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Dynamical phase transitions in supercooled liquids: Interpreting measurements of dynamical activity
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) Scatter plot of the two activity measurements and , in three different -ensembles. The ensembles are characteristic of the active phase ( = 0.000), the coexistence region ( = 0.015), and the inactive phase ( = 0.025). The two activity measurements and are anti-correlated. The trajectory length is = 400Δ. (b) and (c) Marginal distributions of and from the -ensemble with = 0.015. This bimodal behaviour is characteristic of the dynamical phase transition found in Ref. . (d) Scatter plot of and for three values of and = 200Δ. The data for = −3.0 × 10 are similar to the inactive data for = 0.025. The dashed and dotted lines in (a) and (d) are the same in both panels and are obtained by linear regression analyses on data from (a) for the dots and (d) for the dashes.

Image of FIG. 2.
FIG. 2.

(a) and (b) Averaged activities in biased ensembles. Note that panel (b) shows the negatives of the field and the activity, − and ⟨ − ⟩. All data are for = 150 and = 0.6, except for the red-dashed lines, where = 300 and we show the linear response behaviour about equilibrium: ⟨ = ⟨ + ⟨δ + ( ), and similarly for . These linear response results do not capture the non-trivial crossovers, but they do show that the mean and variance of and are approximately extensive in , for = 0 (there is a weak finite-size correction to ⟨: particle motion in smaller systems is known to be slightly slower for this system, compared to the bulk ).

Image of FIG. 3.
FIG. 3.

Numerical test of Eq. (12) . The two quantities should be equal at equilibrium ( = 0), but there is a small difference between them due to our use of a truncated potential (see Appendix B ). The small difference is almost constant for the range of considered.

Image of FIG. 4.
FIG. 4.

(a) Distribution of eigenvalues of the Hessian for both phases. [(a), inset] The difference Δ) = [))] between the phases. The distribution for the active phase is slightly broader, and it associated mean value of ω is larger. (b) Distribution of ω where ω > 0 for both phases.

Image of FIG. 5.
FIG. 5.

(a) Distribution of eigenvalues of the Hessian for inherent structures of both phases. (b) Distribution of ω for inherent structures of both phases. [(b), inset] Dividing (ω) by ω emphasises the lack of low frequency modes associated with the inactive phase.

Image of FIG. 6.
FIG. 6.

A schematic representation of the differences in the energy landscape between the active and inactive phases. In the inactive phase, the barriers between basins (inherent structures) are smaller making rearrangements on large length scales less likely. These correspond to small values of ω. The strongly curving directions around basins are less steep in the inactive phase, allowing more motion on short length scales. These correspond to large values of ω.

Image of FIG. 7.
FIG. 7.

(a) Comparison of the partial pair correlation function for large particles between the active and inactive phases. Although there are some differences (the height of the first peak and the depth of the first trough) they are small. (b) The function 4π () which can be integrated to give . The interesting part of this function occurs around the position of the first peak in the pair correlation function. The inset panel shows the difference in this function between the phases, Δ () = [ ()] − [ ()]. This serves to illustrate that the changes in come from structural changes on short length scales.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamical phase transitions in supercooled liquids: Interpreting measurements of dynamical activity