| Project/Area Number |
15540366
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Niigata University |
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Principal Investigator |
GODA Masaki Niigata University, Faculty of Engineering, Professor, 工学部, 教授 (60018835)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Two-dimensional random system / Disordered System / Absence of exponential localization / Scaling theory og localization / Rigorous theory / Numerical examination / Lyapunov exponent / Minimum positive Lyapunov exponent / 二次元 |
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| Research Abstract |
It has long been believed that the one-parameter scaling theory of localization by Abraham et al. describes an overall feature of the Anderson localization. It describes exponential localization in two-dimension. I collaborated with Dr.Azbel on this problem and wrote a paper suggesting absence of exponential localization in two-dimensional disordered system with very weak disorder. However, the theory contained many subtle points. Thus in the present research I tried to remove the subtle points from our theory and to polish it to be the one as rigorous as possible.
(1)I have studied the standard tightly-binding Anderson model of disordered systems, to remove an "Umklup process" and an "ultra-violet cut-off." which were in the previous paper. (2)The only assumption describing an inequality has numerically been examined extensively. The theory was blushed up by (1), and the numerical examination gave us a positive support.
Some temporal results has been presented in Phys.Stat.Sol.1(2004). Conclusive results will be presented elsewhere after confirming a theoretical point which is still now in consideration.
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