Non-Hermitian systems

As it is known, real systems are not completely decoupled from their environment. Many physical systems are open and may include gain and loss mechanisms that account for the flow of energy and particles between the system and environment. In many cases, the environment's effect can be considered by introducing non-Hermitian terms. Therefore, studying non-Hermitian techniques that describe open, lossy systems is essential. A key feature of non-Hermitian topological insulators is the non-Hermitian skin effect (NHSE), where a large number of eigenstates accumulate at the boundary of the system. It has been shown that NHSE can modify the band topology and break down the bulk-boundary correspondence [1]. In this chapter, I will briefly discuss non-Hermitian systems, focusing on what is essential for transport. I will introduce a biorthogonal response theory and, using Green function techniques, study a generic two-level non-Hermitian Hamiltonian. The interested reader can find more details in the references.