Coherent versus incoherent amplification: from parametric resonance to the kinetic regime in stimulated axion decay

Although the spontaneous decay of axions into two photons is extremely slow on cosmological timescales, it can be strongly enhanced in environments with large bosonic occupation numbers. From a classical field perspective, stimulated axion decay is described by modified Maxwell equations. For a coherent axion background, these equations exhibit a parametric resonance characterized by a photon growth exponent s proportional to g aγ. By contrast, a standard kinetic description, for instance based on Boltzmann equations, involves the squared matrix element of the decay process and therefore would naturally predict a characteristic rate scaling as s proportional to g aγ squared. In this work, we show that these apparently different behaviors originate from the coherence properties of the axion field. Starting from an axion field with a finite momentum dispersion, we show how dephasing among its momentum modes modifies the photon instability and derive an effective evolution equation in which this effect is encoded in a kernel. For a continuous Maxwell-Boltzmann distribution of axion velocities, we obtain an implicit expression for the photon growth exponent that reproduces the two asymptotic regimes and provides an approximate description of the crossover. When amplification develops on scales shorter than the axion coherence length, the parametric resonance scaling s proportional to g aγ is recovered, whereas in the opposite limit an effectively kinetic behavior with s proportional to g aγ squared emerges. Although the detailed form of the crossover depends on the axion momentum distribution, we expect the asymptotic scaling with g aγ to be largely insensitive to the specific distribution assumed.