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日時
2018年9月20日(木) 14:30～16:30
タイトル
Effect of spatial fluctuation on the mean-field density of state of
amorphous solids
講演者
池田晴國氏 (École Normale Supérieure Paris)
場所
東山キャンパス理学館 4F 415号室
アブストラクト
The vibrational density of state (DOS) is a central object to
characterize many physical properties of solids, such as the specific
heat, thermal conduction, and sound attenuation. In the case of perfect
crystals, the DOS is now well understood, which follows the celebrated
Debye law and shows the cubic frequency dependence at low enough
frequency. On the contrary, the DOS of amorphous solids at low frequency
has the extra localized modes, in addition to the standard phonon mode
following the Debye law. It is widely accepted that those extra
localized modes would explain the several unusual properties of
amorphous solids such as the linear specific heat dependence, the
intermediate plateau of the thermal conduction and local avalanches when
applying shear deformation. Interestingly, recent computer simulations
of amorphous solids uncover the strong universal behavior of the
localized modes: the DOS of the low frequency localized modes shows the
quartic frequency dependence, irrespective to the interaction potentials
and spatial dimensions. In this work, we construct a
semi-phenomenological theory to explain this quartic behavior of the DOS
based on the mean-field theory of the amorphous solids. Although several
different models have been proposed such as the spin-glasses,
perceptrons and random network models, in most cases, the Hessian
matrixes of those models belong to the specific classes of the random
matrixes in the mean-field limit/approximation. Relying on the universal
property of the random matrix, we show that the quartic law of the DOS
naturally and robustly appears as a consequence of the spatial
fluctuation of the amorphous solids. We also discuss the quench rate and
pressure dependences of the amplitude of the low-frequency localized
modes.
--
----------
Takeshi Kawasaki, PhD.
Assistant Professor
Department of Physics, Nagoya University,
Nagoya 464-8602, Japan
Tel/Fax: +81-52-789-2438
E-mail Address: kawasaki@r.phys.nagoya-u.ac.jp
URL: http://www.r.phys.nagoya-u.ac.jp/~kawasaki/index.html