Memory Function Formalism Research Articles

Mutual diffusion in a binary isotopic mixture

The mass dependence of the mutual diffusion coefficient, in a binary equimolar mixture ofLennard-Jones fluids, is studied within Mori’s memory function formalism. Aphenomenological form of the memory function is used to study the time evolution of theself- and relative velocity correlation functions. The diffusion coefficients are calculated fromthe relevant velocity correlation functions using the Green–Kubo integral formula. Like theself-diffusion coefficient, the mutual diffusion coefficient is also found to be weaklydependent on the mass ratio. The present study shows that the minimum value that themutual diffusion coefficient in an equimolar mixture of isotopic fluids can have is times the self-diffusion coefficient of any of the species when in isolation. Further, thecontribution of the dynamic/distinct cross correlations to the mutual diffusion coefficient isfound to be small and positive for the whole range of the mass ratio which is consistentwith earlier molecular dynamics results.

Chain dynamics of poly(ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics

We present coarse-grained molecular dynamics simulations of poly(ethylene-alt-propylene) (PEP) melts, ranging in chain length from about N(e) (the entanglement length) to N=6N(e). The coarse-grained parameters, potential of mean force and bare friction, were determined from fully atomistic molecular dynamics simulations carried out on a PEP cell containing 12 chains of 80 monomers each and subjected to periodic boundary conditions. These atomistic simulations were previously validated by means of extensive neutron scattering measurements. Uncrossability constrains were also introduced in the coarse-grained model to prevent unphysical bond crossing. The coarse-grained simulations were carried out at 492 K and focus on chain dynamics. The results obtained were analyzed in terms of Rouse coordinates and Rouse correlators. We observe deviations from Rouse behavior for all chain lengths investigated, even when the chain stiffness is incorporated in the Rouse model. These deviations become more important as the chain length increases. The general scenario emerging from the results obtained is that the deviations from Rouse-like behavior are due to correlations among the forces acting upon a chain bead, which seem to be related with the constraint of uncrossability among the chains. As consequence, nonexponentiality of the Rouse correlators and mode- and time-dependent friction are observed. It seems that, in the molecular weight explored, these effects still give not raise to reptation behavior but to a crossover regime between Rouse and reptation. On the other hand, the results obtained are in qualitative agreement with those expected from the so-called generalized Rouse models, based on memory function formalisms.

Temperature-dependent resistivity of ferromagneticGa1−xMnxAs: Interplay between impurity scattering and many-body effects

The static conductivity of the dilute magnetic semiconductor GaMnAs is calculated using the memory function formalism and time-dependent density-functional theory to account for impurity scattering and to treat Hartree and exchange interactions within the hole gas. We find that the Coulomb scattering off the charged impurities alone is not sufficient to explain the experimentally observed drop in resistivity below the ferromagnetic transition temperature: the often overlooked scattering off the fluctuations of localized spins is shown to play a significant role.

Low frequency structural dynamics of warm dense matter

Measurements of the microscopic response of warm dense matter have been demonstrated by multi-keV inelastic x-ray scattering using laser-based sources. These techniques have been used to study the high frequency electron correlations (plasmons) in low to mid-Z plasmas. The advent of fourth generation light sources will provide high fluxes of narrowband and coherent x rays that will allow to look at the low frequency correlations (the ion-acoustic waves). In this paper we present an analysis of such low frequency modes by calculating the frequency dependent ion-ion structure factor. Our model includes all the relevant multibody contributions arising from strong coupling and nonideal plasma effects. In particular, the ion-ion structure factor is obtained within the memory function formalism by satisfying a finite number of sum rules. This work could be used as a basis to a direct experimental test of dense plasma model as soon as keV free electron laser sources will become available.

