Ece Özdemir (Pamukkale University, Turkey)
Abstract: In this talk, we examine the spectral properties of the non-self adjoint Hill operator, focusing on the asymptotic behavior of its eigenvalues. We consider a class of specially constructed complex-valued potentials and investigate the conditionsunder which these potentials give rise to isospectrality that is, when different potentials yield identical spectra for the same operator.
As a particular case, we study PT-symmetric potentials and analyze how their structural symmetry influences spectral properties. PT-symmetric potentials are of particular interest due to their prominent role in non-Hermitian quantum mechanics, where they often lead to entirely real spectra despite the lack of Hermiticity. This surprising behavior has made PT-symmetric systems a subject of intense study in both mathematics and physics.
This work contributes to the ongoing investigation of spectral behavior and isospectral conditions for non-self adjoint differential operators with complex potentials.
