线性和非线性链模型中的Kapitza热阻：同位素亏损
Kapitza thermal resistance in linear and nonlinear chain models: isotopic defect
摘要：
研究了具有内部缺陷的链模型中的Kapitza阻力问题。对于线性链的情形，导出了任意线性时无关保守夹杂或缺陷的边界阻力的精确解析解。一个简单的情况下，孤立的同位素缺陷进行了更详细的探讨。与线性链中的体电导率相反，Kapitza电阻是有限的。然而，在这种情况下不存在普遍的热力学极限。换句话说，电阻的确切值不是唯一定义的，并且取决于接近链片段的无限长度的方式。由于这个原因，并且还由于对恒温器的参数的明确依赖性，电阻不能被认为是缺陷的局部性质。的热通量的情况下，非常重的缺陷的渐近标度行为进行了探讨，并与非线性同行;相似的标度行为被揭示。对于线性链中的轻质同位素缺陷，人们遇到了典型的温度分布的下降，与衰减区中的局部模式的弱激发有关。如果包括非线性相互作用，这种下降仍然可以出现在一个相对较短的时间尺度，随后消除由于非线性相互作用。这意味着即使在非线性链中，如果温度足够低，线性动力学也可以预测热分布的短时间演化的主要特征。
英文摘要：
Kapitza resistance in the chain models with internal defects is considered. For the case of the linear chain, the exact analytic solution for the boundary resistance is derived for arbitrary linear time-independent conservative inclusion or defect. A simple case of isolated isotopic defects is explored in more detail. Contrary to the bulk conductivity in the linear chain, the Kapitza resistance is finite. However, the universal thermodynamic limit does not exist in this case. In other terms, the exact value of the resistance is not uniquely defined and depends on the way of approaching the infinite lengths of the chain fragments. For this reason, and also due to the explicit dependence on the parameters of the thermostats, the resistance cannot be considered as a local property of the defect. Asymptotic scaling behavior of the heat flux in the case of very heavy defect is explored and compared to the nonlinear counterparts; similarities in the scaling behavior are revealed. For the lightweight isotopic defect in the linear chain, one encounters a typical dip of the temperature profile, related to weak excitation of the localized mode in the attenuation zone. If the nonlinear interactions are included, this dip can still appear at a relatively short time scale, with subsequent elimination due to the nonlinear interactions. This observation implies that even in the nonlinear chains, the linear dynamics can predict the main features of the short-time evolution of the thermal profile if the temperature is low enough.
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