Collective acoustic modes as renormalized damped oscillators: Unified description of neutron and x-ray scattering data from classical fluids

Abstract

In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

Expansion in Lorentzian functions of spectra of quantum autocorrelations

“…Moreover, although the models considered in Ref. [17] referred to classical systems, the present work demonstrates that essentially the same approach can be extended to quantum systems if an analogous modeling is applied to the spectrum of the relaxation function.…”

“…A few years ago we reviewed [17] the theoretical models most commonly employed as spectral functions to be fitted to the experimental or simulated dynamic structure factor S(k,ω) for the analysis of spectra of density fluctuations in classical fluids. All the models there considered are based on a common scheme that assumes for the second-order memory function a time dependence in the form of a combination of a δ function and/or exponential terms.…”

The Spectrum of Density Fluctuations of Noble Gases Probed by THz Neutron and X-ray Spectroscopy

“…However, at low Qs the latter can be expressed through a polynomial Q-expansion (see, e.g., Equations (42)- (45) of [23]), which at the lowest order reads:…”

“…Most importantly, in this measurement the superior accuracy in the count statistics coupled with the unprecedented dense Q-grid, enabled a very detailed analysis of the Q-dependence of line-shape parameters of Equation (2). Best fit values of such parameters are reported in Figure 6 and therein compared with either the simple hydrodynamic prediction (Equations (3a-c)) or a higher-order polynomial expansion (see, e.g., Equations (42)- (45) of [23]). In the same Figure, the result previously obtained by Bell and collaborator on neon is also reported for comparison along with the corresponding simple hydrodynamic prediction of Equations (3a-c).…”

Exposing a dynamical signature of the freezing transition through the sound propagation gap

“…It is significant therefore that for some state points, of several simple fluids studied so far, the sound dispersion curves have gaps-spatial windows where sound is overdamped-for wavevectors around the location of the main maximum in the static structure factor [26][27][28][29] . There is, however, no unique model by which linear hydrodynamics may be extended to finite wavevectors 30,31 , and the results are prone to appreciable fitting errors. For the hard-sphere system in particular, available results are scanty 26,27 .…”