High frequency dynamics in liquids and supercritical fluids: A comparative inelastic x-ray scattering study

The microscopic dynamics of four prototype systems (water, ammonia, nitrogen, and neon) across the critical temperature has been investigated by means of high-resolution inelastic x-ray scattering. The experimental line shape has been described using a model based on the memory function formalism. Two main relaxations, the thermal and the structural one, were observed in all the investigated systems. We found that the microscopic mechanism driving the structural relaxation clearly changes, being mainly governed by intermolecular bond rearrangements below the critical temperature and by binary collisions above it. Moreover, we observed that the relative weight of the thermal relaxation systematically increases on approaching the critical temperature, thus allowing for the observation of a transition from an adiabatic to an isothermal regime of sound propagation. Finally, we found the presence of an additional instantaneous relaxation, likely related to the coupling between collective vibrational modes and intramolecular degrees of freedom.

Mass-dependence of self-diffusion coefficients in disparate-mass binary fluid mixtures

Self-diffusion coefcients of a binary uid mixture with components differing only in their particle masses are studied, in particular the case when mass ratio of light and heavy particles tends to zero. These coefcients were calculated within the memory function formalism, using the systematic subsequence of approximations for the relaxation times of velocity autocorrelation function. We obtained a general relation for the self-diffusion coefcients which show polynomial dependence on the mass ratio . The obtained expression has a correct Brownian limit. We developed the hierarchy of approximations for the self-diffusion coefcients that tends to an exact result from above and below when the order of approximations increases.

Modeling of the absorption profile of the 60 GHz band of atmospheric oxygen using the memory function formalism

The profile of the oxygen absorption band centered at 60 GHz is modeled using the formalism of memory functions. The memory function determines the relation between the initial and final states of a molecule after its collision. The model profile takes into account the spectral exchange and contains two parameters, which depend on temperature and pressure. These parameters characterize the probabilities of spectral exchange between series of lines (branches) corresponding to molecular transitions of different types. To describe the absorption profile in the frequency range of 0–120 GHz in terms of the model proposed, the “+” and “−” branches of fine structure transitions and the series of nonresonance lines with frequencies on the order of 10−3–10−5 GHz are taken into account. The values of the parameters that take into account the spectral exchange are found from the condition of the best fit between the developed model profile and the profile calculated according to the millimeter-wave propagation model. The parameters found have physically substantiated and smooth temperature dependences, which confirms the adequacy of the model. The difference between these models does not exceed 2–3%, which corresponds to the declared uncertainty.

The study of high-frequency dynamics in liquid magnesium by memory-function formalism and computer simulation molecular dynamics

The study of structure and dynamics of particles in liquid magnesium at the two thermodynamical states (at the temperature T = 953 K and T = 1063 K) has been performed by computer simulation molecular dynamics with the "glue" interparticle potential. The calculated equilibrium terms are compared with the experimental data on X-ray scattering. The results of comparative analysis to show adequacy of choice of the interparticle potential for liquid magnesium. The study of collective properties of the magnesium particles on the basis of the dynamic structure factor, S(k,W), for eight wave-numbers k = 0.5, 0.7, 0.9, 1.1, 1.4, 1.6, 1.8 H 2.0 A−1 are carry out. The theoretical analysis of S(k,W) by Zwanzig-Mori's memory-function formalism on the basis of N.N. Bogoliubov's ideas about reduced description of statistical systems and the hierarchy of relaxation time-scales are executed. The results of theoretical calculations are in a good agreement with computer simulation molecular dynamics data.

Longitudinal and bulk viscosities of binary fluid mixtures

Expressions for zeroth, second and fourth sum rules of longitudinal and bulk stress auto correlation functions have been derived for binary fluid mixtures. Longitudinal and bulk viscosities of an Ar–Kr mixture have been calculated using Mori's memory function formalism coupled with the sum rules of longitudinal and bulk stress auto correlation functions. The results obtained are compared with the molecular dynamics simulation. Mass dependence of the longitudinal and bulk viscosities has been studied for different compositions of an isotopic mixture at different densities and temperatures. For very large mass ratio, the longitudinal and bulk viscosities of the isotopic mixture are more dependent on mole fraction than on mass.

