Non-Hermitian dynamics of slowly-varying Hamiltonians

TL;DR

This paper presents a theoretical framework for non-Hermitian quantum dynamics with slowly-varying Hamiltonians, accurately describing phenomena like sudden transitions by incorporating complex eigen-energies and Berry connections.

Contribution

It introduces a new theoretical approach that accounts for adiabatic breakdown in non-Hermitian systems using Schur decompositions and closed-form state amplitude expressions.

Findings

Accurately models sudden transitions in two-level non-Hermitian systems.

Provides closed-form expressions for time-dependent state amplitudes.

Demonstrates the theory's effectiveness with a two-level system example.

Abstract

We develop a theoretical description of non-Hermitian time evolution that accounts for the break- down of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigen-energies as well as inter-band Berry connections calculated using basis sets from appropriately-chosen Schur decompositions. Using a two-level system as an example, we show that our theory accurately captures the phenomenon of "sudden transitions", where the system state abruptly jumps from one eigenstate to another.