Fracton: Difference between revisions
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Fractons are the fractal analogon of [[phonon]]s. 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 schale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different [[frequencies]]. In other words a fractonband, comparable to a phononband. 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. |
Fractons are the fractal analogon of [[phonon]]s. 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 schale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different [[frequencies]]. In other words a fractonband, comparable to a phononband. 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. |
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Revision as of 06:24, 29 September 2006
Template:Linkless-date A fracton is a collective quantized vibration on a substrate with a fractal structure.
Fractons are the fractal analogon 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 schale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different frequencies. In other words a fractonband, comparable to a phononband. 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.
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