On the applicability of the Landau-Zener formula to axion-photon conversion

TL;DR

This paper examines the limitations of the Landau-Zener formula in axion-photon conversion scenarios, deriving a generalized version and proposing an alternative approximation for cases where the original formula fails.

Contribution

The authors derive a generalized Landau-Zener formula accounting for plasma inhomogeneities and introduce a semi-classical approximation for regimes where the original formula is invalid.

Findings

LZ formula fails when oscillation range is small compared to the resonance region.

Failure of LZ is more severe in the adiabatic limit with slow plasma frequency variation.

The paper provides an alternative semi-classical approximation for certain inhomogeneous plasma conditions.

Abstract

Axions and photons resonantly interconvert in regions where the plasma frequency approximately equals the axion mass. This process is directly analogous to an avoided level crossing in quantum mechanics, for which the celebrated Landau-Zener (LZ) formula provides a simple, non-perturbative solution for the conversion probability. The LZ formula is commonly used in studies of axion-photon conversion; however, in this context, it relies on the assumption that the magnetic field variation is small compared to variations of the plasma frequency, which is frequently not the case in real plasmas. We derive a generalised version of the LZ formula by allowing the boundaries to be located at a scale that is similar to the inhomogeneities. We find that the LZ formula fails when the oscillation range is small compared to the resonance region. This failure is more severe in the adiabatic limit, when the plasma frequency varies slowly, resulting in a conversion probability that is not maximal as opposed to a naive application of the LZ formula. Moreover, we consider circumstances where the generalised LZ formula does not apply and present an alternative semi-classical approximation with complementary regime of validity.