Event

Talk
Schroedinger operators on equilateral quantum graphs
Dr. Konstantin Pankrashkin (HU Berlin)
18 Jul 2006, 16:30 – 17:30

Quantum graphs are one-dimensional singular manifolds together with differential operators on them (other names: quantum networks, quantum wires, metric graphs). Such objects have become very popular in the spectral theory, geometric analysis, and mathematical physics in the last years. We provide a description of the spectra of Schroedinger operators on a class of quantum graphs with identical edges in terms of the corresponding discrete Hamiltonians on the underlying combinatorial structures. This gives a rigorous justification of the de Gennes-Alexander correspondence between the tight-binding and quantum network spectra (as used in condensed matter physics) and extends the use of Hill determinants for periodic Sturm-Liouville problems to more general structures. Using this correspondence we provide some global estimates for the spectral gaps, which hold independently of the graph structure. Some open questions and perspectives will be discussed.

Related to:

• Konstantin Pankrashkin