Current Autocorrelation Function Research Articles

Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. V. The Short Time Approximation for the Memory Function

The correlation function for density fluctuations in a monatomic fluid obeys a formally exact kinetic equation containing a memory function. A previously derived short time approximation (STA) for this memory function is tested by comparing its predictions with the results of molecular dynamic simulations of a dense Lennard-Jones fluid at a variety of temperatures. This approximation takes into account the contribution to the correlation function of uncorrelated repulsive binary collisions. The qualitative changes of predicted correlation functions with temperature and wave vector are generally correct. The major exception to this is the transverse current correlation function for small wave vector. The quantitative accuracy is better at short times than long times and better at high temperatures than low temperatures. The major failing of the STA is its underestimation of the amplitudes of the negative dips in the current autocorrelation functions and of the temperature dependence of the amplitudes of the dips. Despite its deficiencies in predicting the time dependence of current correlation functions, the STA gives accurate results for the self-diffusion coefficient and the shear viscosity coefficient at the highest temperatures studied.

Phonons in a one-dimensional Yukawa chain: Dusty plasma experiment and model

Phonons in a one-dimensional chain of charged microspheres suspended in a plasma were studied in an experiment. The phonons correspond to random particle motion in the chain; no external manipulation was applied to excite the phonons. Two modes were observed, longitudinal and transverse. The velocity fluctuations in the experiment are analyzed using current autocorrelation functions and a phonon spectrum. The phonon energy was found to be unequally partitioned among phonon modes in the dusty plasma experiment. The experimental phonon spectrum was characterized by a dispersion relation that was found to differ from the dispersion relation for externally excited phonons. This difference is attributed to the presence of frictional damping due to gas, which affects the propagation of externally excited phonons differently from phonons that correspond to random particle motion. A model is developed and fit to the experiment to explain the features of the autocorrelation function, phonon spectrum, and the dispersion relation.

Studies of thermal conductivity in Fermi–Pasta–Ulam-like lattices

The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta, and Ulam (FPU) can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear oscillators. In this paper we describe the most recent achievements about the divergence of heat conductivity with the system size in one-dimensional (1D) and two-dimensional FPU-like lattices. The anomalous behavior is particularly evident at low energies, where it is enhanced by the quasiharmonic character of the lattice dynamics. Remarkably, anomalies persist also in the strongly chaotic region where long-time tails develop in the current autocorrelation function. A modal analysis of the 1D case is also presented in order to gain further insight about the role played by boundary conditions.

Atomic-scale computations of the lattice contribution to thermal conductivity of single-walled carbon nanotubes

The lattice contribution to thermal conductivity of single-walled carbon nanotubes with three different screw symmetry (chirality) is studied using the Green–Kubo relation from linear response theory and molecular dynamics based thermal current auto-correlation functions. The interactions between carbon atoms are analyzed using the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. The results obtained show that, due to an exponential-decay character of the long-time thermal current auto-correlation functions, quite accurate lattice thermal conductivities can be obtained using computational cells considerably smaller than the phonon mean free path. In addition, the computed lattice contributions to thermal conductivities are found to agree within a factor of two with their counterparts obtained using the Boltzmann transport equation. Also, chirality is found to affect lattice thermal conductivity by as much as 20%.

Thermal conductivity decomposition and analysis using molecular dynamics simulations. Part I. Lennard-Jones argon

Using molecular dynamics simulations and the Green–Kubo method, the thermal transport in the Lennard-Jones argon face centered cubic crystal is described by two time constants related to the decay of the heat current autocorrelation function. The first time scale is associated with short wavelength acoustic phonons that have mean free paths equal to one half of their wavelength. The associated thermal conductivity is independent of temperature, and has a value around 0.09 W/m K. The second time scale is longer, and corresponds to acoustic phonons with mean free paths longer than one half of their wavelength. The associated thermal conductivity is temperature dependent, and ranges from 3.92 W/m K at a temperature of 10 K to 0.08 W/m K at a temperature of 100 K. This decomposition allows for a comparison of the crystal phase results with those from corresponding amorphous and liquid phases.

Collective Motion of Charges in Lithium Tetrafluoroborate Solutions in Acetonitrile

The spectra (cosine Fourier transform) of autocorrelation functions of a microscopic current and their components in lithium tetrafluoroborate solutions in acetonitrile at concentrations of up to 0.75 M are studied by molecular dynamic modeling. The contributions of molecules (M), cations (Kt), and anions (An) to the overall spectrum are determined. The latter is presented as the sum of series of components (MM, MKt + KtM, MAn + AnM, KtKt, KtAn + AnKt, AnAn). The maximums in the MM component at 14 THz and KtKt component at 55 THz are related to IR bands in the spectrum. A negative peak is observed in the (KtAn + AnKt) component at 4 THz. A “microscopic” interpretation is provided for relevant spectra in the terms of intermolecular and ion–molecular interactions. The link between the spectra of the current autocorrelation functions and the nature of ionic association is explained.

