In a recent study, researchers have developed a generalized version of the Landau-Zener (LZ) formula for axion-photon conversion. The LZ formula is widely used in axion physics to calculate the axion-photon resonant conversion probability and relies on two assumptions: the coherence length of the magnetic field is much larger than the length over which the plasma frequency varies, and the resonance length is shorter than the scale of plasma variation. However, the researchers found that the LZ model is not accurate when the boundary is too close to the region of conversion, as determined by the resonance length, and when the conversion is adiabatic.

The researchers generalized the LZ formula to allow for an arbitrary location of the boundary, which enables them to model plasmas with arbitrary coherence lengths. This allows for a better understanding of the impact of plasma inhomogeneities on the conversion probability. The findings highlight the importance of considering alternative methods for analyzing resonant axions, especially when the boundary is close to the region of conversion. The researchers also suggest that the resonance occurs over a segment rather than a single point, which may be relevant for axion-photon conversion in three dimensions.

In conclusion, the study provides new insight into the axion-photon system and the potential limitations of the LZ formula in certain physical situations. These findings have implications for various astrophysical and cosmological contexts where axion-photon conversion is relevant, such as the conversion of dark matter axions into radio waves in the magnetosphere of a neutron star, conversions in the primordial magnetic field of the early universe, and spectral modifications of photon spectra from active galactic nuclei.