arXiv subjects

İsmail Burak Ateş

Publications and source records attributed to İsmail Burak Ateş.

3 recordsLinked to original sources

arXiv2026

Expected values for SUSY hierarchies of Jaynes-Cummings Hamiltonian

The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.

quant-ph↗

arXiv2025

SUSY hierarchies of Jaynes-Cummings Hamiltonians with different detuning parameters

The aim of this work is to show how supersymmetric (SUSY) quantum mechanics can be applied to the Jaynes-Cummings (JC) Hamiltonian of quantum optics. These SUSY transformations connect pairs of Jaynes-Cummings Hamiltonians characterized by different detuning parameters as well as Jaynes-Cummings to anti-Jaynes-Cummings Hamiltonians. Therefore, JC Hamiltonians can be classified in hierarchies or sequences which are connected through SUSY transformations. As a byproduct, the symmetries of JC Hamiltonians are found as well as the special case of a sequence of resonant-like interacting systems having the form of a simple shape invariant JC Hamiltonian hierarchy.

math-ph↗

arXiv2022

Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well

In this paper, a simple method is proposed to get analytical solutions (or with the help of a finite numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic fields. In order to decouple the Dirac-Weyl equation we have assumed a displacement symmetry of the system along a direction and some conditions on the magnetic and electric fields. The resulting equations have the natural form to apply the technique of supersymmetric quantum mechanics. The example of an electric well with square profile is worked out in detail to illustrate some of the most interesting features of this procedure.

math-ph↗