Biorthogonal scattering and generalized unitarity in non-Hermitian systems
Phys. Rev. A 113, 062213 – Published 11 June, 2026
DOI: https://doi.org/10.1103/1kjf-51c3
Abstract
We investigate the two-port scattering process in non-Hermitian dimer models via quantum measurements using external leads. We focus on two exemplary dimer models that preserve parity-time symmetry via spatial gain-loss balance and exhibit nonreciprocity due to directional hopping. The scattering matrix is constructed using the biorthogonality of the left and right scattering states of the Hamiltonian, allowing us to calculate the reflection and transmission probabilities. Our analysis compares the reflection and transmission coefficients derived from the left, right, and combined scattering states, revealing that, unlike in Hermitian systems, the non-Hermitian scattering process does not adhere to unitarity when considering only the right scattering states. Furthermore, non-Hermitian scattering can enhance the reflection and transmission probabilities, with distinct physical contributions arising from complex eigenvalues and the nonorthogonality of eigenstates, which can be isolated and analyzed separately in different minimal models. Our results clarify how biorthogonality restores generalized unitarity and identify distinct physical origins of enhanced transport in -symmetric and nonreciprocal dimers, providing insights into quantum transport in non-Hermitian systems.
