Non-random perturbations of the Anderson Hamiltonian in the 1-D case

作者：Holt J^*; Molchanov S; Vainberg B

来源：Applicable Analysis, 2013, 92(8): 1755-1765.

DOI：10.1080/00036811.2012.698272

• Anderson Hamiltonian
• Schrodinger operator
• negative eigenvalues

Recently (S. Molchanov and B. Vainberg, Non-random perturbations of the Anderson Hamiltonian, J. Spectral Theory 50 (2) (2011), pp. 179-195), two of the authors applied the Lieb method to the study of the negative spectrum for particular operators of the form H=H-0-W. Here, H-0 is the generator of the positive stochastic (or sub-stochastic) semigroup, W(x)0 and W(x)0 as x on some phase space X. They used the general results in several exotic%26apos; situations, among them the Anderson Hamiltonian H-0. In the 1-D case, the subject of this article, we will prove similar, but more precise results.

• 出版日期2013-8-1