  We show that the coherent axion field spontaneously decays by emitting axion
particles via quantum tunneling if axion potential has more than one minimum.
By employing the $\hbar$-expansion and mean field approximation, we develop a
formalism to trace the real-time dynamics of the axion particle production
including its backreaction to the coherent axion field. We also present
numerical results for the time evolution of various physical quantities
including the strength of the coherent axion field, phase-space density of
produced axion particles, energy density, and pressure. Phenomenological
implications of our results are also discussed.
