On the spectrum of Schrödinger operators with a random potential
On the spectrum of Schrödinger operators with a random potential
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DOI：
10.1007/3-540-11192-1_68
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发表时间：
1982-09
影响因子：
2.4
通讯作者：
W. Kirsch;F. Martinelli
中科院分区：
文献类型：
--
作者：
W. Kirsch;F. Martinelli
研究了Hω算子的谱：Hω=−Δ+∑qi(ω)f(x−xi+ζi(ω))(qi(ω)和ζi(ω)独立同分布随机变量，i∈ℤd).我们建立了hω的谱与确定性周期薛定谔算子谱之间的强联系。由此，我们得到了在ω谱中存在“禁区”的条件。对于随机一维Kronig-Penney势和三维Kronig-Penney势，给出了它的谱。
We investigate the spectrum of Schrödinger operatorsHωof the type:Hω=−Δ+∑qi(ω)f(x−xi+ζi(ω))(qi(ω) and ζi(ω) independent identically distributed random variables,i∈ℤd). We establish a strong connection between the spectrum ofHωand the spectra of deterministic periodic Schrödinger operators. From this we derive a condition for the existence of “forbidden zones” in the spectrum ofHω. For random one- and three-dimensional Kronig-Penney potentials the spectrum is given explicitly.