Partially classical limit of the Nelson model
摘要
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a situation where the number of Bose excitations becomes infinite while the coupling constant tends to zero in a suitable sense. In that limit the appropriately rescaled Bose field converges to a classical solution of the free wave or Klein-Gordon equation depending on whether the mass of the field is zero or not, the quantum fluctuations around that solution satisfy the wave or Klein-Gordon equation and the evolution of the nonrelativistic particles is governed by a quantum dynamics with an external potential given by the previous classical solution.
引用
@article{arxiv.math-ph/0411046,
title = {Partially classical limit of the Nelson model},
author = {J. Ginibre and F. Nironi and G. Velo},
journal= {arXiv preprint arXiv:math-ph/0411046},
year = {2007}
}
备注
latex, 24 pages