On the temperature dependence of the density of states of liquids at low energies

We report neutron-scattering measurements of the density of states (DOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we confirm the presence of a universal low-energy linear scaling of the experimental DOS as a function of the frequency, g(ω )= a(T) ω g ( ω ) = a ( T ) ω , which persists at all temperatures. The low-frequency scaling of the DOS exhibits a sharp jump at the melting point of water, below which the standard Debye’s law, g(ω ) ∝ ω ² g ( ω ) ∝ ω 2 , is recovered. On the contrary, in Fomblin, we observe a continuous transition between the two exponents reflecting its glassy dynamics, which is confirmed by structure measurements. More importantly, in both systems, we find that the slope a ( T ) grows with temperature following an exponential Arrhenius-like form, a(T) ∝ exp (- E /T) a ( T ) ∝ exp ( - ⟨ E ⟩ / T ) . We confirm this experimental trend using molecular dynamics simulations and show that the prediction of instantaneous normal mode (INM) theory for a ( T ) is in qualitative agreement with the experimental data.