Eigenvalues restricted by Lyapunov exponent of eigenstates

TL;DR

This paper reveals that the Lyapunov exponent of eigenstates constrains eigenvalues, enabling non-Hermitian Hamiltonians to have real spectra without symmetry, thus opening new avenues in non-Hermitian physics research.

Contribution

It introduces a novel connection between Lyapunov exponents and eigenvalue restrictions in non-Hermitian systems, independent of symmetry considerations.

Findings

Lyapunov exponents restrict eigenvalues in non-Hermitian systems.

Real spectra can occur without symmetry if Lyapunov exponents inhibit imaginary parts.

New approach to studying non-Hermitian physics based on eigenstate properties.

Abstract

We point out that the Lyapunov exponent of the eigenstate places restrictions on the eigenvalue. Consequently, with regard to non-Hermitian systems, even without any symmetry, the non-conservative Hamiltonians can exhibit real spectra as long as Lyapunov exponents of eigenstates inhibit imaginary parts of eigenvalues. Our findings open up a new route to study non-Hermitian physics.