  We introduce an effective field theory to study \emph{indirect} mixing of two
fields induced by their couplings to a common decay channel in a medium. The
extension of the method of Lee, Oehme and Yang, the cornerstone of analysis of
CP violation in flavored mesons, to include mixing of particles with different
masses provides a guide to and benchmark for the effective field theory. The
analysis reveals subtle caveats in the description of mixing in terms of the
widely used non-Hermitian effective Hamiltonian, more acute in the
non-degenerate case. The effective field theory describes the dynamics of field
mixing where the common intermediate states populate a bath in thermal
equilibrium, as an \emph{open quantum system}. We obtain the effective action
up to second order in the couplings, where indirect mixing is a consequence of
off-diagonal self-energy components. We find that if only one of the mixing
fields features an initial expectation value, indirect mixing induces an
expectation value of the other field. The equal time two point correlation
functions exhibit asymptotic approach to a stationary thermal state, and the
emergence of long-lived \emph{bath induced} coherence which display quantum
beats as a consequence of interference of quasinormal modes in the medium. The
amplitudes of the quantum beats are resonantly enhanced in the nearly
degenerate case with potential observational consequences.
