Search for: All records

We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function that is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz–Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional. 

Sound attenuation in low-temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here, we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. Small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-affine displacements’ contribution to the sound wave propagation coefficient coming from the frequency shell of the sound wave. Our expression involves only quantities that pertain to solids’ static configurations. It can be used to evaluate the low-temperature sound damping coefficients without directly simulating sound attenuation. 

The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation Γ obeys quartic, Rayleigh scattering scaling for small wavevectors k and quadratic scaling for wavevectors above the Ioffe–Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavevectors Γ ∼ k 1.5 for an aging glass, but Γ ∼ k 2 when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ ∼ k 2 at small wavevectors, then a crossover to Rayleigh scattering scaling Γ ∼ k 4 , followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses. 

The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency ω , which is quantified by thermal diffusivity d ( ω ). Here we study d ( ω ) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d ( ω ), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d ( ω ), but the wave packet is no longer well described by a Gaussian as for high frequencies. In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d ( ω ) ∼ ω −4 at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.