8 papers
Resolvent expansions for self-adjoint operators via boundary triplets
Yuri Latushkin, Selim Sukhtaiev
In this paper we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations of their domains. We use the abstract theory of boundary trip…
Random Hamiltonians with Arbitrary Point Interactions
David Damanik, Jake Fillman, Mark Helman +2
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real l…
Zero Measure and Singular Continuous Spectra for Quantum Graphs
David Damanik, Licheng Fang, Selim Sukhtaiev
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial sin…
Localization for Anderson Models on Metric and Discrete Tree Graphs
David Damanik, Jake Fillman, Selim Sukhtaiev
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contain…
An index theorem for Schrödinger operators on metric graphs
Yuri Latushkin, Selim Sukhtaiev
We show that the spectral flow of a one-parameter family of Schrödinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the ve…
Limits of Quantum Graph Operators With Shrinking Edges
Gregory Berkolaiko, Yuri Latushkin, Selim Sukhtaiev
We address the question of convergence of Schrödinger operators on metric graphs with general self-adjoint vertex conditions as lengths of some of graph's edges shrink to zero. We…