Field Mixing of Axions in Early Universe and in Condensed Matter

Motivated by Kaon mixing, we presented a general framework for (pseudo-)scalar fields mixing using both Keldysh formalism and quantum master equation, where a mixing between two fields is induced by common finite-temperature intermediate states. Results from both methods agree at the desired (leading) order of perturbation, in which we found a nonvanishing long-time correlation between two fields and an oscillation between populations of two species while the envelope of oscillations exhibits an exponential decaying behavior approaching to the thermal equilibrium set by the thermal intermediate states. The results imply that the axion condensate in the early universe may seed a parity asymmetry in other species, e.g., pions, which may be amplified by the instability near phase transitions. If the axion condensate persists until today, quasi-axionic excitations in some novel materials may be induced via the same mixing mechanism, providing a potential search scheme for cosmic axion with an efficiency proportional to the leading order of axion-photon coupling.