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Browsing by Author "Erman, Fatih"
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Existence of Hamiltonians for some singular interactions on manifolds
Doğan, Çağlar; Erman, Fatih; Turgut, O. Teoman (American Institute of Physics Publising, 201204)The 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 ... 
Green's function formulation of multiple nonlinear Dirac deltafunction potential in one dimension
Erman, Fatih; Uncu, Haydar (Elsevier, 2020)In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then ... 
A manybody problem with point interactions on twodimensional manifolds
Erman, Fatih; Turgut, O. Teoman (IOP Publishing, 201302)A nonperturbative renormalization of a manybody problem, where nonrelativistic bosons living on a twodimensional Riemannian manifold interact with each other via the twobody Dirac delta potential, is given by the help ... 
Nondegeneracy of the ground state for nonrelativistic Lee model
Erman, Fatih; Malkoç, Berkin; Turgut, Osman Teoman (American Institute of Physics Publising, 201408)In 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 ... 
On scattering from the onedimensional multiple Dirac delta potentials
Erman, Fatih; Gadella, Manuel; Uncu, Haydar (Institute of Physics Publishing, 201803)In this paper, we propose a pedagogical presentation of the LippmannSchwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a onedimensional system with a ... 
On the number of bound states of point interactions on hyperbolic manifolds
Erman, Fatih (World Scientific Publishing, 201701)We study the bound state problem for N attractive point Dirac δinteractions in two and threedimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit ... 
On the number of bound states of semirelativistic Hamiltonian with Dirac delta potentials in one dimension
Erman, Fatih (Canadian Science Publishing, Nrc Research Press, 2018)We study the bound state problem for semirelativistic N attractive Dirac deltapotentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it. 
Onedimensional semirelativistic Hamiltonian with multiple Dirac delta potentials
Erman, Fatih; Gadella, Manuel; Uncu, Haydar (Amer Physical Soc, 2017)In this paper, we consider the onedimensional semirelativistic Schrdinger equation for a particle interacting with N Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of ... 
A perturbative approach to the tunneling phenomena
Erman, Fatih; Turgut, Osman Teoman (Frontiers Media S.A., 201905)The doublewell potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely pathintegral, WKB, and instanton calculations. ... 
Point interactions in quantum mechanics
Tunalı, Seçil (Izmir Institute of Technology, 2014)In this thesis, the point interactions in quantum mechanics in the context of renormalization are reviewed. Some spectral properties for special configuration of the centers of point interactions are given in detail. ... 
The Propagators for delta and delta ' Potentials With TimeDependent Strengths
Erman, Fatih; Gadella, Manuel; Uncu, Haydar (Frontiers Media Sa, 2020)We study the timedependent Schrodinger equation with finite number of Dirac delta and delta ' potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths ... 
Recursion formula for the Green's function of a Hamiltonian for several types of Dirac deltafunction potentials in curved spaces
Erman, Fatih (TÜBİTAK, 2016)In this short article, we nonperturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Dirac ... 
Renormalization of Dirac delta potentials through minimal extension of Heisenberg algebra
Erman, Fatih (IOP Publishing, 201709)We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other ... 
A singular onedimensional bound state problem and its degeneracies
Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, Haydar (Springer, 201708)We give a brief exposition of the formulation of the bound state problem for the onedimensional system of N attractive Dirac delta potentials, as an N× N matrix eigenvalue problem (ΦA= ωA). The main aim of this paper is ... 
Solitonic solutions and particle localization in higher dimensional spaces
Erman, Fatih (Izmir Institute of Technology, 2003)First the basic extra dimensional theory (i.e. KaluzaKlein theory) and the main aspects of solitons are reviewed. Then the current status of extra dimensional models and the application of solitons (especially kinks) in ...