标题： 三维随机哈特里非线性薛定谔方程来自具有白噪声势的多体量子系统 显示英文标题

标题： Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential

摘要： 本文中，我们考虑了在三维环面 \(T^3\) 上具有白噪声外势的无聚焦Hartree非线性薛定谔方程，即线性部分由安德森哈密顿量给出的Hartree非线性薛定谔方程。通过摄动论证建立了关于安德森哈密顿量的Strichartz型估计，并在安德森哈密顿量的定义域和形式域上考虑了不同正则性假设下的Hartree相互作用下初值问题的整体和局部适定性。此外，我们建立了安德森Hartree非线性薛定谔方程作为描述多体玻色系统的有效方程，并且特别证明了对于库仑相互作用，多体系统的线性薛定谔方程收敛于BBGKY层次结构。 显示英文摘要

摘要： In this paper, we consider the defocusing Hartree NLS with white noise external potential on T^3 i.e. the Hartree NLS whose linear part is given by the Anderson Hamiltonian. A Strichartz-type estimate is established for the Anderson Hamiltonian using perturbative arguments and the local and global well-posedness of the NLS is considered with initial data in the domain and form-domain of the Anderson Hamiltonian under different regularity assumptions on the Hartree interaction. Furthermore, we establish the Anderson Hartree NLS as an effective equation describing many-body Bosonic systems and, in particular, we prove the convergence of the linear Schr\"odinger equation for the many body system to the BBGKY hierarchy for the Coulomb interaction.