Non-Adiabatic Transition in Spin-Boson Model and Generalization of the Landau-Zener Formula

TL;DR

This paper extends the Landau-Zener formula to multiple scattering points in a spin-boson model by introducing an effective gap, with the generalized formula matching numerical results and aiding experimental analysis.

Contribution

The paper introduces a generalized Landau-Zener formula for multiple scattering points in a spin-boson model using an effective gap concept.

Findings

Generalized formula agrees with numerical simulations

Effective gap accurately captures non-adiabatic transition behavior

Enhances analysis of magnetic-moment inversion experiments

Abstract

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau-Zener formula, which describes the case of a single scattering point, we define an ``effective gap'' for a set of scattering points. The generalized formula agrees very well with numerical results of the non-adiabatic dynamics, which we obtained by a direct numerical method. This will make the Landau-Zener formula yet more useful in analyzing experimental data of magnetic-moment inversion.