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中文摘要：
在晶体中，杂质原子或晶格缺陷形成的二能级系统会对声子产生弹性散射．利用压电晶体作为共振腔的低温声腔中，这种散射过程的存在导致高频泛音的损失．这种散射可以解释为压电晶体中应变场与二能级系统的耦合，并且能够用一个相互作用哈密顿量描述．根据这个相互作用哈密顿量和二阶微扰论，得到了一个基于声子-二能级系统弹性散射的声子损失公式．根据这个公式，得到了声波损失如何受声波频率和环境温度的变化，而这种分析给出了一个合理的损失机制，解释了M．Goryachev等人在2013年对石英体声腔品质因子的测量结果．希望该丁作可以为降低低温声腔激发的高频声波损失提供了理论支持．
英文摘要：
The purpose of this work is to provide a reason explanation for an experiment in 2013 ,which measureed the quality factor of bulk acoustic wave excited by the cryogenic acoustic cavities. We demonstrate that two-level systems （T1.Ss） ,which are caused by impuri＊y atoms or lattice defects,lead to a kind of acoustic phonon elastic scattering. As a result,this kind of scattering processes result in an attenuation of high overtones in cryogenic acoustic cavities made of piezoelectric crystals. The elastic scattering between phonons and TLSs can be interpreted as the coupling between strain field and TLSs in acoustic cavities, which can be described by an interaction Hamiltonian. Based on this interaction Hamiltonian and the second-order perturbation theory, we obtain a formula of the attenuation resulted from the acoustic wave elastic scattering by TI.Ss. Consequently, we show how input frequency of the excited acoustie wave and environmental temperature influence this attenuation. Such analysis gives a reasonable loss mechanism for the recent experiment. Firstly,our theory provides an interpretation for the law that the qualityfactor Q is inversely proportional to third power of frequency, i. e. , Q × f^3 = const. This law is different from usual frequency dependences which derive from other usual loss mechanisms, such as phonon-phonon interactions and thermoelastic damping. Secondly, our formula expresses anabnormal temperature tendency that the Q factor tends to lower with an increase of temperature. It violates general loss feature, but consists with the temperature tendency as the experience shows. We believe that our work offers a useful support for decreasing the losses for excited high-fie quency acoustic wave in cryogenic acoustic cavities.
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