Biorthogonal scattering and generalized unitarity in non-Hermitian systems

TL;DR

This paper explores quantum scattering in non-Hermitian systems, revealing how biorthogonality restores a form of unitarity and elucidating the physical origins of enhanced transport in PT-symmetric and non-reciprocal dimers.

Contribution

It introduces a biorthogonal scattering framework for non-Hermitian systems, clarifying unitarity restoration and physical mechanisms behind transport enhancement.

Findings

Non-Hermitian scattering does not follow traditional unitarity when using only right states.

Biorthogonality restores generalized unitarity in non-Hermitian scattering.

Enhanced transport arises from complex eigenvalues and eigenstate non-orthogonality.

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 non-reciprocity 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 independently from complex eigenvalues and the non-orthogonality of eigenstates. Our results clarify how biorthogonality restores generalized unitarity and identify distinct physical origins of enhanced transport in PT-symmetric and non-reciprocal dimers, providing new insights into quantum transport in non-Hermitian systems.