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 -