Project/Area Number 
12640376

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  Shimane University 
Principal Investigator 
TANAKA Hiroshi Shimane Univ., Fac. Sci. & Eng., Assoc. Prof., 総合理工学部, 助教授 (10284019)

CoInvestigator(Kenkyūbuntansha) 
IITAKA Toshiaki Riken, Comp. Sci., Researcher, 計算科学技術, 研究員 (60212700)
TOKIHIRO Tetsuji Tokyo Univ., Mathematical Science, Prof., 大学院・数理科学研究科, 教授 (10163966)
ITOH Masakai Shimane Univ., Fac. Sci. & Eng., Prof., 総合理工学部, 教授 (90184689)

Project Period (FY) 
2000 – 2001

Project Status 
Completed (Fiscal Year 2001)

Budget Amount *help 
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)

Keywords  recursive polynomials / Green function / aperiodic system / ordered N / first principles calculation / error estimation / 直交多項式展開 / 数値解析 
Research Abstract 
We developed a new method to evaluate the Green function for the system described by a huge Hamiltonian matrix on the basis of recursive polynomial expansion. It has the following features ; (1) it is not necessary to diagonalize the Hamiltonian, (2) we can evaluate offdiagonal elements of the Green function as well as diagonal elements, (3) it is possible to evaluate products of the Green functions and other quantum operators. Then, several physical properties can be evaluated, (4) the method is applicable to the system with discrete nature, (5) we can also evaluate eigenvalues and eigenvectors on the same algorithm, (6) CPU time and memory size needed in the calculation is proportional to the system size N (i.e. ordered N method). Combining this method with the first principles calculations, we can analyze several physical properties such as electronic conductivities from first principles in the large disordered systems. In practice, we applied this method to bcc and amorphous Fe system, and shows the usefulness of the method. We also compared the method with timedependent method such as particle source method and forced oscillator method, and showed that the time evolution operator can be derived from the Fourier transformation of the Green function obtained by our method. Furthermore, we showed that the method can be extended to the evaluation of thermal Green function by analytical continuation to the imaginary time. In the practical calculations, we have to terminate the expansion at finite order. We estimate the numerical error due to the termination, and showed that it decreases as proportional to the expansion order N.
