bosonic Hamiltonian system in presence of a strong drive beyond the standard approximation of a classical, undepleted driving field. We employ a perturbative…

We consider interacting $N$-Bosons in three dimensions. It is known that the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$. We investigate the time…

We study the many body Schr\"odinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles.…

A Hartree-Bose mean-field approximation for the IBM-3 is presented. A Hartree- Bose transformation from spherical to deformed bosons with charge-dependent parameters is proposed which allows bosonic pair correlations and includes higher…

We calculate the renormalized Fermi surface and the quasiparticle properties in the Fermi liquid phase of three-dimensional dipolar fermions to second order in the dipole-dipole interaction. Using parameters relevant to an ultracold gas of…

We consider a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference…

In this work, an effective fermion model with particular higher order interactions given by: $I_{II} = \sum_n^N g_{2^n} (\bar{\psi}_a \psi_a)^{2^n}$, for finite $N$, is investigated by means of the auxiliary field method by taking into…

We present a calculation of next-to-leading order QCD corrections to gamma jj production via weak-boson fusion at a hadron collider in the form of a flexible parton-level Monte Carlo program which allows us to study cross sections and…

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 a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schr\"odinger evolution in the mean-field regime and the effective…