Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Completeness Relation in Renormalized Quantum Systems(Frontiers Media SA, 2025) Erman, F.; Turgut, O.T.In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made precise by a renormalization scheme) supported at a point in two- and three-dimensional compact manifolds or Euclidean spaces. The formulation can be easily extended to an (Formula presented.) center case and the case where delta interaction is supported on curves in the plane or space. We finally give an interesting application for the sudden perturbation of the support of the delta potential. © © 2025 Erman and Turgut.Article Explicit Derivation of the Propagator for a Point Interaction in Three Dimensional Hyperbolic Space(Springer/plenum Publishers, 2024) Erman, FatihThe explicit expression for the propagator of the Dirac delta potential in three dimensional hyperbolic spaces is derived using the integral transform of the Krein's type of the resolvent formula, obtained after the renormalization procedure.Article Citation - WoS: 4Citation - Scopus: 4On Schrödinger Operators Modified by Δ Interactions(Academic Press, 2023) Akbaş, Kaya Güven; Erman, Fatih; Turgut, O. TeomanWe study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly. © 2023 Elsevier Inc.Article Citation - WoS: 12Citation - Scopus: 37Running of the Top Quark Mass From Proton-Proton Collisions at S=13 TeV(Elsevier B.V., 2020) Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Bergauer, T.; Dragicevic, M.; Erö, J.; Alves, G.A.The running of the top quark mass is experimentally investigated for the first time. The mass of the top quark in the modified minimal subtraction (MS‾) renormalization scheme is extracted from a comparison of the differential top quark-antiquark (tt¯) cross section as a function of the invariant mass of the tt¯ system to next-to-leading-order theoretical predictions. The differential cross section is determined at the parton level by means of a maximum-likelihood fit to distributions of final-state observables. The analysis is performed using tt¯ candidate events in the e± μ∓ channel in proton-proton collision data at a centre-of-mass energy of 13 TeV recorded by the CMS detector at the CERN LHC in 2016, corresponding to an integrated luminosity of 35.9fb−1. The extracted running is found to be compatible with the scale dependence predicted by the corresponding renormalization group equation. In this analysis, the running is probed up to a scale of the order of 1 TeV. © 2020 The Author(s)Article Citation - WoS: 2Citation - Scopus: 3Renormalization of Dirac Delta Potentials Through Minimal Extension of Heisenberg Algebra(IOP Publishing Ltd., 2017) Erman, FatihWe 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 regularization schemes given in the literature.Article Citation - WoS: 1Citation - Scopus: 1Recursion Formula for the Green's Function of a Hamiltonian for Several Types of Dirac Delta-Function Potentials in Curved Spaces(TUBITAK, 2016) Erman, FatihIn 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 delta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentials supported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulation allows us to find the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.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.Article Citation - WoS: 32Citation - Scopus: 32Quantum Renormalization of the Spin Hall Effect(American Physical Society, 2010) Gu, Bo; Gan, Jing-Yu; Bulut, Nejat; Ziman, Timothy; Guo, Guang-Yu; Nagaosa, Naoto; Maekawa, SadamichiBy quantum Monte Carlo simulation of a realistic multiorbital Anderson impurity model, we study the spin-orbit interaction (SOI) of an Fe impurity in Au host metal. We show, for the first time, that the SOI is strongly renormalized by the quantum spin fluctuation. Based on this mechanism, we can explain why the gigantic spin Hall effect in Au with Fe impurities was observed in recent experiments, while it is not visible in the anomalous Hall effect. In addition, we show that the SOI is strongly renormalized by the Coulomb correlation U. Based on this picture, we can explain past discrepancies in the calculated orbital angular momenta for an Fe impurity in an Au host. © 2010 The American Physical Society.