### Abstract

A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature T and pressure p. Variational arguments and effective medium theory identically predict a non-trivial temperature scale T<sup>∗</sup> ∼ p<sup>(2-a)/(1-a)</sup> with a ≈ 0.17 such that low-energy vibrational properties are hard-sphere like for T >∼ T<sup>∗</sup> and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating T, p, and the packing fraction φ, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of T and φ. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

Original language | English (US) |
---|---|

Article number | 164503 |

Journal | Journal of Chemical Physics |

Volume | 142 |

Issue number | 16 |

DOIs | |

State | Published - Apr 28 2015 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*142*(16), [164503]. https://doi.org/10.1063/1.4918737

**Theory of the jamming transition at finite temperature.** / Degiuli, E.; Lerner, E.; Wyart, M.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 142, no. 16, 164503. https://doi.org/10.1063/1.4918737

}

TY - JOUR

T1 - Theory of the jamming transition at finite temperature

AU - Degiuli, E.

AU - Lerner, E.

AU - Wyart, M.

PY - 2015/4/28

Y1 - 2015/4/28

N2 - A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature T and pressure p. Variational arguments and effective medium theory identically predict a non-trivial temperature scale T∗ ∼ p(2-a)/(1-a) with a ≈ 0.17 such that low-energy vibrational properties are hard-sphere like for T >∼ T∗ and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating T, p, and the packing fraction φ, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of T and φ. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

AB - A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature T and pressure p. Variational arguments and effective medium theory identically predict a non-trivial temperature scale T∗ ∼ p(2-a)/(1-a) with a ≈ 0.17 such that low-energy vibrational properties are hard-sphere like for T >∼ T∗ and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating T, p, and the packing fraction φ, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of T and φ. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

UR - http://www.scopus.com/inward/record.url?scp=84928715331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928715331&partnerID=8YFLogxK

U2 - 10.1063/1.4918737

DO - 10.1063/1.4918737

M3 - Article

AN - SCOPUS:84928715331

VL - 142

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 16

M1 - 164503

ER -