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32 papers · 1 filter
On Schrödinger Operators Modified by Interactions
Kaya Güven Akbaş, Fatih Erman, O. Teoman Turgut
We study the spectral properties of a Schrödinger operator modified by interactions and show explicitly how the poles of the new Green's function are rearranged relative…
Hamiltonian formalism for nonlinear Schrödinger equations
Ali Pazarci, Umut Can Turhan, Nader Ghazanfari +1
We study the Hamiltonian formalism for second order and fourth order nonlinear Schrödinger equations. In the case of second order equation, we consider cubic and logarithmic nonlin…
Rank One Perturbations Supported by Hybrid Geometries and Their Deformations
Fatih Erman, Sema Seymen, Osman Teoman Turgut
We study the hybrid type of rank one perturbations in and , where the perturbation supported by a circle/sphere is considered together with the delta p…
Variational symmetries of Lagrangian systems with higher-order derivatives
Ege Coban, Ilmar Gahramanov, Dilara Kosva
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples…
A Direct Method For the Low Energy Scattering Solution of Delta Shell Potentials
Fatih Erman, Sema Seymen
A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one usin…
Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors
Mikhail B. Sheftel
The complex Monge-Ampère equation in a two-component form is treated as a bi-Hamiltonian system. I present explicitly the first nonlocal symmetry flow in each of the two hi…
Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations
M. B. Sheftel, D. Yazıcı
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown enters only in the form of the 2nd-order partial derivatives. For such equations which possess a…
Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
Mikhail B. Sheftel, Devrim Yazıcı
We show that evolutionary Hirota type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Ampère form. We consider integrable equations of this type in the sense t…
Quantum Mechanics on Periodic and Non-Periodic Lattices and Almost Unitary Schwinger Operators
Metin Arik, Medine Ildes
In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operato…
Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
Mikhail B. Sheftel, Devrim Yazıcı
We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmet…
On the Thermodynamic Limit of Bogoluibov's Theory of Bose Gas
Levent Akant, Ebru Dogan, Emine Ertugrul +1
Assuming that Bogoliubov's theory of weakly interacting dilute Bose gas defines a self-consistent model Hamiltonian, we investigate its thermodynamic limit as we take the volume to…
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
M. B. Sheftel, A. A. Malykh, D. Yazıcı
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equ…
Infinitely many singular interactions on noncompact manifolds
Burak Tevfik Kaynak, O. Teoman Turgut
We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separa…
Exact results for a toy model exhibiting dynamic criticality
David C. Kaspar, Muhittin Mungan
In this article we discuss an exactly solvable, one-dimensional, periodic toy charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103}, 46002 (2013)]. In part…
Nondegeneracy of the Ground State for Nonrelativistic Lee Model
Fatih Erman, Berkin Malkoc, Osman Teoman Turgut
In the present work, we first briefly sketch construction of the nonrelativistic Lee model on Riemannian manifolds, introduced in our previous works. In this approach, the renormal…
Bose-Einstein Condensation on a Manifold with Nonnegative Ricci Curvature
Levent Akant, Emine Ertugrul, Ferzan Tapramaz +1
The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kern…
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors
Mikhail B. Sheftel, Andrei A. Malykh
We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can…
Compact submanifolds supporting singular interactions
Burak Tevfik Kaynak, O. Teoman Turgut
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the p…
A Many-body Problem with Point Interactions on Two Dimensional Manifolds
Fatih Erman, O. Teoman Turgut
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 D…
A Klein Gordon Particle Captured by Embedded Curves
Burak Tevfik Kaynak, O. Teoman Turgut
In the present work, a Klein Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspectiv…
Singular interactions supported by embedded curves
Burak Tevfik Kaynak, O. Teoman Turgut
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We…
Existence of Hamiltonians for Some Singular Interactions on Manifolds
Çağlar Doğan, Fatih Erman, O. Teoman Turgut
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…
Non-relativistic Lee Model on two Dimensional Riemannian Manifolds
Fatih Erman, O. Teoman Turgut
This work is a continuation of our previous work (JMP, Vol. 48, 12, pp. 122103-1-122103-20, 2007), where we constructed the non-relativistic Lee model in three dimensional Riemanni…
General heavenly equation governs anti-self-dual gravity
A. A. Malykh, M. B. Sheftel
We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov \cite{fer}, governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric go…