Fracton

Synonym of phonon

Not to be confused with a fracton (subdimensional particle), an excitation that is immobile when in isolation.

A fracton is a collective quantized vibration on a substrate with a fractal structure.[1][2]

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 fractal 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 that encompass smaller and smaller parts of the substrate.[citation needed]

## References

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1. ^ Alexander, S; C. Laermans; R. Orbach; H.M. Rosenberg (15 October 1983). "Fracton interpretation of vibrational properties of cross-linked polymers, glasses, and irradiated quartz". Physical Review B. 28 (8): 4615–4619\. Bibcode:1983PhRvB..28.4615A. doi:10.1103/physrevb.28.4615.
2. ^ Srivastava, G. P. (1990), The Physics of Phonons, CRC Press, pp. 328–329, ISBN 9780852741535.

## Literature

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* Gromov, Andrey; Radzihovsky, Leo (5 January 2024). "Colloquium : Fracton matter". Reviews of Modern Physics. 96 (1). doi:10.1103/RevModPhys.96.011001.

## External links

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* The ‘Weirdest’ Matter, Made of Partial Particles, Defies Description

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