A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators

Masahiro Kaminaga, Takuya Mine, Fumihiko Nakano

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We prove the Schrödinger operator with infinitely many point interactions in Rd(d= 1 , 2 , 3) is self-adjoint if the support Γ of the interactions is decomposed into infinitely many bounded subsets {Γj}j such that inf j kdist (Γ j, Γ k) > 0. 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.

Original languageEnglish
Pages (from-to)405-435
Number of pages31
JournalAnnales Henri Poincare
Volume21
Issue number2
DOIs
Publication statusPublished - 2020 Feb 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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