2012 Fiscal Year Final Research Report
Localization of long-wavelength acoustic phonons in a new anomalous lattice
| Project/Area Number |
22540385
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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 新潟大学, 自然科学系, 名誉教授 (60018835)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 特異格子 / 音響フォノン / 音波 / 局在 / 音響絶縁体 |
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| Research Abstract |
We numerically calculated the damping rate γof acoustic phonons in an anomalous solid with parabolic phonon dispersion relation, in the cases of one-dimensional string (of length L), quasi-one-dimensional strip (of width W and length L), and quasi-one-dimensional rod (of cross section W×W and length L). In all cases, we got anomalous peaky structure in the frequency (ω) dependence of the damping rate γin the low frequency region, which proves a strong localization character of the long-wavelength acoustic phonons. However, we could not determine the numerical value of γ(ω,W→∞,L) in the limiting cases of two- and three-dimensions, because the peak values are of the order of 10^-5 or less in the unit of the inverse of the lattice constant. That means the localization length of the long-wavelength acoustic phonons in the anomalous disordered system is of the order of 0.1mm or more, in the cases of two- and three-dimensions, assuming that the lattice constant is 1nm.
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