Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 1Citation - Scopus: 1Rank One Perturbations Supported by Hybrid Geometries and Their Deformations(American Institute of Physics, 2022) Erman, Fatih; Seymen, Sema; Turgut, O. TeomanWe study the hybrid type of rank one perturbations in ℝ2 and ℝ3, where the perturbation supported by a circle/sphere is considered together with the delta potential supported by a point outside of the circle/sphere. The construction of a self-adjoint Hamiltonian operator associated with formal expressions for the rank one perturbation supported by a circle and by a point is explicitly given. Bound state energies and scattering properties for each problem are also studied. Finally, we consider the rank one perturbation supported by a deformed circle/sphere and show that the first order change in bound state energies under small deformations of the circle/sphere has a simple geometric interpretation.Article Citation - WoS: 5Citation - Scopus: 5A Many-Body Problem With Point Interactions on Two-Dimensional Manifolds(IOP Publishing Ltd., 2013) Erman, Fatih; Turgut, O. TeomanA 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.