WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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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: 2Non-Relativistic Lee Model in Two-Dimensional Riemannian Manifolds(American Institute of Physics, 2012) Erman, Fatih; Turgut, Osman TeomanThis work is a continuation of our previous work [F. Erman and O. T. Turgut, J. Math. Phys. 48, 122103 ( 2007)], where we constructed the non-relativistic Lee model in three-dimensional Riemannian manifolds. Here we renormalize the two-dimensional version by using the same methods and the results are shortly given since the calculations are basically the same as in the three-dimensional model. We also show that the ground state energy is bounded from below due to the upper bound of the heat kernel for compact and Cartan-Hadamard manifolds. In contrast to the construction of the model and the proof of the lower bound of the ground state energy, the mean field approximation to the two-dimensional model is not similar to the one in three dimensions and it requires a deeper analysis, which is the main result of this paper. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705355]Article Citation - WoS: 1Citation - Scopus: 2Nondegeneracy of the Ground State for Nonrelativistic Lee Model(American Institute of Physics, 2014) Erman, Fatih; Malkoç, Berkin; Turgut, Osman TeomanIn the present work, we first briefly sketch the construction of the nonrelativistic Lee model on Riemannian manifolds, introduced in our previous works. In this approach, the renormalized resolvent of the system is expressed in terms of a well-defined operator, called the principal operator, so as to obtain a finite formulation. Then, we show that the ground state of the nonrelativistic Lee model on compact Riemannian manifolds is nondegenerate using the explicit expression of the principal operator that we obtained. This is achieved by combining heat kernel methods with positivity improving semi-group approach and then applying these tools directly to the principal operator, rather than the Hamiltonian, without using cut-offs.Article Citation - WoS: 6Citation - Scopus: 7Existence of Hamiltonians for Some Singular Interactions on Manifolds(American Institute of Physics, 2012) Doğan, Çağlar; Erman, Fatih; Turgut, Osman TeomanThe existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.