期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2022
卷号：119
期号：8
DOI：10.1073/pnas.2119288119
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
We present a theory, based on an unstable elasticity model with thermally fluctuating elastic constants, which explains the salient features of the instantaneous normal mode (INM) spectrum of a numerically simulated liquid over a large range of temperatures. The INM spectrum of a liquid is obtained in a molecular dynamics (MD) simulation by considering the harmonic eigenvalue spectrum of the potential energy, taken at a given instant (snapshot). Because the INM spectrum records the curvatures of the fluctuating potential landscape of the liquid, an understanding of this spectrum may pave the way toward understanding the liquid to glass transformation process.
We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures
T. We find that the spectrum of eigenvalues
ρ
(
λ
)
has a sharp maximum near (but not at)
λ
=
0
and decreases monotonically with
|
λ
|
on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for
ρ
(
λ
)
, which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature
T. More importantly, we find an empirical correlation of the positions of the maxima of
ρ
(
λ
)
with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to
T
=
0
from the temperature
T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.
