A unified solution of the specific-heat–phonon spectrum inversion problem
A unified solution of the specific-heat–phonon spectrum inversion problem
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DOI：
10.1209/epl/i2003-00288-6
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发表时间：
2003-03
期刊：
影响因子：
1.8
通讯作者：
D. Ming;Tao Wen;J. Dai;W. Evenson;X. Dai;X. Dai;X. Dai
中科院分区：
文献类型：
--
作者：
D. Ming;Tao Wen;J. Dai;W. Evenson;X. Dai;X. Dai;X. Dai
在比热声子谱反演问题（SPI）中，采用修正的Mobius反演公式（N。X. Chen Phys. Rev. Lett. 64（1990）1193）是新颖的并且引起极大兴趣。同时，利用Dai的精确解公式，通过引入一个参数s来消除发散，成功地得到了一系列精确解，并利用该公式从YBCO的真实的具体数据中得到了声子谱。本文将证明，利用逆拉普拉斯变换的积分表示和Riemann zeta函数的某些性质，可以从戴氏公式导出Chen的解，而不必使用Mobius反演公式。此外，还得到了Chen解的存在唯一性定理和级数的收敛性。文中还指出，戴氏参数和渐近行为控制条件在推导过程中起着至关重要的作用。
In the specific-heat–phonon spectrum inversion problem (SPI), Chen's solution with modified Mobius inversion formula (N. X. Chen Phys. Rev. Lett. 64 (1990) 1193) was novel and of great interest. Meanwhile, Dai's exact solution formula with a parameter s for canceling the divergence has succeeded in obtaining a series of exact solutions and was employed to obtain a phonon spectrum from real specific data of YBCO. In this paper we will show that, by using an integral representation of inverse Laplace transformations and some properties of the Riemann zeta-function, Chen's solution can be derived from Dai's formula, without necessarily using the Mobius inversion formula. Furthermore, the unique existence theorem and convergence of the series of Chen's solution were also obtained. It is also shown that Dai's parameter s and the asymptotic behavior control condition are of crucial importance in the derivation.