Speaker
Description
Physicists are trained to analyze spectra, such as energies, frequencies, and other observables. However, spectra can become ill-conditioned when the underlying operator is highly non-normal, i.e. when it does not commute with its Hermitian conjugate. In such cases, spectral instabilities emerge that typically become more severe with increasing system size. Despite this, spectral measures are commonly used even in regimes where non-normality is strong.
In this talk, we consider open quantum systems whose dynamics are described by Lindblad master equations. By analyzing two simple, non-chaotic models, we demonstrate how their Liouvillian spectra may nevertheless exhibit signatures reminiscent of full level repulsion and chaotic spectral statistics. We show that this is an artifact of spectral instability, where numerical round-off errors are amplified by non-normality.
Our results suggest that spectral diagnostics provide only limited information about systems with strong non-normality, and that alternative measures are required. Such measures should be based on physically meaningful and numerically robust quantities. More broadly, our findings raise a fundamental question: what physical information is actually encoded in the spectra of non-Hermitian or non-normal operators?