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25
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85034920519
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Note that the definition of [formula omitted] here is different from [formula omitted] the ratio of phase space volumes in the barrier and well regions of Ref 8, by a factor of (in the harmonic approximation) [formula omitted] where [formula omitted] is the barrier frequency.
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26
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84950571596
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For a pair of neighboring barrier and well associated with the same frequency ω and located at a fixed distance from each other, the vertical energy difference scales as [formula omitted] This is expected to hold for modes of strong local character, i.e., large [formula omitted]
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27
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84950571597
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Numerically we see a large accumulation of [formula omitted] modes in the [formula omitted] spectrum [see Fig. 4(a)], pointing to the importance of contributions not from saddles and not from well bottoms.
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28
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84950571594
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We believe that the large estimate for the parameter [formula omitted] (α is the number of atoms in the independent rearranging regions) results from this assumption. For a modest [formula omitted] this would imply [formula omitted] This implies that the dimension of the saddle—the number of downward directions and z is the typical saddle has 8 reactive directions, while the fit to the diffusion constant uses one such direction.
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29
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84950571595
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Ensembles of 2000 configurations and of 50 configurations were used for the 100 particle system and the 400 particle system, respectively.
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30
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84950571592
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This is done by defining [formula omitted] and using windows of constant width in x. The natural alternative, to use windows of fixed width in ω, i.e., [formula omitted] with [formula omitted] was used to construct the histograms for [formula omitted] and [formula omitted] in Figs. 1 and 2. Making the same choice here yields very similar results with somewhat bigger scatter of data in the large [formula omitted] range.
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31
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84950571593
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A possible exception is ln[formula omitted] in the high density fluid, which we found to be represented almost as well by both forms, i.e., the best fit would be to [formula omitted] with [formula omitted]
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