The spectral minimum for random displacement models
Let a potential \(V\) be given as follows: Fix a single-site potential \(f\) which is supported in an interval of length less than 1. Construct \(V\) by placing a translate of \(f\) into each unit interval \([n,n+1]\) for an integer \(n\), where otherwise the positions of each translate are arbitrary. The main question of the paper is: Which configuration of single site minimizes the spectral minimum of Schrödinger operator with potential \(V\)? A conjecture on the solution of this question is formulated. A partial result toward its verification is proved. Results of numerical calculations, providing additional evidence for correctness of the conjecture, are presented.
scientific article; zbMATH DE number 1872878