Crossing resonance of wave fields in a medium with an inhomogeneous coupling parameter
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Crossing Resonance of Wave Fields in a Medium with an Inhomogeneous Coupling Parameter V. A. Ignatchenko and D. S. Polukhin L. V. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia Siberian Federal University, Svobodnyi pr. 79, Krasnoyarsk, 660041 Russia email: [email protected], [email protected] Received June 4, 2013
Abstract—The dynamic susceptibilities (Green’s functions) of the system of two coupled wave fields of dif ferent physical natures in a medium with an arbitrary relation between the mean value ε and rms fluctuation Δε of the coupling parameter have been examined. The selfconsistent 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 Gmm and Guu of the matrix Green’s function, which describe spin and elastic waves in the case of magnetic and elastic excitations, and for the offdiagonal elements Gmu and Gum, 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 onedimensional inhomogeneities with an increase in Δε and with a decrease in ε under the condition that the sum of the squares of these quan tities is conserved: two peaks in the frequency dependences of imaginary parts of Gmm and Guu 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 offdiagonal ele 0. ments vanish in the limit ε DOI: 10.1134/S1063776113130049
1. INTRODUCTION Crossing resonance appears at the crossing point of the dispersion curves of two interacting wave fields of different physical natures. Crossing resonance in a homogeneous medium is manifested in the lift of the degeneracy of the interacting wave field frequencies at this point, in the appearance of two resonance peaks in the frequency dependences of the Green’s functions of both wave fields, and in the resonant enhancement of the excitation of waves of one physical nature by the waves of the other physical nature coupled to the former waves. Both the gap between the energy levels in the spectrum and the spacing between the maxima of each Green’s function, is determined by the cou pling parameter ε between the wave fields. Crossing resonance in an inhomogeneous medium was studied in the Bourret approximation [1, 2] (single scattering of waves from inhomogeneities) in [3–5] for the extremely inhomogeneous model of the interac tion between two wave fields, where
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