arXiv subjects
Publications and source records attributed to Ji Oon Lee.
The mean field dynamics of an $N$-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schrödinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty} (\mathbb{R}^3)$.
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 Schrödinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.
Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $Λ$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $ρ= N / L^3$ fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, Λ)}{N} \geq 4 πa ρ[ 1 - O(ρ^{1/3} |\log ρ|^3) ],$$ as $ρ\to 0$, where $a$ is the scattering length of $V$.
It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is $E=4πa ρN$ when the particles interact via a non-negative, finite range, symmetric, two-body potential. Here, $N$ is the number of particles, $ρ$ is the density of the gas, and $a$ is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.