Absolutely Continuous Spectrum and Spectral Transition for some Continuous Random Operators

Proceedings Mathematical Sciences

M Krishna¹ 

[1] Institute of Mathematical Sciences, Taramani, Chennai 00 , India$$

关键词: Random operators;    a.c. spectrum.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we consider two classes of random Hamiltonians on $L^2(mathbb{R}^d)$: one that imitates the lattice case and the other a Schrödinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for the Anderson model in higher dimension.

【 授权许可】

Unknown