Eigenvalue estimates for Schroedinger operators on metric trees

Abstract

We consider Schroedinger operators on regular metric trees and prove Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.

References in corpus (2)

• Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
• On semiclassical and universal inequalities for eigenvalues of quantum graphs

Cited by in corpus (6)

• NLS ground states on metric trees: existence results and open questions
• Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
• Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover
• On the absence of absolutely continuous spectra for Schrödinger operators on radial tree graphs
• On the Decomposition of the Laplacian on Metric Graphs
• On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy