Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
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DOI：
10.1209/0295-5075/114/40002
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Junjie Liu;Baowen Li;Changqin Wu
中科院分区：
文献类型：
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作者：
Junjie Liu;Baowen Li;Changqin Wu
在这封信中，我们扩展了以前提出的变分方法，系统地研究一般动量非守恒非线性晶格。首先揭示了最优参考系的两个内在恒等式，从而导出了最优变分参数的显式表达式。由此产生的最佳谐波参考系统提供的信息的带隙以及动量非守恒非线性晶格中的重正化声子的色散。作为演示，我们考虑一维晶格。我们发现，声子带隙赋予一个简单的幂律温度依赖性弱随机制度预测的色散是可靠的，通过与数值结果比较。此外，在整个温度范围内的晶格系综平均值之间的精确关系被发现，而不考虑强随机性阈值的存在。
In this letter, we extend a previously proposed variational approach to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities characterizing optimal reference systems are firstly revealed, which enables us to derive explicit expressions for optimal variational parameters. The resulting optimal harmonic reference systems provide information for the band gap as well as the dispersion of renormalized phonons in momentum-nonconserving nonlinear lattices. As a demonstration, we consider the one-dimensional lattice. We show that the phonon band gap endows a simple power-law temperature dependence in the weak stochasticity regime where predicted dispersion is reliable by comparing with numerical results. In addition, an exact relation between ensemble averages of the lattice in the whole temperature range is found, regardless of the existence of the strong stochasticity threshold.