Memory Function Formalism Research Articles

Spin-wave damping in the two-dimensional ferromagneticXYmodel

$〈{\mathrm{LS}}_{\mathbf{q}}^{\ensuremath{\perp}}{\mathrm{LS}}_{\ensuremath{-}\mathbf{q}}^{\ensuremath{\perp}}〉,$ which is related to the effect of damping of spin waves in a two-dimensional classical ferromagnetic $\mathrm{XY}$ model, is considered. The damping rate ${\ensuremath{\Gamma}}_{\mathbf{q}}$ is calculated using the leading diagrams due to the quartic-order deviations from the harmonic spin Hamiltonian. The resulting four-dimensional integrals are evaluated by extending the techniques developed by Gilat and others for spectral density types of integrals. ${\ensuremath{\Gamma}}_{\mathbf{q}}$ is included into the memory function formalism due to Reiter and Solander, and Menezes, to determine the dynamic structure function $S(\mathbf{q},\ensuremath{\omega}).$ For the infinite sized system, the memory function approach is found to give nondivergent spin-wave peaks, and a smooth nonzero background intensity (``plateau'' or distributed intensity) for the whole range of frequencies below the spin-wave peak. The background amplitude relative to the spin-wave peak rises with temperature, and eventually becomes higher than the spin-wave peak, where it appears as a central peak. For finite-sized systems, there are multiple sequences of weak peaks on both sides of the spin-wave peaks whose number and positions depend on the system size and wave vector in integer units of $2\ensuremath{\pi}/L.$ These dynamical finite-size effects are explained in the memory function analysis as due to either spin-wave difference processes below the spin-wave peak or sum processes above the spin-wave peak. These features are also found in classical Monte Carlo--spin-dynamics simulations.

Viscosity of liquid water from computer simulations with a polarizable potential model

The longitudinal and shear viscosity of water are calculated by molecular dynamics simulation with a polarizable potential model at room temperature. To overcome the difficulty of evaluating directly the stress autocorrelation function of a system with intrinsically many-body forces, we have resorted to the analysis of the wave-vector-dependent longitudinal and transverse-current correlation functions. In a memory function formalism, the generalized viscosity can be evaluated as a function of the wave vector k. By extrapolating to k=0, we find longitudinal and shear viscosity values in better agreement with the experimental value than the corresponding quantities evaluated by making use of a nonpolarizable potential model. This result points out that for a realistic reproduction of transport quantities, it is crucial to take into account many-body contributions to the interaction potential.

Dynamics of a charged simple fluid with exponential memory and two relaxation times

The memory function formalism is applied to the study of charge fluctuations in a symmetric simple fluid. We assume the ions interact through the Rammanathan-Friedman potential. We calculate the distribution function using the hypernetted-chain approximation and use an exponential form, depending on two relaxation times, for the second-order memory function. Following this procedure, two algebraic equations for the relaxation times are obtained. These can be solved using the fourth- and sixth-order frequency momenta, yielding expressions for the relaxation times in terms of the characteristic parameters of the system. This approach allows the analysis of the dynamical structure factor and the dynamical behavior of the charge fluctuations. A comparison of these results with some recently reported in which the distribution function is calculated via mean spherical approximation theory, shows clearly the limitations of mean-field formalisms to describe the dynamics of charged fluids.

The effect of spin alignment on the metal-insulatortransition in two-dimensional systems

We propose a mechanism for the observed suppression of the two-dimensional(2D) conducting phase when there is an in-plane magnetic field. We applyour approach, which is based on the memory function formalism, tothe spin-polarized electron system. This takes into account bothdisorder and exchange-correlation effects. We show that spinpolarization significantly favours localization because of theenhancement of the exchange-correlations. A key outcome is that theconducting phase for the fully spin-polarized system is suppressed.The in-plane magnetic field needed to generate the fully spin-polarized state is of the order of 1 T and depends on the carrierdensity. We determine the metal-insulator phase boundary for theunpolarized and polarized systems, and we estimate the dependence ofthe critical magnetic field on carrier density.

Quenching of the 2D Metallic State by Aligning the Electron Spins

We discuss the destabilisation of the electron 2D metallic state by an in-plane magnetic field. We demonstrate that such a field can destabilise the metallic state through spin polarisation which significantly enhances the exchange correlations between electrons. We find that the conducting phase of the fully spin polarised system is almost completely suppressed. We discuss this phenomenon within a memory function formalism which treats both disorder and exchange-correlation effects. We determine the shift in the position of the metal–insulator phase boundary as the system is polarised by an increasing parallel magnetic field.

