Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5341
Title: A many-body problem with point interactions on two-dimensional manifolds
Authors: Erman, Fatih
Turgut, O. Teoman
Erman, Fatih
Keywords: Bosons
Renormalization
Quantum mechanics
Bound states
Renormalization group equations
Wavefunction
Issue Date: Feb-2013
Publisher: IOP Publishing Ltd.
Source: Erman, F., and Turgut, O.T. (2013). A many-body problem with point interactions on two-dimensional manifolds. Journal of Physics A: Mathematical and Theoretical, 46(5). doi:10.1088/1751-8113/46/5/055401.
Abstract: A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two-dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean-field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the beta function is exactly calculated for the general case, which includes all particle numbers.
URI: https://doi.org/10.1088/1751-8113/46/5/055401
http://hdl.handle.net/11147/5341
ISSN: 1751-8113
1751-8121
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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