Abstract:
Operators play a crucial role in the field of physics, especially in quantum mechanics and
optics, serving as mathematical tools for describing transformations and physical quantities.
While normal operators (i.e., Hermitian and unitary operators) have received significant
attention, less is known about non-normal operators that may emerge in various physical
systems and effects. Defective operators are a particular type of non-normal operator char
acterized by their non-diagonalizability. Recently, research has revealed the occurrence of
defective operators in systems with complete non-reciprocity of light and degeneracy of eigen
values and eigenvectors of Hamiltonian. These systems have important applications, such as
the isolation of light and quantum sensing. This thesis aims to investigate the physics and
applications of systems where defective operators arise.