Statistical quantifiers of memory for an analysis of human brain and neuro-system diseases

On the basis of a memory function formalism for correlation functions of time series we investigate statistical memory effects by the use of appropriate spectral and relaxation parameters of measured stochastic data for neuro-system diseases. In particular, we study the dynamics of the walk of a patient who suffers from Parkinson’s disease (PD), Huntington’s disease (HD), amyotrophic lateral sclerosis (ALS), and compare against the data of healthy people (CO — control group). We employ an analytical method which is able to characterize the stochastic properties of stride-to-stride variations of gait cycle timing. Our results allow us to estimate quantitatively a few human locomotion function abnormalities occurring in the human brain and in the central nervous system (CNS). Particularly, the patient’s gait dynamics are characterized by an increased memory behavior together with sizable fluctuations as compared with the locomotion dynamics of healthy patients. Moreover, we complement our findings with peculiar features as detected in phase-space portraits and spectral characteristics for the different data sets (PD, HD, ALS and healthy people). The evaluation of statistical quantifiers of the memory function is shown to provide a useful toolkit which can be put to work to identify various abnormalities of locomotion dynamics. Moreover, it allows one to diagnose qualitatively and quantitatively serious brain and central nervous system diseases.

Dynamics of the quantum integer spinS one-dimensional Heisenberg antiferromagnet coupled to phonons

We present the low-temperature dynamic properties of the quantumone-dimensional Heisenberg antiferromagnet with integer spinS coupled to phonons. The calculation of the relaxation function is performedusing the combination of the memory function formalism with the modifiedspin-wave theory. The procedure includes up to two-magnon and magnon–phononprocesses. We show that the phonon–magnon coupling smooths the double-peakstructure obtained for the model in the absence of phonons, when the wavevectorq movesfrom q = π.

Dynamical structure factor of liquid Li, Na and Al

The dynamical structure factors, S(q,ω) of liquid lithium, sodium and aluminium have been studied near their melting points using Mori’s memory function formalism. The second order memory function was obtained by exploiting non-Markovian nature of the fourth order memory function and assuming that memory functions at their alternate stage have the same functional time dependence. We obtain an analytical expression for the second order memory function, whose form depends on wave number q. Results obtained for dynamical structure factor over a wide range of q values for liquid Na and Al have been found to be in good agreement with recent inelastic X-ray scattering experiments in contrast to the case of liquid Li. The behavior of non-Markovity parameter is also studied as a function of frequency, ω, at different values of q.

Plasmon dispersion in quasi-one- and one-dimensional systems with non-magnetic impurities

We calculate the plasmon dispersion in quasi-one-dimensional quantum wires, in the presence of non-magnetic impurities, taking into consideration the memory function formalism and the role of the forward scattering. The plasma frequency is reduced by the presence of impurities. We also calculate, analytically, the plasmon dispersion in the Born approximation, for the scattering of the electrons by the non-magnetic impurities. We compare our result with the numerical results of Sarma and Hwang.

Enhanced carrier scattering rates in dilute magnetic semiconductors with correlated impurities

In III-V dilute magnetic semiconductors such as ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$, the impurity positions tend to be correlated, which can drastically affect the electronic transport properties of these materials. Within the memory function formalism we have derived a general expression for the current relaxation kernel in spin and charge disordered media and have calculated spin and charge scattering rates in the weak-disorder limit. Using a simple model for impurity clustering, we find a significant enhancement of the charge scattering. The enhancement is sensitive to cluster parameters and may be controllable through postgrowth annealing.

