Role of the single-particle dynamics in the transverse current autocorrelation function of a liquid metal.

A recent simulation study of the transverse current autocorrelation of the Lennard-Jones fluid [Guarini et al., Phys. Rev.

Universal Matsubara time decay of quantum autocorrelations for Boltzmann particles.

The general properties of time dependent autocorrelations in many-body quantum systems are here analyzed at thermodynamic equilibrium in the Boltzmann canonical ensemble at temperature T, by means of the exponential expansion theory (EET). It is shown that the Kubo-Martin-Schwinger (KMS) symmetry applied to the exponential expansion of the correlation leads to the existence of two different sets of decay modes (channels) here indicated as "Matsubara modes" and "system modes," respectively. The Matsubara modes are a series of pure decay channels with time constants representing a direct action of the thermostat upon the correlation, with a characteristic principal decay time τ_{1}=ℏ/(2πk_{B}T), where ℏ and k_{B} are the Planck and Boltzmann constants, and T is the temperature.

Exponential series expansion for correlation functions of many-body systems.

We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c(t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C̃(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades.

Expansion in Lorentzian functions of spectra of quantum autocorrelations.

We show that in a quantum mechanical many-body system of Boltzmann particles having space inversion symmetry the spectrum of the autocorrelation function of a local observable can always be given, similarly to the classical case [Phys. Rev. E 85, 022102 (2012)], in terms of a series of Lorentzian functions multiplied by the proper quantum detailed balance factor.

Exact exponential function solution of the generalized Langevin equation for autocorrelation functions of many-body systems.

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.

Characteristic times in the nanometer-picosecond translational collective dynamics of molecular liquids.

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.

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

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.

Dynamic structure of He-Ne mixtures by molecular dynamics simulation: from hydrodynamic to fast and slow sound modes.

Molecular dynamics (MD) results for the dynamic structure of a He(0.77)Ne(0.23) gas mixture at two densities (15.