Exact solution of the specific-heat-phonon spectrum inversion from the Mobius inverse formula

被引：8

作者：

Ming, DM ^{[1
]}

Wen, T

Dai, JX

Dai, XX

Evenson, WE

机构：

[1] Fudan Univ, Grp Quantum Stat & Methods Theoret Phys, Shanghai 200433, Peoples R China

[2] NYU, Dept Chem, New York, NY 10003 USA

[3] Brigham Young Univ, Dept Phys & Astron, Provo, UT 84602 USA

来源：

PHYSICAL REVIEW E | 2000年 / 62卷 / 03期

关键词：

Integral equations - Interpolation - Inverse problems - Laplace transforms - Phonons - Specific heat - Spectrum analysis;

D O I：

10.1103/PhysRevE.62.R3019

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main difficulty arises from the fact that the Mobius function mu(n) is not completely known for large n in practice. In this paper, some exact solutions of SPI are obtained by using the Mobius inversion formula, most importantly the Debye spectrum as a special case, and the problem of the unknown Mobius function mu(n) for large n is avoided. It is shown that the Mobius inversion formula can be useful for exact solutions to spectral inversion problems.

引用

页码：R3019 / R3022

页数：4

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