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Fracton
A fracton is a collective quantized vibration on a substrate with a fractal structure.〔.〕
Fractons are the fractal analog of phonons. Phonons are the result of applying translational symmetry to the potential in a Schrödinger equation. Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational symmetry. Translational symmetry is symmetry under displacement or change of position, and self-similarity is symmetry under change of scale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different frequencies. In other words, a fracton band is comparable to a phonon band. The vibrational modes are restricted to part of the substrate and are thus not fully delocalized, unlike phonon vibrational modes. Instead there is a hierarchy of vibrational modes which encompass smaller and smaller parts of the substrate.
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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