Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface

doi:10.7498/aps.67.20180469

	Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface
	Zhang Ke 1,2,3; Fan Cheng-Yu1 ; Fan Hong-Yi 2
	2018-09-05
发表期刊	ACTA PHYSICA SINICA
ISSN	1000-3290
通讯作者	Fan Cheng-Yu(cyfan@aiofm.ac.cn)
摘要	The influence of diffusion and defects of crystal surface on the crystal vibration mode are an important and basic subject in surface physics research. The frequency of lattice vibration corresponds to the energy band of the system. Since the vibrations of the atoms in the crystal lattice are not isolated from each other, and the crystal lattice is periodic, thereby forming a lattice wave in the crystal. The lattice wave represents that all the atoms in the crystal vibrate at an identical frequency, which is often called a vibration mode. The lattice chain model has been studied as the vibrating mode of phonon and the energy-band in solid state physics. The vibrating modes of the lattice chain model have been analyzed with the Newton equation and the Born-von-Karman boundary condition in the literaure. In general, it is difficult to solve this problem due to the complex nonlinear characteristic of the interactions between the matter particles and the environment. Noting the complicacy in directly diagonalizing quantum Hamiltonian operator of a long chain, we introduce the invariant eigenoperator method (IEO) for deriving the energy g(a)p of a given crystal lattice without solving its eigenstates in the Heisenberg picture. The Heisenberg equation is as important as the Schrodinger equation. However, it has been seldom used for directly deriving the energy-gap in previous studies. Following the Heisenberg's original idea that most observable physical quantity in quantum mechanics is energy spectrum, Hong-yi Fan, one of the authors of the present paper, developed the IEO method. This method provides a natural result of combining both the Schrodinger operator and the Heisenberg equation. Using the IEO method, we study the vibration modes of crystal lattice, which are affected by absorbing an atom with mass m(0), which is different from the mass of atom in the crystal. Moreover, the attractive potential constant beta(0) of the lattice surface differs from the inner constant beta. With the help of invariant eigen-operator method, we deduce the vibration mode omega = root 2 beta(1-cosh alpha)/hm, where alpha = ln [ - m beta(0) + m(0)(-2 beta+beta(0))+root beta(0)root-4mm(0)beta + (m + m(0))(2)beta(0)/2m(0)beta]. Our numerical results show that vibration mode omega depends not only on the absorption potential and the mass of the absorbed atom, but also on the mass of the lattice atom and the inner potential. In general, by discussing the vibration modes via some numerical solutions or approximate methods, we show the relations between the system vibration modes with different parameters which describe the environment influences. These results can deepen our understanding of quantum Brownian motion and demonstrate the applicability of the IEO method.
关键词	vibration modes surface adsorption potential invariant eigen-operator
DOI	10.7498/aps.67.20180469
关键词[WOS]	COUPLED IDENTICAL OSCILLATORS ; ARBITRARY NUMBER ; SPECTRUM ; VIRTUE
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of the Anhui Higher Education Institutions of China[KJ2014A236] ; Natural Science Foundation of the Anhui Higher Education Institutions of China[KJ2014A236]
项目资助者	Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China ; Natural Science Foundation of the Anhui Higher Education Institutions of China
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000443944600002
出版者	CHINESE PHYSICAL SOC
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.hfcas.ac.cn:8080/handle/334002/38758
专题	中科院安徽光学精密机械研究所
通讯作者	Fan Cheng-Yu
作者单位	1.Chinese Acad Sci, Anhui Inst Opt & Fine Mech, Key Lab Atmospher Composit & Opt Radiat, Hefei 230031, Anhui, Peoples R China 2.Univ Sci & Technol China, Grad Sch, Sci Isl Branch, Hefei 230031, Anhui, Peoples R China 3.Huainan Normal Univ, Sch Elect Engn, Huainan 232038, Peoples R China
第一作者单位	中科院安徽光学精密机械研究所
通讯作者单位	中科院安徽光学精密机械研究所
推荐引用方式 GB/T 7714	Zhang Ke,Fan Cheng-Yu,Fan Hong-Yi. Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface[J]. ACTA PHYSICA SINICA,2018,67(17):7.
APA	Zhang Ke,Fan Cheng-Yu,&Fan Hong-Yi.(2018).Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface.ACTA PHYSICA SINICA,67(17),7.
MLA	Zhang Ke,et al."Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface".ACTA PHYSICA SINICA 67.17(2018):7.