Landau-Zener transitions through a pair of higher order exceptional points

TL;DR

This paper introduces a PT-symmetric non-Hermitian N-level Landau-Zener model with two higher-order exceptional points, deriving transition probabilities and analyzing adiabatic behavior despite non-Hermitian breakdown.

Contribution

It presents an analytically solvable model with two higher-order exceptional points, expanding understanding of non-Hermitian Landau-Zener dynamics.

Findings

Transition probabilities follow a binomial pattern.

Final populations relate to binomial coefficient ratios.

Adiabatic analysis explains behavior despite non-Hermitian breakdown.

Abstract

Non-Hermitian quantum systems with explicit time dependence are of ever-increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a PT-symmetric non-Hermitian $N$-level Landau-Zener type problem with two exceptional points of $N$th order is introduced. The system is Hermitian for asymptotically large times, far away from the exceptional points, and has purely imaginary eigenvalues between the exceptional points. The full Landau-Zener transition probabilities are derived, and found to show a characteristic binomial behaviour. In the adiabatic limit the final populations are given by the ratios of binomial coefficients. It is demonstrated how this behaviour can be understood on the basis of adiabatic analysis, despite the breakdown of adiabaticity that is often associated with non-Hermitian systems.