Thermal conductivity of diamond and related materials from molecular dynamics simulations

Based on the Green–Kubo relation from linear response theory, we calculated the thermal current autocorrelation functions from classical molecular dynamics (MD) simulations. We examined the role of quantum corrections to the classical thermal conduction and concluded that these effects are small for fairly harmonic systems such as diamond. We then used the classical MD to extract thermal conductivities for bulk crystalline systems. We find that (at 300 K) C12 isotopically pure perfect diamond has a thermal conductivity 45% higher than natural (1.1% C13) diamond. This agrees well with experiment, which shows a 40%–50% increase. We find that vacancies dramatically decrease the thermal conductivity, and that it can be described by a reciprocal relation with a scaling as nv−α, with α=0.69±0.11 in agreement with phenomenological theory (α=1/2 to 3/4). Such calculations of thermal conductivity may become important for describing nanoscale devices. As a first step in studying such systems, we examined the mass effects on the thermal conductivity of compound systems, finding that the layered system has a lower conductivity than the uniform system.

Thermal Conductivity of Solid Argon by Classical Molecular Dynamics

AbstractFollowing the Green-Kubo formalism in linear response theory, the lattice thermal conductivity of solid argon is determined by using classical molecular dynamics simulation to calculate the heat current correlation function. Comparing the absolute conductivities obtained using the Lennard-Jones potential with experiments, we find the predicted results to uniformly underestimate the measurements in magnitude, whereas the calculated temperature dependence corresponds well with the data. The temporal behavior of the heat current autocorrelation function shows that while a single exponential decay description is appropriate at elevated temperatures, below the half of the Debye temperature, the heat current relaxation clearly consists of two stages, an initial rapid decay associated with local dynamics followed by a slower component associated with the dynamics of lattice vibrations (phonons).

Hot-phonon effect on noise and diffusion in GaAs

We analyse the effects of a non-equilibrium phonon population on noise and diffusion phenomena in polar semiconductors. We calculate the current and energy autocorrelation functions and the current-energy cross-correlation functions, for both the case with and without hot-phonon effects. Owing to the presence of hot phonons, we find an increase of the noise equivalent temperature and of the longitudinal diffusion coefficient at intermediate field strengths below the threshold for negative differential mobility.

Collective motions in liquids with a normal mode approach

We present a theory of collective dynamics in simple liquids within a harmonic approximation. We extend the normal mode approximation, which has previously been applied to single-particle properties, such as the velocity autocorrelation function, to the calculation of the longitudinal and transverse particle current autocorrelation functions. Within the harmonic approximation, these autocorrelation functions may be related to a configuration-averaged phonon Green’s function, which is a generalization of the conventional Green’s function for a perfect crystal. We show that the calculation of this Green’s function is equivalent to the evaluation of a propagator in a random walk problem, in which a walker with internal states hops among sites located at the particles of the fluid. We develop an approximate, self-consistent theory for this Green’s function, which is used to calculate the longitudinal current correlation function for a dense Lennard-Jones fluid. The results are compared to previous computer simulations of this correlation function.

Mutual and self-diffusion in fluids undergoing strong shear.

We derive a Green-Kubo relation for the mutual diffusion tensor (MDT) of a binary fluid mixture subject to a strong Couette shear field. We calculate the MDT of a Lennard-Jones (LJ) mixture and the self-diffusion tensor (SDT) of a pure LJ fluid as functions of state point and strain rate. The qualitative dependence of the diffusion tensors upon these variables is explained in greater detail by analyzing the velocity and mass current autocorrelation functions. Finally, we compare the zero-color field color conductivity with the SDT. For nonzero shear rates we find that the color conductivity and the SDT are different, confirming the prediction by Evans, Baranyai, and Sarman [Mol. Phys. (to be published)], according to which these two transport coefficients should only be related at zero shear rate.

Fluidity and diffusion coefficient of simple liquids: a velocity field approach

The transverse current autocorrelation function, CT(k,t), can be represented as a sum of a velocity autocorrelation or 'self' term, CsT(k,t), and a cross-velocity or 'distinct' term, CdT(k,t). By means of the Langevin equation a generalized (i.e. k-dependent) fluidity, eta -1(k), may be introduced which is conveniently the sum of the contributions from the two components of the transverse current. The authors concentrate on CsT(k,t) and for the first time compare a theoretical prediction of this quantity for both liquid Rb and liquid Ar with computer simulation data. The success of the theory suggests a model for the associated fluidity, eta s-1 (k). They show how to use it to predict the diffusion coefficient of a number of simple liquids, with an estimated accuracy of 20 percent or better, given the shear viscosity coefficients as input data. A satisfactory representation of the distinct component, eta d-1(k), is more difficult to achieve, but they discuss the general features which are revealed by computer simulation studies.

