44 citations · 281 across the 35 of their papers we have counts for
14 papers · 1 filter
Generalized Hamiltonian formalism for spatially nonlocal nonlinear differential equations
Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov
In this work, we develop a generalized Hamiltonian formalism for spatially nonlocal field theories whose Lagrangian densities depend explicitly on both the local field and its spat…
Hamiltonian formulation of the supersymmetric KdV equation
Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov
We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical versi…
Ising 100: review of solutions
Oğuz Alp Ağırbaş, Anıl Ata, Eren Demirci +13
We present several known solutions to the two-dimensional Ising model. This review originated from the ``Ising 100'' seminar series held at Boğaziçi University, Istanbul, in 2024.
Algebraic Structures Behind the Yang-Baxterization Process
Cansu Özdemir, Ilmar Gahramanov
We review the Yang-Baxterization process of braid group representations. We discuss the corresponding -CB algebras in the Yang-Baxterization process. We present diagrams of the…
The Gross-Pitaevskii equation from the Heisenberg spin chain
Osman Erkan Kaluc, Ilmar Gahramanov
In this paper, we revise the derivation of the Gross-Pitaevskii equation from the Heisenberg spin chain stressing physical aspects and all technicalities.
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…
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…
Bailey pairs for the q-hypergeometric integral pentagon identity
Ilmar Gahramanov, Osman Erkan Kaluc
In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality o…
Gamma function solutions to the star-triangle equation
Ege Eren, Ilmar Gahramanov, Shahriyar Jafarzade +1
In the paper, we clarify some relations between solutions to the star-triangle equation via the gauge/YBE correspondence. We consider two solutions to the star-triangle relation in…
Pentagon identities arising in supersymmetric gauge theory computations
Deniz N. Bozkurt, Ilmar Gahramanov
The partition functions of three-dimensional N=2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition fun…
Integrable lattice spin models from supersymmetric dualities
Ilmar Gahramanov, Shahriyar Jafarzade
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mec…
Comments on the multi-spin solution to the Yang-Baxter equation and basic hypergeometric sum/integral identity
Ilmar Gahramanov, Shahriyar Jafarzade
We present a multi-spin solution to the Yang-Baxter equation. The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights…
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Ilmar Gahramanov, Andrew P. Kels
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previous…
Mathematical structures behind supersymmetric dualities
Ilmar Gahramanov
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to p…