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RISS 인기검색어
- 검색키워드
- 저자 : Shigetoshi Sota (검색결과 3 건)
- 무료
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Numerical Study of Roton-Like Collective Excitations in Glassy Materials
Shigetoshi Sota,Masaki Itoh 한국물리학회 2009 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.54 No.1
Roton-like collective excitations of non-quantum origin have been recognized for quite a long time in many structurally disordered materials. A classical study is attempted of a computer-quenched Lennard-Jones glass in the present article. We show that the collective excitations involve vortex motions, as argued by Feynman for quantum liquids. Adopting the harmonic approximation, we constructed the dynamical structure factor and calculated its eigenvectors at several frequencies in order to visualize the respective atomic motions. Some of them are just like those predicted by Feynman, although we obtained them irrelevant of the Bose statistics. We also calculated the dynamical structure factor and confirmed the characteristic roton minimum in the dispersion relation, which is quantitatively close to that observed for liquid Ar.
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Shigetoshi Sota,Masaki Itoh 한국물리학회 2009 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.54 No.1
The kernel polynomial method (KPM), developed by Voter et al, has been recognized as an effective order-N method for calculating the eigenvalue spectrum of a large Hamiltonian. The efficiency of its algorithm is due to the three-term recurrence formula of the polynomial. The central issue is, however, how the Gibbs oscillation can be suppressed and the technique of the Gibbs damping factor has been used with the aid of a particular property of the Chebysheff polynoimial. In this study, we propose a new method that substitutes for the original KPM by using Legendre polynomial. Instead of using the damping factor, we introduce a new basis set by regulating the polynomial in such a way that the series is bound to converge to the exact Green's function without having Gibbs oscillations. The scheme is general enough to deal with the entire family of physical quantities that can be related to the Green's function. This includes the two-particle properties such as electron transport. It further enables the eigenvectors to be calculated in the same algorithm. In all these calculations, the numerical precision is unlimited and is controlled solely by the order of the truncation. The accuracy is confirmed up to six digits in our numerical tests for the dynamics of a simple cubic lattice of 19^3 atoms. We also show a preliminary calculation of the dc transport for the 2D-Anderson model. The kernel polynomial method (KPM), developed by Voter et al, has been recognized as an effective order-N method for calculating the eigenvalue spectrum of a large Hamiltonian. The efficiency of its algorithm is due to the three-term recurrence formula of the polynomial. The central issue is, however, how the Gibbs oscillation can be suppressed and the technique of the Gibbs damping factor has been used with the aid of a particular property of the Chebysheff polynoimial. In this study, we propose a new method that substitutes for the original KPM by using Legendre polynomial. Instead of using the damping factor, we introduce a new basis set by regulating the polynomial in such a way that the series is bound to converge to the exact Green's function without having Gibbs oscillations. The scheme is general enough to deal with the entire family of physical quantities that can be related to the Green's function. This includes the two-particle properties such as electron transport. It further enables the eigenvectors to be calculated in the same algorithm. In all these calculations, the numerical precision is unlimited and is controlled solely by the order of the truncation. The accuracy is confirmed up to six digits in our numerical tests for the dynamics of a simple cubic lattice of 19^3 atoms. We also show a preliminary calculation of the dc transport for the 2D-Anderson model.
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