General theory of slow non-Hermitian evolution

TL;DR

This paper develops a comprehensive theory for slow non-Hermitian system evolution, resolving contradictions in existing results, and demonstrating that the final state depends only on the final Hamiltonian, with implications for experimental and device applications.

Contribution

It introduces a generalized adiabatic theorem for non-Hermitian systems, including effects of noise, and clarifies the final state determination, advancing understanding of non-Hermitian dynamics.

Findings

Proves an adiabatic theorem for non-Hermitian systems.

Shows the final state depends only on the final Hamiltonian.

Provides tools for predicting system evolution without extensive simulations.

Abstract

Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research, showcasing surprising behaviors that include apparent violation of the adiabatic theorem and chiral topological conversion related to encircling exceptional points (EPs). These have both fundamental interest and potential practical applications. Yet the current literature features a number of apparently irreconcilable results. Here we develop a general theory for slow evolution of non-Hermitian systems and resolve these contradictions. We prove an analog of the adiabatic theorem for non-Hermitian systems and generalize it in the presence of uncontrolled environmental fluctuations (noise). The effect of noise turns out to be crucial due to inherent exponential instabilities present in non-Hermitian systems. Disproving common wisdom, the end state of the system is determined by the final Hamiltonian only, and is insensitive to other details of the evolution trajectory in parameter space. Our quantitative theory, leading to transparent physical intuition, is amenable to experimental tests. It provides efficient tools to predict the outcome of the system's evolution, avoiding the need to follow costly time-evolution simulations. Our approach may be useful for designing devices based on non-Hermitian physics and may stimulate analyses of classical and quantum non-Hermitian-Hamiltonian dynamics, as well as that of quantum Lindbladian and hybrid-Liouvillian systems.