Theory of Stress Distribution in Granular Materials: the Memory Formalism

ABSTRACTA theoretical approach to the description of stress distribution in granular compacts is presented on the basis of a memory function formalism. Experiments which have motivated the approach are mentioned. The formalism is shown to provide an explanation of observed features of stress distribution in compacts, and to lead to existing theories in extreme limits, thereb y providing a unification of the theories. The memory functions are shown to be intimately related to characteristic spatial correlations in the granular system and are discussed on the basis of stochastic considerations.

On the dynamical properties of the liquid Li–Na alloy

Several dynamical properties of the liquid Li–Na alloy have been studied by both molecular dynamics simulations and by a theoretical memory function formalism. We present results for the Li 0.61Na 0.39 system where comparison is performed with the experimental inelastic neutron scattering data. The obtained results for the partial dynamic structure factors reveal the existence of propagating sound modes for wavevectors k < 1.4 Å −1.

Frequency moments analysis of the dynamic structure factor of statistical systems

General relations of the theory of classical moments and orthogonal polynomials are applied to the construction of approximate expressions for the dynamic structure factor of statistical systems. With the help of the Nevanlinna theorem the respective expressions which interpolate the dynamic scattering function are constructed in terms of the static structure factor and a set of moments which are considered to be given because of their connection with spectral line shape parameters (integral intensitivity of scattering; shift, dispersion and asymmetry of spectral line, etc.). The efficiency of choice of respective interpolational expressions is proposed to be controlled self-consistently with the help of appropriate Tchebycheff–Markov inequalities. The correct limiting transitions to well-known results obtained within the memory function formalism are demonstrated. The possible application of the given approach to studying critical dynamic light scattering data, is demonstrated.

Structural properties of undercooled liquid sodium and caesium

Extensive theoretical results for the temperature dependence of the static and dynamical structure of undercooled alkali metals using Na and Cs as examples are presented. The static structural properties are obtained from the HMSA integral equations using pair potentials derived from an accurate non-local pscudopotential. The dynamical properties obtained from viscoelastic theory are compared with experiments and the results of memory function formalism. The study indicates that collective density excitations are more dominant in the undercooled region than at their melting points, and that the dynamical properties of Na and Cs exhibit subtle differences in their gross features.

Temperature dependence of the resistivity in the double-exchange model

The resistivity around the ferromagnetic transition temperature in the double-exchange model is studied by the Schwinger-boson approach. The spatial spin correlation responsible for scattering of conduction electrons are taken into account by adopting the memory function formalism. Although the correlation shows a peak lower than the transition temperature, the resistivity in the ferromagnetic state monotonically increases with increasing temperature due to a variation of the electronic state of the conduction electron. In the paramagnetic state, the resistivity is dominated by the short-range correlation of scattering and is almost independent of the temperature. It is attributed to a cancellation between the nearest-neighbor spin correlation, the fermion bandwidth, and the fermion kinetic energy. This result implies the importance of the temperature dependence of the electronic states of the conduction electron as well as the localized spin states in both ferromagnetic and paramagnetic phases.

Theoretical and computer simulation study of density fluctuations in liquid binary alloys

The dynamical properties of liquid alloys are investigated by means of memory function equations and molecular-dynamics simulation. A simple model for the second-order memory function in a binary liquid, based on Mori's memory function formalism, is proposed and applied in numerical calculations of the time correlation functions and dynamic structure factor of liquid K0.7Cs0.3 and K0.3Cs0.7 alloys. Obtained results are discussed in comparison with the results of computer simulations.

Self-diffusion in an isotopic fluid

An expression for the sixth-frequency sum rule of the velocity correlation function is derived for a two-component system. This, along with lower-order frequency sum rules and Mori's memory-function formalism, have been used to study the mass dependence of self-diffusion in an isotopic Lennard-Jones fluid. The effect of inclusion of the sixth-frequency sum rule on the mass dependence of a self-diffusion coefficient of a single heavy particle in a fluid has been studied explicitly. It is found that the ratio of the self-diffusion coefficient of a heavy particle to that of a fluid particle is not affected by the inclusion of the sixth-order sum rule. It is also found that for very high mass ratios the self-diffusion coefficients of a heavy particle can have a minimum value which is $1/\sqrt{2}$ times the self-diffusion coefficient of fluid particles. The mole fraction dependence and thermodynamic state dependence of the mass dependence of self-diffusion of a heavy particle in the host fluid are also studied.

