论文标题
无限多个粒子的Hartree和Schrodinger方程的稳态稳定性
Stability of Steady States for Hartree and Schrodinger Equations for Infinitely Many Particles
论文作者
论文摘要
我们证明，对于随机场的Hartree方程，在某些稳态附近的散射结果。该方程描述了无限多个粒子系统的演变。这是对密度矩阵通常的hartree方程的类似公式。我们对待尺寸2和3，扩大了我们先前的结果。我们达到了大量的相互作用势，其中包括非线性Schrodinger方程。该结果在密度矩阵框架中有发病率。证明依赖于用于研究非线性Schrodinger方程散射的分散技术，以及使用明确的低频取消的使用，如Lewin和Sabin的工作。为了与密度矩阵相关，我们使用弗兰克和萨宾的正交系统的strichartz估计以及整体运营商的莱布尼兹规则。
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation for density matrices. We treat dimensions 2 and 3, extending our previous result. We reach a large class of interaction potentials, which includes the nonlinear Schrodinger equation. This result has an incidence in the density matrices framework. The proof relies on dispersive techniques used for the study of scattering for the nonlinear Schrodinger equation, and on the use of explicit low frequency cancellations as in the work of Lewin and Sabin. To relate to density matrices, we use Strichartz estimates for orthonormal systems from Frank and Sabin, and Leibniz rules for integral operators.
