Perturbative approach to time-dependent quantum systems and applications to one-crossing multistate Landau-Zener models

TL;DR

This paper develops a perturbative method to analyze multi-level time-dependent quantum systems, specifically deriving analytical transition probabilities for one-crossing multistate Landau-Zener models, providing benchmarks where exact solutions are unavailable.

Contribution

Introduces a perturbative approach for multi-level quantum systems with time-dependent parameters, deriving analytical transition probabilities for a class of Landau-Zener models.

Findings

Derived transition probabilities up to 4th order in couplings.

Provided analytical formulas serving as benchmarks for complex MLZ models.

Enhanced understanding of multi-level quantum dynamics with crossing points.

Abstract

We formulate a perturbative approach for studying a class of multi-level time-dependent quantum systems with constant off-diagonal couplings and diabatic energies being odd functions of time. Applying this approach to a general multistate Landau-Zener (MLZ) model with all diabatic levels crossing at one point (named the one-crossing MLZ model), we derive analytical formulas of all its transition probabilities up to $4$th order in the couplings. For one-crossing MLZ models it is difficult to obtain such analytical results by other kinds of approximation methods; thus, these perturbative results can serve as reliable benchmarks for future studies of any one-crossing MLZ models that have not been exactly solved.