Quantum graphs with singular two-particle interactions. / Bolte, Jens; Kerner, Joachim.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 4, 045206, 2013.

Research output: Contribution to journalArticle

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Abstract

We construct quantum models of two bosonic particles on a compact metric
graph with singular two-particle interactions. The Hamiltonians are self-adjoint
realisations of Laplacians acting on functions defined on pairs of edges in
such a way that the interaction is provided by boundary conditions. In order
to find such Hamiltonians closed and semi-bounded quadratic forms are
constructed, from which the associated self-adjoint operators are extracted.
We provide a general characterisation of such operators and, furthermore,
produce certain classes of examples. Finally, we show that these operators
possess purely discrete spectra and that the eigenvalues are distributed
following an appropriate Weyl asymptotic law.
Original languageEnglish
Article number045206
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number4
Early online date15 Jan 2013
DOIs
Publication statusPublished - 2013
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 4667402