论文标题
由超对称sigma模型引起的安德森模型状态的综合密度中的相变
Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model
论文作者
论文摘要
我们研究了与超对称Sigma-Model有关的某些加强随机过程中出现的随机Schrödinger操作员的综合密度（ID）。我们依靠对超对称Sigma模型的先前结果在所有维度的频谱底部附近ID的渐近行为上获得下限和上限。我们显示了较大或等于三个的弱障碍状态之间ID的相变，这是从相应的随机过程中的相变和超对称Sigma模型中的。特别是，我们表明，IDS在强大的疾病制度中没有表现出Lifshitz的尾巴，证实了最近的猜想。这与其他无序系统（如Anderson模型）形成鲜明对比。还会得出Wegner类型估计值，在ID上给出上限并显示函数的规律性。
We study the Integrated Density of States (IDS) of the random Schrödinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model. We rely on previous results on the supersymmetric sigma-model to obtain lower and upper bounds on the asymptotic behavior of the IDS near the bottom of the spectrum in all dimension. We show a phase transition for the IDS between weak and strong disorder regime in dimension larger or equal to three, that follows from a phase transition in the corresponding random process and supersymmetric sigma-model. In particular, we show that the IDS does not exhibit Lifshitz tails in the strong disorder regime, confirming a recent conjecture. This is in stark contrast with other disordered systems, like the Anderson model. A Wegner type estimate is also derived, giving an upper bound on the IDS and showing the regularity of the function.
