The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
Continuum limit of the vibrational properties of amorphous solids
Open accessAbstract
Significance: The thermal properties of crystalline solids follow universal laws that are explained by theories based on phonons. Amorphous solids are also characterized by universal laws that are, however, anomalous with respect to their crystalline counterparts. These anomalies begin to emerge at very low temperatures, suggesting that the vibrational properties of amorphous solids differ from phonons, even in the continuum limit. In this work, we reveal that phonons coexist with soft localized modes in the continuum limit of amorphous solids. Importantly, we discover that the phonons follow the Debye law, whereas the soft localized modes follow another universal non-Debye law. Our findings provide a firm theoretical basis for explaining the thermal anomalies of amorphous solids.
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Introduction to Solid State Physics
Kittel, C., & Fan, H. Y. (1957) · American Journal of Physics · doi:10.1119/1.1934457 · Cited by 22,240
Introduction to Solid State Physics
Kittel, C., & Dexter, D. L. (1953) · American Journal of Physics · doi:10.1119/1.1933590 · Cited by 13,240
Anomalous low-temperature thermal properties of glasses and spin glasses
Anderson, P. W., Halperin, B. I., & Varma, C. M. (1972) · Philosophical Magazine · doi:10.1080/14786437208229210 · Cited by 3,494
Thermal Conductivity and Specific Heat of Noncrystalline Solids
Zeller, R. C., & Pohl, R. O. (1971) · Physical Review B · doi:10.1103/physrevb.4.2029 · Cited by 1,954
Jamming at zero temperature and zero applied stress: The epitome of disorder
O’Hern, C. S., Silbert, L. E., Liu, A. J., & Nagel, S. R. (2003) · Physical Review E · doi:10.1103/physreve.68.011306 · Cited by 1,599
Amorphous Solids: Low-Temperature Properties
(1981) · Topics in Current Physics · doi:10.1007/978-3-642-81534-8 · Cited by 866
Mean-field theory of hard sphere glasses and jamming
Parisi, G., & Zamponi, F. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.789 · Cited by 705
Amorphous systems in athermal, quasistatic shear
Maloney, C. E., & Lemaître, A. (2006) · Physical Review E · doi:10.1103/physreve.74.016118 · Cited by 666
Fractal free energy landscapes in structural glasses
Charbonneau, P., Kurchan, J., Parisi, G., Urbani, P., & Zamponi, F. (2014) · Nature Communications · doi:10.1038/ncomms4725 · Cited by 484
Interaction of soft modes and sound waves in glasses
Buchenau, U., Galperin, Y. M., Gurevich, V. L., Parshin, D. A., Ramos, M. A., & Schober, H. R. (1992) · Physical Review B · doi:10.1103/physrevb.46.2798 · Cited by 452
Metadata
- Authors
- Mizuno, H., Shiba, H., & Ikeda, A.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2017-10-31
- Volume
- 114
- Issue
- 46
- Pages
- E9767-E9774
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2601686816
- Cited by
- 267
- References
- 32
- FWCI
- 12.99
- Type
- journal article
- Language
- en
- Open access
- green
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