## 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.

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 language | English |
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Article number | 045206 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 4 |

Early online date | 15 Jan 2013 |

DOIs | |

Publication status | Published - 2013 |