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We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected., (© 2012 American Physical Society)

Molecular-dynamics calculations of the translational dynamic structure factor in liquid CO2 and CD4 are analyzed by means of the generalized Langevin equation for the intermediate scattering function in the second-order memory function approximation. We give a rigorous general relation among the decay times of the memory and the lifetimes of the modes of the density-density correlation function. The comparison of the various characteristic times among them and with the collision time, carried out as a function of the wave vector, reveals strong relationships between the memory relaxation and the density-density correlation modes, some of which have purely "collisional" and other "collective" character. We show that essential information about the life time of structural properties in a molecular liquid at nanometer dimensions can be obtained if the time behavior of the correlation function is considered in addition to that of the memory function.

Anisotropic interactions of liquid CD4 are studied in detail by comparison of inelastic neutron Brillouin scattering data with molecular dynamics simulations using up to four different models of the methane site-site potential. We demonstrate that the experimental dynamic structure factor S(Q,omega) acts as a highly discriminating quantity for possible interaction schemes. In particular, the Q evolution of the spectra enables a selective probing of the short- and medium-range features of the anisotropic potentials. We show that the preferential configuration of methane dimers at liquid densities can thus be discerned by analyzing the orientation-dependent model potential curves, in light of the experimental and simulation results.

The density response of supercooled glycerol to an impulsive stimulated thermal grating (q=0.63 microm(-1)) has been studied in the temperature range (T=200-340 K) where the structure rearrangement (alpha relaxation) and the thermal diffusion occur on the same time scale. A strong interaction between the two modes occurs giving rise to a dip in the T dependence of the apparent thermal conductivity and a flattening of the apparent alpha-relaxation time upon cooling. A nonequilibrium thermodynamic model for the long time response has been developed. The model is capable to reproduce the experimental data and to explain the observed phenomenology.

Molecular dynamics (MD) results for the dynamic structure of a He(0.77)Ne(0.23) gas mixture at two densities (15.8 and 36.1 nm(-3)) show a clear crossover from hydrodynamic modes to distinct excitations for the two species. The higher density dispension curve neatly shows high- and low-frequency branches setting on with a rather localized transition. The lower density results agree very well with existing neutron scattering data and, in particular, display hydrodynamic behavior up to k approximately 2 nm(-1), in contrast with the conclusions of previous simulation studies. A smooth transition to fast sound is shown to take place for 2

The dynamics of the fragile glass-forming orthoterphenyl have been investigated by transient grating experiments with an heterodyne detection technique. We measured the relaxation processes of this glass former over more than six decades in time with an excellent signal-to-noise ratio. Acoustic, structural, and thermal relaxations have been clearly identified in a time-frequency window not covered by previous spectroscopic studies and their characteristic dynamic parameters have been measured as a function of temperature and wave vector. A detailed comparison with the density response function, calculated on the basis of generalized hydrodynamic model, has been worked out.

We present a molecular dynamics study of the collective dynamics of a model for the fragile glass former orthoterphenyl. In this model, introduced by Mossa, Di Leonardo, Ruocco, and Sampoli [Phys. Rev. E 62, 612 (2000)], the intramolecular interaction among the three rigid phenyl rings is described by a set of force constants whose value has been fixed in order to obtain a realistic isolated molecule spectrum. The interaction between different molecules is described by a Lennard Jones site-site potential. We study the behavior of the coherent scattering functions F(t)(q,t), considering the density fluctuations of both molecular and phenyl-ring centers of mass; moreover we directly simulate the neutron scattering spectra taking into account both the contributions due to carbon and hydrogens atoms. We compare our results with the main predictions of the mode-coupling theory and with the available coherent neutron scattering experimental data.

A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so-called microscopic (or, instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation and allows one to relate to each other (1) the characteristic time and strength of this process, (2) the low frequency limit of the dynamic structure factor of the glass, and (3) the high frequency sound attenuation coefficient, with its observed quadratic dependence on the momentum transfer.