DOI: 10.1088/1742-5468/2007/08/l08003. Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses

Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses

10.1088/1742-5468/2007/08/l08003

Crossref journal-article

IOP Publishing

Journal of Statistical Mechanics: Theory and Experiment (266)

Abstract

In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network. This result enables one to study the free energy landscape of hard spheres, which was previously accessible only via density functional theory. In our formalism normal modes can easily be defined and computed. In this work we use these tools to analyze the activated transitions between meta-basins, both in the ageing regime deep in the glass phase and near the glass transition. We observe numerically that structural relaxation occurs mostly along a very small number of nearly unstable extended modes. This number decays for denser packing and is significantly lowered as the system undergoes the glass transition. This observation supports the assertion that structural relaxation and marginal modes share common properties. In particular, theoretical results show that these modes extend at least on some length scale l *∼(ϕc−ϕ)−1/2 where ϕc corresponds to the maximum packing fraction, i.e. the jamming transition. This prediction is consistent with very recent numerical observations of dynamical length scales in sheared systems near the jamming threshold, where a similar exponent is found, and with the commonly observed growth of the rearranging regions with compression near the glass transition.

Bibliography

Brito, C., & Wyart, M. (2007). Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses. Journal of Statistical Mechanics: Theory and Experiment, 2007(08), L08003âL08003.

Authors 2

Carolina Brito (first)
Matthieu Wyart (additional)

References 42 Referenced 94

10.1103/PhysRevE.52.1694 / Phys. Rev. (1995)
10.1016/S0022-3093(98)00582-1 / J. Non-Cryst. Solids (1998)
10.1103/PhysRevLett.96.185701 / Phys. Rev. Lett. (2006)
10.1063/1.470551 / J. Chem. Phys. (1995)
10.1126/science.1120714 / Science (2005)
10.1126/science.287.5453.627 / Science (2000)
10.1103/PhysRevLett.80.2338 / Phys. Rev. Lett. (1998)
10.1016/S0022-3093(00)00225-8 / J. Non-Cryst. Solids (2000)
10.1103/PhysRevLett.96.057801 / Phys. Rev. Lett. (2006)
10.1103/PhysRevE.71.041505 / Phys. Rev. (2005)
10.1088/0953-8984/17/50/R01 / J. Phys.: Condens. Matter (2005)
10.1007/978-3-642-81534-8 (1981)
10.1016/S0370-1573(97)00069-0 / Phys. Rep. (1998)
10.1140/epje/i2002-10088-x / Eur. Phys. J. (2002)
10.1021/jp963706h / J. Phys. Chem. (1997)
10.1103/PhysRevLett.88.055502 / Phys. Rev. Lett. (2002)
10.1209/epl/i2006-10175-8 / Europhys. Lett. (2006)
10.1126/science.220.4599.787 / Science (1983)
10.1209/epl/i2006-10238-x / Europhys. Lett. (2006)
10.1209/epl/i2005-10245-5 / Europhys. Lett. (2005)
10.1103/PhysRevE.72.051306 / Phys. Rev. (2005)
10.1051/anphys:2006003 / Ann. Phys., Fr. (2005)
10.1103/PhysRevE.68.011306 / Phys. Rev. (2003)
10.1103/PhysRevLett.95.098301 / Phys. Rev. Lett. (2005)
10.1103/PhysRevLett.93.135502 / Phys. Rev. Lett. (2004)
10.1103/PhysRevLett.97.258001 / Phys. Rev. Lett. (2006)
10.1209/epl/i2003-10190-3 / Europhys. Lett. (2004)
{'year': '1976', 'key': '28-1'} (1976)
10.1142/S0219477505002367 / Fluct. Noise Lett. (2005)
10.1088/0953-8984/15/11/336 / J. Phys.: Condens. Matter (2003)
10.1007/s100510050038 / Eur. Phys. J. (2000)
10.1088/0953-8984/12/29/310 / J. Phys.: Condens. Matter (2000)
10.1103/PhysRevLett.88.055502 / Phys. Rev. Lett. (2002)
10.1103/PhysRevE.58.801 / Phys. Rev. (1998)
10.1103/PhysRevE.61.R41 / Phys. Rev. (2000)
10.1103/PhysRevLett.53.1244 / Phys. Rev. Lett. (1984)
10.1103/PhysRevE.48.4364 / Phys. Rev. (1993)
10.1103/PhysRevE.60.687 / Phys. Rev. (1999)
10.1103/PhysRevE.62.2510 / Phys. Rev. (2000)
{'year': '2007', 'key': '40-1'} (2007)
10.1038/nphys572 / Nature Physics (2007)
10.1103/PhysRevLett.98.175502 / Phys. Rev. Lett. (2007)

Dates

Type	When
Created	18 years ago (Aug. 8, 2007, 11:13 p.m.)
Deposited	8 months, 1 week ago (Dec. 12, 2024, 6:14 a.m.)
Indexed	1 month, 3 weeks ago (July 4, 2025, 6:04 p.m.)
Issued	18 years ago (Aug. 1, 2007)
Published	18 years ago (Aug. 1, 2007)
Published Online	18 years ago (Aug. 8, 2007)
Published Print	18 years ago (Aug. 1, 2007)

Funders 0

None

BibTeX

@article{Brito_2007, title={Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses}, volume={2007}, ISSN={1742-5468}, url={http://dx.doi.org/10.1088/1742-5468/2007/08/l08003}, DOI={10.1088/1742-5468/2007/08/l08003}, number={08}, journal={Journal of Statistical Mechanics: Theory and Experiment}, publisher={IOP Publishing}, author={Brito, Carolina and Wyart, Matthieu}, year={2007}, month=aug, pages={L08003–L08003} }

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