Dynamics in non-Hermitian systems with nonreciprocal coupling

TL;DR

This paper explores how non-Hermitian systems with nonreciprocal coupling can inherently amplify states without external gain, due to complex eigenenergies and non-orthogonal eigenstates, revealing fundamental differences in amplification mechanisms.

Contribution

It introduces the concept of inherent amplification in non-Hermitian nonreciprocal systems and analyzes the roles of complex eigenenergies and non-orthogonal eigenstates.

Findings

Inherent amplification occurs without external gain.

Differences between amplification from complex eigenenergies and non-orthogonal eigenstates.

Analysis of two extreme Hamiltonian cases with distinct eigenenergy and eigenstate properties.

Abstract

We reveal that non-Hermitian Hamiltonians with nonreciprocal coupling can achieve amplification of initial states without external gain due to a kind of inherent source. We discuss the source and its effect on time evolution in terms of complex eigenenergies and non-orthogonal eigenstates. Demonstrating two extreme cases of Hamiltonians, namely one having complex eigenenergies with orthogonal eigenstates and one having real eigenenergies with non-orthogonal eigenstates, we elucidate the differences between the amplifications from complex eigenenergies and from non-orthogonal eigenstates.