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A unified solution of the specific-heat–phonon spectrum inversion problem

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 s...

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Bibliographic Details
Published in:Europhysics letters 2003-03, Vol.61 (6), p.723-728
Main Authors: Ming, DengMing, Wen, Tao, Dai, JiXin, Evenson, W. E, Dai, XianXi
Format: Article
Language:English
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/epl/i2003-00288-6