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Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator |
| Meng Xiang-Guo(孟祥国)a)†, Fan Hong-Yi(范洪义) a), and Wang Ji-Suo(王继锁)a)b) |
| a Department of Physics, Liaocheng University, Liaocheng 252059, China; b Department of Physics, Liaocheng University, Liaocheng 252059, China;Department of Physics, Qufu Normal University, Qufu 273165, China |
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Abstract Noticing that the equation $\frac{ d ^{2} O_{ n }}{ d t^{2}}=\{H_{ c },\{H_{ c }, O_{ n }\}\}=\lambda O_{ n }$ with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Lett. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invariant eigen-operator method.
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Revised: 18 January 2010
Accepted manuscript online:
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PACS:
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63.20.-e
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(Phonons in crystal lattices)
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03.65.Fd
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(Algebraic methods)
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02.10.Ud
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(Linear algebra)
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02.30.Hq
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(Ordinary differential equations)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10574060), the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23) and the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07). |
Cite this article:
Meng Xiang-Guo(孟祥国), Fan Hong-Yi(范洪义), and Wang Ji-Suo(王继锁) Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator 2010 Chin. Phys. B 19 070303
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Myers H P 1990 Introductory Solid State Physics (London: Taylor and Francis) endfootnotesize
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