Spectral theory of time-periodic many-body systems
Spectral theory of time-periodic many-body systems
复制标题
时间周期多体系统的谱论
DOI：
10.1016/j.aim.2003.10.003
复制
发表时间：
2004
影响因子：
1.7
通讯作者：
E. Skibsted
中科院分区：
文献类型：
--
作者：
J. S. Møller;E. Skibsted
研究了在时间平均为零的时间周期外场中N体量子系统的单值算符谱。这包括AC-斯塔克和圆极化场，以及具有局部奇异性直到（并包括）库仑奇异性的对势。在Floquet理论的框架下，我们证明了一个局部交换子估计，并用它来证明一个限制吸收原理的Floquet哈密顿量以及指数衰减估计的非阈值特征函数。这两个结果，然后用于获得嵌入本征值的二阶微扰理论。主要工具是一个新的扩展的神经网络理论。
We study the spectrum of the monodromy operator for an N-body quantum system in a time-periodic external field with time-mean equal to zero. This includes AC-Stark and circularly polarized fields, and pair potentials with a local singularity up to (and including) the Coulomb singularity. In the framework of Floquet theory we prove a local commutator estimate and use it to prove a Limiting Absorption Principle for the Floquet Hamiltonian as well as exponential decay estimates on non-threshold eigenfunctions. These two results are then used to obtain a second-order perturbation theory for embedded eigenvalues. The principal tool is a new extended Mourre theory.