Author:
Picari E.,Ponno A.,Zanelli L.
Abstract
AbstractWe prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative $$L^p$$
L
p
-estimate, for any $$p \ge 1$$
p
≥
1
, is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.
Funder
Università degli Studi di Padova
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics