TY - JOUR

T1 - A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators

AU - Kaminaga, Masahiro

AU - Mine, Takuya

AU - Nakano, Fumihiko

N1 - Funding Information:
The work of T. M. is partially supported by JSPS KAKENHI Grant No. JP18K03329. The work of F. N. is partially supported by JSPS KAKENHI Grant No. JP26400145.
Funding Information:
The work of T. M. is partially supported by JSPS KAKENHI Grant No. JP18K03329. The work of F. N. is partially supported by JSPS KAKENHI Grant No. JP26400145.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00023-019-00869-1

DO - 10.1007/s00023-019-00869-1

M3 - Article

AN - SCOPUS:85075126259

VL - 21

SP - 405

EP - 435

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 2

ER -