Effect of signal discreteness on correlation functions

Number or density autocorrelation functions can sometimes be obtained in terms of electron emission current autocorrelation functions if the current fluctuations are related to the number fluctuations. This is the case in field emission where the fluctuations in adsorbate number in a small probed region, caused by surface diffusion, are essentially proportional to the field emission current fluctuations. The autocorrelation function of the current fluctuations then mirrors that of the adsorbate number fluctuations. When correlation intervals are very short they may contain an average number of electrons so small that the rms electron fluctuation resulting from adsorbate number fluctuations is less than 1 e− and thus shows up only infrequently. The electron fluctuation can then ‘‘miss’’ most adsorbate fluctuations. We have examined this problem by Monte Carlo modeling and confirm the existence of this effect when the electron fluctuation number is truncated to integer values. Even in this case the electron fluctuation correlation images the adsorbate number correlation function quite well to values of rms electron fluctuations as low as 0.4 e− per correlation interval. When shot noise is included imaging is good to the lowest value tested, 0.18 e−, but the number of summations required to overcome noise goes up very steeply. The reason for the improvement in imaging is that shot noise circumvents the problem of electron fluctuation inadequacy, since very small changes in mean electron emission probability, corresponding to much less than 1 e− per correlation interval, are reflected in the Poisson distribution. Thus shot noise in a way ‘‘amplifies’’ the fluctuations but at the price of vastly increased noise. This conclusion is probably not confined to the specific case examined here but seems generally valid.

A test of the timescale separation in solutions containing interacting Brownian-type particles

Theoretical work has shown that the timescale separation required for the application of the Smoluchowski, Fokker-Planck and Langevin equations to interacting Brownian particles in concentrated liquid solutions may not exist. In particular, it was suggested that the current autocorrelation function of the Brownian particles may not decay sufficiently quickly in comparison with the intermediate scattering function at appropriate wave vectors. Here, molecular dynamics (MD) calculations are performed for hard-soft-sphere liquid solutions containing Brownian-type particles of large mass and volume. The mass and volume ratio are varied systematically. The MD results indicate the following: (i) for solutions of equally sized particles, the current autocorrelation function of the massive particles decreases sufficiently quickly compared with the intermediate scattering function, thus ensuring timescale separation; (ii) massive particles of large volume diluted among light and small particles show a time decay of the current autocorrelation function, which approaches that of the intermediate scattering function. However, the similarity of the two correlation functions reduces with increasing mass ratio. Hence, for asymptotic conditions timescale separation can be expected.

Extraction of transport coefficients from correlation functions.

In this paper we apply a new method to the calculation of transport coefficients by computer simulation of fluids. It differs from previous methods in two essential respects. Firstly, it involves the simultaneous fitting of all of the correlations among conserved hydrodynamic variables, rather than just the density or current autocorrelation function. This gives more detailed information on the hydrodynamics, and, in particular, makes it possible to separate some of the effects of viscoelasticity, which may seriously bias transport-coefficient estimates. Secondly, it is formulated in a simple way, which avoids certain complicating approximations traditionally made in computing fluid correlation functions. Results of pilot calculations for the soft-sphere viscosity agree with those of previous workers. The most conspicuous physical effect observed is a strong wave-vector dependence of the thermal diffusivity, in agreement with previous work.

Unified formalism for excess current noise in random-walk models.

Excess current noise in random-walk models with a frequency-independent conductivity is studied from a general point of view. By introducing a ``dynamical'' diffusion constant, it is shown that the current autocorrelation function in an external field probes the equilibrium dynamical diffusion-constant autocorrelation function. From this a number of results, previously shown for particular models, are derived. Also, it is shown that the external-field current autocorrelation function is proportional to the equilibrium autocorrelation function for the absolute value of the current. Thus, the excess-noise spectrum probes the equilibrium-speed autocorrelation function. In the treatment advanced here, the study of excess current noise in random-walk models reduces to a study of the stochastic point process constituted by the particle-jump times. This point process contains all information about the noise. As an illustration of the general theory, the continuous-time random-walk model is briefly reviewed and a simple derivation of the excess noise in the model is given. Finally, the role of Fermi statistics in models for 1/f noise is discussed. It is argued that number-fluctuation models, i.e., models with long trapping times, are incompatible with Fermi statistics. On the other hand, it is shown there is a peculiar ``single-particle'' 1/f noise which is due to Fermi statistics but has nothing to do with the observed 1/f current noise.

