Non-Hermitian Skin Effect

Boundary accumulation of non-Hermitian eigenmodes and failure of naive Bloch bulk spectra. The main concepts are non-Bloch bands, spectral winding, open boundaries. Each must be defined in the context of a concrete physical model, mathematical representation, or experimental task. Terminology alone does not establish the behavior of the system.

Non-Hermitian bands describe effective operators with gain, loss or asymmetric transport. In a nonreciprocal one-dimensional tight-binding model, different left and right hopping amplitudes can produce point-gap spectral winding and a dramatic difference between periodic- and open-boundary spectra. Many open-boundary eigenmodes then accumulate near one end of the chain. This skin effect is not implied by every imaginary on-site potential or every exceptional point.

Diagonalize finite chains under periodic and open boundary conditions, compare eigenvalue loci and map localization profiles. Test whether the observed spectral accumulation survives changing length and nonreciprocity, and quantify sensitivity to small boundary terms using pseudospectral analysis. Distinguish an engineered non-Hermitian effective Hamiltonian from the complete unitary evolution of a system plus environment.