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Cem Yetişmişoğlu

Publications and source records attributed to Cem Yetişmişoğlu.

10 recordsLinked to original sources
arXiv2025

Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry

Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann's equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer matrix methods to deal with the corresponding scattering problems. We use a dynamical formulation of stationary scattering to study the low-frequency scattering of these waves when the inhomogeneities of the medium causing the scattering are confined to a planar slab. This formulation relies on the construction of an effective two-level non-Hermitian quantum system whose time-evolution operator determines the transfer matrix. We use it to construct the low-frequency expansions of the transfer matrix and the reflection and transmission coefficients of the medium, introduce a generalization of Brewster's angle for inhomogeneous slabs at low frequencies, and derive analytic conditions for transparency and reflectionlessness of PT-symmetric and non-PT-symmetric slabs at these frequencies. We also discuss the application of this method to deal with the low-frequency scattering of TE and TM waves when the carrier medium occupies a half-space and the waves satisfy boundary conditions with planar symmetry at the boundary of the half-space. Because acoustic waves propagating in a compressible fluid with planar symmetry are also described by Bergmann's equation, our results apply to the low-frequency scattering of these waves.

physics.optics↗
arXiv2024

Drinfel'd Doubles, Twists and All That... in Stringy Geometry and M Theory

Drinfel'd double of Lie bialgebroids plays an important role in T-duality of string theories. In the presence of $H$ and $R$ fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel'd double yields a Courant algebroid. However for U-duality, more complicated direct sum decompositions that are not described by dual vector bundles appear. In a previous work, we extended the notion of a Lie bialgebroid for vector bundles that are not necessarily dual. We achieved this by introducing a framework of calculus on algebroids and examining compatibility conditions for various algebroid properties in this framework. Here our aim is two-fold: extending our work on bialgebroids to include both $H$- and $R$-twists, and generalizing proto Lie bialgebroids to pairs of arbitrary vector bundles. To this end, we analyze various algebroid axioms and derive twisted compatibility conditions in the presence of twists. We introduce the notion of proto bialgebroids and their Drinfel'd doubles, where the former generalizes both bialgebroids and proto Lie bialgebroids. We also examine the most general form of vector bundle automorphisms of the double, related to twist matrices, that generate a new bracket from a given one. We analyze various examples from both physics and mathematics literatures in our framework.

hep-th↗
arXiv2023

Drinfel'd Double of Bialgebroids for String and M Theories: Dual Calculus Framework

We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the matched pairs of Leibniz algebroids. By examining a rather general set of fundamental algebroid axioms, we present the compatibility conditions between two calculi on vector bundles which are not dual in the usual sense. Given two algebroids equipped with calculi satisfying the compatibility conditions, we construct its double on their direct sum. This generalizes the Drinfel'd double of Lie bialgebroids. We discuss several examples from the literature including exceptional Courant brackets. Using Nambu-Poisson structures, we construct an explicit example, which is important both from physical and mathematical point of views. This example can be considered as the extension of triangular Lie bialgebroids in the realm of higher Courant algebroids, that automatically satisfy the compatibility conditions. We extend the Poisson generalized geometry by defining Nambu-Poisson exceptional generalized geometry and prove some preliminary results in this framework. We also comment on the global picture in the framework of formal rackoids and we slightly extend the notion for vector bundle valued metrics.

hep-th↗
arXiv2023

Discrete Dynamics and Supergeometry

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories. The latter are embedded symplectic submanifolds of an odd-dimensional symplectic structure. When suitably defined, symplectic geometry in odd dimensions is exactly the structure needed for covariance. A fundamentally probabilistic viewpoint allows classical supergeometries to describe discrete dynamics. We solve the problem of how to construct probabilistic measures on supermanifolds given a (possibly odd dimensional) supersymplectic structure. This relies on a superanalog of the Hodge star for differential forms and a description of probabilities by convex cones. We also show how stochastic processes such as Markov chains can be described by supergeometry.

math-ph↗
arXiv2022

A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions

Following earlier works of Dereli and collaborators, we study a three dimensional toy model where we extend the topologically massive gravity with electrodynamics by the most general $RF^2$-type non-minimal coupling terms. Here $R$ denotes the possible curvature terms and $F$ denotes the electromagnetic 2-form. We derive the variational field equations and look for exact solutions on constant negative curvature space-times with a constant, self-dual electromagnetic field. The notion of self-dual electromagnetic fields in three dimensions is introduced by Dereli and collaborators in the study of exact solutions of models with gravity-electromagnetism couplings. We note the conditions that the parameters of the model have to satisfy for these self-dual solutions to exist.

gr-qc↗
arXiv2020

The Variational Field Equations of Cosmological Topologically Massive Supergravity

We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. We compare these field equations with the partial results given in the literature using a second order variational formalism.

gr-qc↗
arXiv2019

Kaluza-Klein Reduction of the 6 Dimensional \\ Dirac Equation on $\mathbb{S}^3 \cong SU(2)$ and \\ Non-abelian Topological Insulators

In this work, the Kaluza-Klein reduction of the Dirac equation on a 6 dimensional spacetime $\mathbb{M}^{1+5} := \mathbb{M}^{1+2} \times \mathbb{S}^3$ is studied. Because of the group structure on $\mathbb{S}^3$, $\mathbb{M}^{1+5}$ can be seen as a principal $SU(2)$ bundle over the model Lorentzian spacetime $\mathbb{M}^{1+2}$. The dimensional reduction induces non-minimal $SU(2)$ couplings to the theory on $\mathbb{M}^{1+2}$. These interaction terms will be investigated by comparing with a minimally $SU(2)$ coupled Dirac equation on $\mathbb{M}^{1+2}$. We hope that these results may help us to understand non-abelian interactions of topological insulators.

math-ph↗