Abstract

The crossing resonance of two wavefields m(x, t) and u(x, t) of different natures in an inhomogeneous medium with zero mean value of the coupling parameter η between fields has been studied. The stages of formation of the fine structure of the crossing resonance have been analyzed. It has been shown within the model of independent crystallites that the removal of the degeneracy of eigenfrequencies of these fields at the crossing resonance point has a threshold character in the coupling parameter and occurs under the condition η > η_c, where η_c = |Γ_u – Γ_m|/2, Γ_u and Γ_m are the relaxation parameters of the corresponding wavefields. At η > η_c, each random implementation of the Green’s functions \(\tilde {G}_{{mm}}^{{''}}\) and \(\tilde {G}_{{uu}}^{{''}}\) of wavefields has the form of two resonance peaks with the same half-width (Γ_u + Γ_m)/2 spaced by the interval 2η; this form is standard for crossing resonances. At η < η_c, the functions \(\tilde {G}_{{mm}}^{{''}}\) and \(\tilde {G}_{{uu}}^{{''}}\) are different: if Γ_u > Γ_m, the function \(\tilde {G}_{{mm}}^{{''}}\) has the form of a narrow resonance peak at ω = ω_r, whereas the function \(\tilde {G}_{{uu}}^{{''}}\) has the form of a broader resonance peak split at the top by a narrow antiresonance. Averaging over regions where η > η_c leads to the formation of a broad resonance with a resonance line half-width of about 〈η²〉^1/2 on the both averaged Green’s functions, which is due to the stochastic distribution of resonance frequencies. Averaging over regions where η < η_c results in the sharpening of a resonance peak on the function \(G_{{mm}}^{{''}}\) and an antiresonance peak on the function \(G_{{uu}}^{{''}}\) at the same frequency ω = ω_r. As a result, a pattern of the crossing resonance in the inhomogeneous medium is formed, consisting of identical broad peaks on both functions with the narrow resonance peak of the fine structure on the function \(G_{{mm}}^{{''}}\) and the antiresonance peak on the function \(G_{{uu}}^{{''}}\). Thus, the fine structure of the spectrum of any crossing resonance of two wavefields of different natures in the inhomogeneous medium is due to the contribution of random realizations corresponding to degenerate states of the natural oscillations of the system. In a ferromagnet with a spatially inhomogeneous coupling parameter, spin and elastic waves acquire damping parameters Γ_m(k) ∝ k_c\({{{v}}_{m}}\) and Γ_u(k) ∝ k_c\({{{v}}_{u}}\) proportional to the correlation wavenumber k_c of inhomogeneities and to the velocities of the corresponding waves, which are summed with the homogeneous damping parameters Γ_m and Γ_u of the same waves. This situation has been considered in a new self-consisting approximation for the case where the contribution of homogeneous damping parameters is negligibly small. It has been shown that the form of the fine structure on the functions \(G_{{mm}}^{{''}}\) and \(G_{{uu}}^{{''}}\) at the second (high-frequency) crossing point of dispersion curves of spin and elastic waves changes to the opposite form: narrow resonance peaks of the fine structure appear on the function \(G_{{uu}}^{{''}}\), and antiresonance peaks arise on the function \(G_{{mm}}^{{''}}\) because \({{{v}}_{m}}\) < \({{{v}}_{u}}\) and \({{{v}}_{m}}\) > \({{{v}}_{u}}\) at the first and second crossing points, respectively.

中文翻译：

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非均匀介质中波场交叉共振谱的精细结构

摘要

研究了不同性质的两个波场m（x，t）和u（x，t）在非均匀介质中的交叉共振，其中场之间的耦合参数η均值为零。分析了交叉共振的精细结构的形成阶段。已经示出的模型独立的晶粒，该去除在交叉共振点这些字段的本征频率的简并性的具有在连接参数的阈值特性和条件η下>η发生内_Ç，其中η _Ç = |Γ _ü - Γ_米| / 2，Γ _û和Γ_米是相应的波场的松弛参数。在η>η _Ç，每个随机执行的格林函数\（\代字号{G} _ {{毫米}} ^ {{ ''}} \）和\（\代字号{G} _ {{UU}} ^ {{'}} \）波场的具有两个共振峰与所述形式相同的半宽度（Γ _û +Γ_米）/ 2由间隔2η间隔开; 这种形式是交叉共振的标准。在η<η _Ç，则各功能\（\代字号{G} _ {{毫米}} ^ {{ ''}} \）和\（\代字号{G} _ {{UU}} ^ {{'} } \）是不同的：如果Γ _ù >Γ_米，函数\（\代字号{G} _ {{毫米}} ^ {{ ''}} \）具有窄的共振峰在ω=ω形式_{- [R}，而函数\（\代字号{G} _ {{UU}} ^ {{“”}} \）具有在更宽的共振峰分裂的形式首先是狭窄的反共振。平均过区域，其中η>η _Ç导致形成一个宽的共振具有约<η一个谐振线的半宽度² > ^1/2的两个平均格林函数，这是由于谐振频率的随机分布。平均过区域，其中η<η _Ç在上的功能的谐振峰值的锐化结果\（G _ {{毫米}} ^ {{ ''}} \）和在功能上的反共振峰\（G _ {{UU} } ^ {{''}} \）以相同的频率ω=ω_[R 。结果，在不均匀介质中形成了交叉共振的模式，该模式由两个函数上相同的宽峰与函数\（G _ {{mm}} ^ {{''上的精细结构的窄共振峰组成}} \）和反共振峰在函数\（G _ {{uu}} ^ {{{''}} \\）上。因此，非均匀介质中两个不同性质的波场的任何交叉共振的频谱的精细结构是由于对应于系统自然振荡的简并状态的随机实现的贡献。在具有空间非均匀耦合参数铁磁体，自旋和弹性波获得阻尼参数Γ_米（ķ）α ķ _Ç\（{{{V}} _ {M}} \）和Γ _Ù（ķ）α ķ _Ç \（{{{V}} _ {ù}} \）成比例的相关波数ķ _Ç不均匀性，并相应的波的速度，这是求和与均匀阻尼参数Γ_米和Γ _ü同一波。对于均匀阻尼参数的贡献可以忽略不计的情况，已经在一种新的自洽近似中考虑了这种情况。结果表明，函数\（G _ {{mm}} ^ {{''}} \）和\（G _ {{uu}} ^ {{''}} \）上的精细结构形式在自旋和弹性波的色散曲线的第二个（高频）交点处改变为相反的形式：精细结构的窄共振峰出现在函数\（G _ {{uu}} ^ {{''}}上\）和反共振峰出现在函数\（G _ {{mm}} ^ {{''}} \）上，因为\（{{{v}} _ {m}} \） < \（{{{v }} _ {ù}} \）和\（{{_ {M}} \）{v}} > \（{{_ {ù}} \）{v}}在第一和第二交叉点，分别。