Exact results for state-to-state transition probabilities in the multistate Landau-Zener model by non-stationary perturbation theory

TL;DR

This paper develops a new analytical approach using non-stationary perturbation theory to derive exact state-to-state transition probabilities in multistate Landau-Zener models, including degenerate cases.

Contribution

It introduces a novel technique for summing perturbation series and provides explicit formulas for transition probabilities in complex multistate scenarios.

Findings

Derived exact transition probabilities for non-degenerate cases.

Extended results to degenerate potential curves with multiple extreme slopes.

Validated analytical expressions for survival probabilities at specific potential curves.

Abstract

Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. New expressions for some state-to-state transition probabilities are derived in degenerate cases.