Comment on "Exact results for survival probability in the multistate Landau-Zener model"

TL;DR

This paper corrects the proof of the Brundobler-Elser formula for multistate Landau-Zener models, clarifying the mathematical approach and establishing a connection to the bow-tie model for better understanding of survival probabilities.

Contribution

It provides a corrected proof of the BEF, introduces an alternative variable change, and links the BEF to the solvable bow-tie model, enhancing theoretical understanding.

Findings

Corrected the proof of the BEF for multistate Landau-Zener models.

Established a connection between the BEF and the bow-tie model.

Highlighted the significance of extremal slope diabatic levels.

Abstract

We correct the proof of Brundobler-Elser formula (BEF) provided in [2004 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907]. After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general $N$-level Landau-Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.