Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model

TL;DR

This paper extends the adiabatic-impulse approximation, a key concept of the Kibble-Zurek mechanism, to non-Hermitian Landau-Zener models, analyzing phase transitions and providing an exact solution.

Contribution

It generalizes the adiabatic-impulse approximation to non-Hermitian systems and presents an exact solution for the non-Hermitian Landau-Zener model.

Findings

The AI approximation can be applied to PT-symmetric non-Hermitian models.

The Kibble-Zurek mechanism is valid near critical points in non-Hermitian systems.

An exact solution to the non-Hermitian LZ problem is provided.

Abstract

We investigate the transition from PT-symmetry to PT-symmetry breaking and vice versa in the non-Hermitian Landau-Zener (LZ) models. The energy is generally complex, so the relaxation rate of the system is set by the absolute value of the gap. To illustrate the dynamics of phase transitions, the relative population is introduced to calculate the defect density in nonequilibrium phase transitions instead of the excitations in the Hermitian systems. The result shows that the adiabatic-impulse (AI) approximation, which is the key concept of the Kibble-Zurek (KZ) mechanism in the Hermitian systems, can be generalized to the PT-symmetric non-Hermitian LZ models to study the dynamics in the vicinity of a critical point. Therefore, the KZ mechanism in the simplest non-Hermitian two-level models is presented. Finally, an exact solution to the non-Hermitian LZ-like problem is also shown.