Orbital dynamics: The origin of the anomalous optical spectra in ferromagnetic manganites

We discuss the role of orbital degeneracy in the transport properties of perovskite manganites, focusing in particular on the optical conductivity in the metallic ferromagnetic phase at low temperatures. Orbital degeneracy and strong correlations are described by an orbital t-J model which we treat in a slave-boson approach. Employing the memory-function formalism we calculate the optical conductivity, which is found to exhibit a broad incoherent component extending up to bare bandwidth accompanied by a strong suppression of the Drude weight. Further, we calculate the constant of T-linear specific heat. Our results are in overall agreement with experiment and suggest low-energy orbital fluctuations as the origin of the strongly correlated nature of the metallic phase of manganites.

Time correlation functions in low-dimensional conservative chaotic systems: A memory function approach

Time correlation functions are studied for some conservative chaotic systems with both discrete and continuous time dynamics. For low-dimensional systems a memory function formalism on a microcanonical ensemble turns out to be able to yield useful information on the time correlation function and its energy dependence.

Resonant magnetopolaron effects in GaAs/AlGaAs multiple quantum well structures

A detailed experimental study of electron cyclotron resonance (CR) has been carried out at 4.2 K in three modulation-doped GaAs/Al 0.3Ga 0.7As multiple quantum well samples in fields up to 30 T. A strong avoided-level-crossing splitting of the CR energies due to resonant magnetopolaron effects is observed for all samples near the GaAs reststrahlen region. Resonant splittings in the region of AlAs-like interface phonon modes of the barriers are observed in two samples with narrower well width and smaller doping concentration. The interaction between electrons and the AlAs interface optical phonon modes has been calculated for our specific sample structures in the framework of the memory-function formalism. The calculated results are in good agreement with the experimental results, which confirms our assignment of the observed splitting near the AlAs-like phonon region is due to the resonant magnetopolaron interaction of electrons in the wells with AlAs-like interface phonons.

Non-Markovian shape of the magnetic resonance line

On the basis of a magnetic resonance theory in the memory function formalism developed by one of the authors, we have investigated quantitatively the shape of the absorption line under classical conditions of magnetic resonance in solids. We have found that the theoretical curves provide a good description of the plateau-like shape of the experimental lines, but have somewhat wider wings. In addition, they are nontrivial (non-Gaussian and non-Lorentzian), as follows from the non-Markovian theory of line shapes, and behave “in the Provotorov fashion” with increase in the amplitude of the variable field (the Gaussian line shape transforms into a Lorentzian line shape).

Mutual diffusion in binary systems

Expressions for the second and fourth sum rules of relative and cross velocity correlation functions are derived for two component systems. These sum rules and Mori’s memory function formalism have been used to study the mutual, self- and distinct diffusion in equimolar Ar–Kr mixture and molten salts. It is found that distinct diffusion, which is a measure of effect of cross correlations representing momentum spread to neighbouring particles, is positive for Ar–Kr mixture and is negative for molten salts. These findings are in agreement with molecular dynamics predictions. The positive value of distinct diffusion was not accounted for by Darken’s and common force models.

STRUCTURE FACTORS OF 3HE-4HE MIXTURES

We briefly summarize the present understanding of the dynamic structure factors of liquid3He-4He mixtures in the phonon-maxon-roton region and then present a new calculation using the memory function formalism. Results agree well with experimental data.

Dynamics of simple charged fluids with hard/soft sphere short range interaction

By using the memory function formalism we studied the charge-charge fluctuations in a charged symmetric simple fluid. We consider a hard/soft sphere short range interaction to deal with the divergence caused by the hard sphere pure potential. We assumed an exponential dependence for the second order memory function. This hypothesis together with the distribution function obtained by using the mean spherical approximation (MSA) yields an algebraic equation for the relaxation time. This equation can be solved by the use of the fourth and sixth order frequency momenta. In this way, we obtain some expressions for the relaxation times. On this basis, we analyze the structure factor of the charge-charge fluctuations and the dielectric response function of symmetric molten salts.

Generalized mode approach 3. Generalized transport coefficients of a Lennard-Jones fluid

In this work we develop a free-parameter scheme for calculation of the generalized transport coefficients (GTCs) within the generalized mode approach. Explicit expressions for GTCs as functions of wavenumber k and frequency ω in M-mode approximation are derived using the memory function formalism. For a Lennard-Jones fluid at reduced density n * = nσLJ 3 = 0·845 and reduced temperature T * = k B T/εLJ = 1·706 we have performed numerical calculations of the generalized bulk viscosity, the generalized thermal conductivity and the transport coefficient describing the coupling of heat and stress fluxes. The results are obtained in the five-, seven- and nine-variable approximations and discussed in comparison with the molecular dynamic data as well as with the results known previously.