Wei-Norman-Kolokolov approach for Landau-Zener problems

TL;DR

This paper applies the Wei-Norman-Kolokolov method to analyze Landau-Zener tunneling in spin systems under time-dependent magnetic fields and colored noise, providing insights into quantum transition dynamics.

Contribution

It introduces a novel application of the Wei-Norman-Kolokolov approach to Landau-Zener problems involving arbitrary spins and noise regimes.

Findings

Effective description of tunneling probabilities under various noise conditions

Characterization of fast and slow noise regimes

Extension of Lie group techniques to complex spin systems

Abstract

The tunneling between the $2S+1$ Zeeman multiplets of an arbitrary spin $S$ using the $SU(2)$ Lie group exponential ordering Wei-Norman technique is investigated. A spin subjected to a regular time-dependent magnetic field and a transverse colored noise is considered and the regimes of fast and slow noise examined.