Executive Summary : | Non-Hermitian (NH) topological systems have gained prominence in various fields, including quantum physics, optics, photonics, and condensed matter physics. One unique feature of NH systems is an exceptional point (EP), where both eigenvalues and eigenvectors become degenerate. Energy eigenvalues live on an N-sheeted Riemann surface near the EP, resulting in interesting topology around EPs. However, there is a lack of knowledge about higher order EPs and their properties. This project aims to explore the role of symmetry in higher order EPs, including breaking parity-time symmetry, time-reversal, charge-conjugation, inversion, and their combinations. The project also plans to explore the impact of driving on higher order EPs using the framework of Floquet theory, starting from Hamiltonians for higher order EPs. The aim is to gain a comprehensive understanding of different facets of higher order EPs. |