A Self-adjointness Criterion for the Schroedinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators
A Self-adjointness Criterion for the Schroedinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators
复制标题
无穷多点相互作用薛定谔算子的自伴性判据及其在随机算子中的应用
DOI：
10.1007/s00023-019-00869-1
复制
发表时间：
2020
影响因子：
1.5
通讯作者：
Takuya Mine and Fumihiko Nakano
中科院分区：
文献类型：
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作者：
Masahiro Kaminaga;Takuya Mine and Fumihiko Nakano
我们证明了具有无穷多个点相互作用的Schrödinger算子，如果相互作用的支持被分解成无穷多个有界子集，使得。利用这一事实，证明了Schrödinger算子在晶格的随机扰动或泊松组态上具有点相互作用的自伴随性。我们还确定了具有泊松-安德森型随机点相互作用的Schrödinger算子的谱。
We prove the Schrödinger operator with infinitely many point interactions inis self-adjoint if the supportof the interactions is decomposed into infinitely many bounded subsetssuch that. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson–Anderson type.