一维“大”遍历系统的共振
Resonances for "large" ergodic systems in one dimension: a review
摘要：
本文综述了最近关于约束在大盒子中的一维量子各态历经系统共振态的研究结果。在离散情况下，我们仅限于一维模型。我们考虑了半轴上的两种遍历势：周期势和随机势。对于这两种模型，我们描述了一个大的典型样本的潜在的实轴附近的共振的行为。在这两种情况下，其实部的线性密度由全遍历系统的态密度给出。而在周期性的情况下，共振分布在一个很好的分析曲线上（一旦它们的虚部被适当地重正化），在随机的情况下，共振（再次在实部和虚部两者的适当重正化之后）形成二维泊松云。
英文摘要：
The present note reviews recent results on resonances for one-dimensional quantum ergodic systems constrained to a large box. We restrict ourselves to one dimensional models in the discrete case. We consider two type of ergodic potentials on the half-axis, periodic potentials and random potentials. For both models, we describe the behavior of the resonances near the real axis for a large typical sample of the potential. In both cases, the linear density of their real parts is given by the density of states of the full ergodic system. While in the periodic case, the resonances distribute on a nice analytic curve (once their imaginary parts are suitably renormalized), In the random case, the resonances (again after suitable renormalization of both the real and imaginary parts) form a two dimensional Poisson cloud.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