Anomalies in the dynamical resistivity due to a quantum critical point

Non-Fermi-liquid (NFL) properties are observed in many heavy fermion systems and frequently attributed to a nearby quantum critical point (QCP). A QCP can arise by suppressing the transition temperature ${T}_{N}$ of an antiferromagnetic phase to zero, e.g., by chemical or applied pressure or an external magnetic field. We consider a QCP arising from the nesting of Fermi surfaces of an electron pocket and a hole pocket separated by a wave vector $\mathbf{Q}$. The nesting together with the remaining interaction between the carriers after the heavy particles are formed give rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a QCP is obtained as ${T}_{N}\ensuremath{\rightarrow}0$. The NFL contribution to the dynamical resistivity is calculated using the Kubo formula and a memory function formalism. The mismatched nesting has the following consequences. (i) The specific heat $\ensuremath{\gamma}$ coefficient and the magnetic susceptibility increase with the logarithm of the temperature as $T$ is lowered. (ii) For the tuned QCP the linewidth of the quasiparticles is sublinear in $T$ and $\ensuremath{\omega}$. (iii) The specific heat and the linewidth display a crossover from non-Fermi-liquid $(\ensuremath{\sim}T)$ to Fermi-liquid $(\ensuremath{\sim}{T}^{2})$ behavior with increasing nesting mismatch and decreasing temperature. (iv) For the tuned QCP the electrical resistivity acquires a quasilinear temperature dependence. This behavior is exponentially suppressed at very low $T$ if the QCP is not tuned. (v) For the tuned QCP and at low $T$ the dynamical conductivity deviates from the usual Drude behavior.

Self-diffusivity and velocity autocorrelation functions for xenon in NaY using memory kernels

The applicability of the memory function formalism to the study of the dynamics of rare gas atoms in zeolite NaY is assessed. Solutions to the memory equation are obtained by solving the memory kernel with different analytic closure schemes. Inputs to the models are the frequency moments, which are obtained from molecular dynamics simulations. The model predictions are compared with the results obtained using molecular dynamics simulations for Xe in zeolite NaY at loadings of one atom/cage at different temperatures. Predictions from the secant hyperbolic memory kernel were found to yield the most accurate of the various models investigated, with quantitative predictions above temperatures of 300 K. Since the frequency moments can be computed in a Monte Carlo simulation, the method outlined here suggests an alternate route to the dynamics of confined fluids.

Self-consistent approach in the microdynamics description of supercooled liquids and glasses

A study of the microdynamics of supercooled liquids and glasses is executed through calculations of the dynamic structure factor S ( k , ω ). The theory developed on the basis of a self-consistent approach in the framework of the memory function formalism is applied to define the frequency spectra ( m / k B T ) S ( k , ω ) of supercooled argon at the temperature T = 5 K for the wavenumber region from 2 to 8.5nm -1 . The results obtained are in good agreement with the molecular dynamics simulation data.

Pressure effect on water dynamics in tert-butyl alcohol/water solutions

We report here a quasi-elastic neutron scattering (QENS) investigation of the effect ofpressure on the diffusivity properties of water in a dilute aqueous solution of hydrophobicmolecules (tert-butyl alcohol, TBA). The experiment was performed at fixed TBAconcentration (0.02 molar fraction) by varying pressure from 1 to 2000 bar at two differenttemperatures (268 and 278 K). The quasi-elastic line-shapes have been analysed in termsof a model based on the memory function formalism. Our data indicate that,on increasing pressure up to 2000 bar, the diffusion coefficient of water in theTBA/water mixture exhibits a relative increase larger than that of pure waterunder the same thermodynamic conditions. The extent of this effect increaseswith decreasing temperature. The observed behaviour is described in terms ofpressure-induced distortions of the H-bonded random network of liquid water.

Validity of the Franck-Condon Principle in the Optical Spectroscopy: Optical Conductivity of the Fröhlich Polaron

The optical absorption of the Fröhlich polaron model is obtained by an approximation-free diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: (i) a strong coupling expansion, based on the Franck-Condon principle, well describes the optical conductivity for large coupling strengths (alpha > 10); (ii) a memory function formalism with phonon broadened levels reproduces the optical response for weak coupling strengths (alpha < 6) taking the dynamic lattice relaxation into account. In the coupling regime 6 < alpha < 10, the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.

Self-Diffusion in Sheared Colloidal Suspensions: Violation Of Fluctuation-Dissipation Relation

Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e., Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature.