Crossing resonance of wave fields in a medium with an inhomogeneous coupling parameter

The dynamic susceptibilities (Green's functions) of the system of two coupled wave fields of different physical natures in a medium with an arbitrary relation between the mean value ɛ and rms fluctuation Δɛ of the coupling parameter have been examined. The self-consistent approximation involving all diagrams with noncrossing correlation lines has been developed for the case where the initial Green's function of the homogeneous medium describes the system of coupled wave fields. The analysis has been performed for spin and elastic waves. Expressions have been obtained for the diagonal elements G_mm and G_uu of the matrix Green's function, which describe spin and elastic waves in the case of magnetic and elastic excitations, and for the off-diagonal elements G_mu and G_um, which describe these waves in the case of cross excitation. Change in the forms of these elements has been numerically studied for the case of one-dimensional inhomogeneities with an increase in Δɛ and with a decrease in ɛ under the condition that the sum of the squares of these quantities is conserved: two peaks in the frequency dependences of imaginary parts of G_mm and G_uu are broadened and then joined into one broad peak; a fine structure appears in the form of narrow resonance at the vertex of the Green's function of one wave field and narrow antiresonance at the vertex of the Green's function of the other field; peaks of the fine structure are broadened and then disappear with an increase in the correlation wavenumber of the inhomogeneities of the coupling parameter; and the amplitudes of the off-diagonal elements vanish in the limit ɛ → 0.