Rearrangement reactions in the barbaralyl cation

Hyperspherical coordinates are used to define reaction paths for rearrangements of the C9H9+ barbaralyl cation and energy profiles are obtained from Gaussian 82 calculations using an STO-3G basis. A formula for the reaction rate is derived from the current autocorrelation function in the WKB approximation.

Anomalous fluctuations in random walk dynamics

The anomalous dispersion of noninteracting particles randomly walking in a network is considered. It is shown that the existence of large dangling branches attached to a backbone induces a 1/f-like behavior in the current autocorrelation function at low frequencies. The waiting times associated with dangling loops scale like t/sup -3/2/. The size of the dangling branches provides a lower cutoff to the power law behavior. When the side branches are infinite, self-similar structures, the power law behavior persists up to a zero frequency. The currents the authors consider are created either by a bias on the random walk or by a current source. They consider both the total current, which is often referred to in the literature, and the current measured at endpoints of a specimen attached to a (model) battery. The differences and similarities between the two corresponding correlations are analyzed. In particular, they find that in the second case 1/f noise exists only for large bias. When a statistical distribution of dangling branches is considered, they find that the largest power of frequency in the spectrum is 1.13. Much of their results are true when the dangling branches are replaced by traps having waiting time distributions that equalmore » those of the branches. The waiting time associated with a power law distribution of dangling loops (m/sup -x/: m is the length of the loop) scales like t/sup -1-(x/2)/. However, it is shown that geometry alone can be responsible for the appearance of power laws in the spectra. Random geometry can be regarded as a model (or source) of random hopping times.« less

Field-transverse spin response of degenerate normal and neutral Fermi liquids in dc magnetic fields

The microscopic approach to the formulated problem is presented. For dc magnetic fields H such that Hμ⪡ε F (ε F is the Fermi energy, μ the particle magnetic moment) only the H-transverse spin response is affected by H. The vertices of the transverse spin and the transverse spin current and their correlation functions are investigated. General formulae are obtained expressing correlation functions of transverse spin and transverse spin current by analogous correlation functions taken at H=0. Formulae for correlation functions are discussed in three various limits of the variable λ= kv/(ω-2μ H), namely ¦λ¦⪡1, ¦λ¦⪢1, and ¦λ¦∼1, where v is the Fermi velocity and ω, k the frequency and the wave vector of the perturbing external field, respectively. In the quasihomogeneous limit, ¦λ¦⪡1, the dispersion of the excitations with a gap of the order 2μ H will be found, for all orbital, l, and all magnetic, m, quantum numbers. The wave-vector longitudinal excitations ( m=0) contribute to the spin autocorrelation, whereas the longitudinal as well as transverse ones ( m=±1) contribute to the spin current autocorrelation functions. All residues of the quasihomogeneous autocorrelation functions are found if they are of the order O (λ 4) or greater. In the limit ¦λ¦⪢1, the correlation functions do not have polar character; their imaginary parts, due to Landau damping, are of the order of their real parts. The limit ¦λ¦∼1 corresponds to the threshold of Landau damping. Nonanalytic character of such functions leads to the nonexponential damping, with the depth of the absorber, of the ac magnetic field. The main part of the calculations are performed without any restrictions imposed on the Landau parameters, though in the final formula for ¦λ¦⪢1 and ∼1 it is necessary to restrict oneself to the parameters vanishing, e.g., at l⩾2 or 3, i.e. respectively to the SP and SPD approximations. For comparison, autocorrelation functions for m=0 and m=±1 are calculated in SP and SPD approximation, respectively, without restrictions imposed on λ.

Computation and analysis of the transverse current autocorrelation function, Ct(k,t), for small wave vectors: A molecular-dynamics study for a Lennard-Jones fluid.

Molecular-dynamics (MD) calculations are reported for three thermodynamic states of a Lennard-Jones fluid. Systems of 2048 particles and ${10}^{5}$ integration steps were used. The transverse current autocorrelation function, ${C}_{t}$(k,t), has been determined for wave vectors of the range 0.5l\ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\sigma}l1.5. ${C}_{t}$(k,t) was fitted by hydrodynamic-type functions. The fits returned k-dependent decay times and shear viscosities which showed a systematic behavior as a function of k. Extrapolation to the hydrodynamic region at k=0 gave shear viscosity coefficients in good agreement with direct Green-Kubo results obtained in previous work. The two-exponential model fit for the memory function proposed by other authors does not provide a reasonable description of the MD results, as the fit parameters show no systematic wave-vector dependence, although the ${C}_{t}$(k,t) functions are somewhat better fitted. Similarly, the semiempirical interpolation formula for the decay time based on the viscoelastic concept proposed by Akcasu and Daniels fails to reproduce the correct k dependence for the wavelength range investigated herein.