Current Density Correlation Functions Research Articles

Spatially resolved collective excitations of nano-plasmas via molecular dynamics simulations and fluid dynamics

Collective excitations in nano-plasmas are described by dynamical bi-local auto-correlation functions. These excitations, which are related to the plasmon excitations in bulk plasmas, arise in the classical as well as the quantum regime. Instead of the wave-vector-dependent dynamical structure factor, which is not well defined in finite systems, two different signatures are considered to characterize collective excitations: the bi-local particle density correlation function and the bi-local current density correlation function. The relation between both signatures is not as trivial as in the homogeneous case and is given here. Exemplary calculations are performed for expanding nearly spherical clusters of sodium atoms after excitation by a high-intensity short pulse laser beam. The lowest collective excitations obtained in the classical regime using molecular dynamics simulations agree well with the lowest collective excitations obtained from quantum calculations using fluid dynamics. The energy, damping and structure of the lowest collective modes are given. The dynamical bi-local correlation functions are of relevance for the optical properties, in particular the determination of photo absorption coefficients of nano-plasmas.

Investigations of instabilities in nuclear matter in stochastic relativistic models

Abstract The spinodal instabilities for symmetric nuclear matter at finite temperature are studied within different relativistic mean-field models in the semi-classical approximation and the relativistic results are compared with Skyrme type non-relativistic calculations. Qualitatively similar results appear in the unstable response of the system in both non-relativistic and relativistic descriptions. Furthermore, the early growth of baryon, scalar and current density correlation functions are calculated for hot symmetric nuclear matter.

Exact scaling relations in relativistic hydrodynamic turbulence

We consider the steady state statistics of turbulence in general classes of dissipative hydrodynamic equations, where the fluctuations are sustained by a random source concentrated at large scales. It is well known that in some particular cases, such as non-relativistic incompressible turbulence, a Kolmogorov-type exact scaling relation for a correlation function holds. We show that all such scaling relations follow from a general relation on the current-density correlation function. The derivation does not require an energy cascade picture and suggests that this traditional interpretation of the Kolmogorov relation for incompressible turbulence may be misleading. Using this we derive exact scaling results for compressible turbulence in relativistic hydrodynamics, which reduce in the slow motion limit to the Kolmogorov relation. We discuss the experimental implications of the results.

Charge and Current Sum Rules in Quantum Media Coupled to Radiation II

This paper is a continuation of the previous study [\v{S}amaj, L.: J. Stat. Phys. {\bf 137}, 1-17 (2009)], where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov's fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).

New relations for correlation functions in Navier–Stokes turbulence

We consider the steady-state statistics of turbulence in the inertial interval. The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current–density correlation function. Using that, we derive an analogous flux relation for compressible turbulence and a new exact relation for incompressible turbulence.

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper is a continuation of the previous study [\v{S}amaj, L.: J. Stat. Phys. {\bf 137}, 1-17 (2009)], where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov's fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).

The heat current density correlation function: sum rules and thermal conductivity

Expressions for the second and fourth sum rules of the heat current density correlationfunction have been derived in an appropriate ensemble. The thermal conductivity ofLennard-Jones fluids has been calculated using these sum rules for the heat current densitycorrelation function and the Gaussian form of the memory function. It is found that theresults obtained for the thermal conductivity are in good agreement with the moleculardynamics simulation results over a wide range of densities and temperatures. Earlierresults obtained using the energy current density correlation function are alsodiscussed.

Theory of photoluminescence in semiconductors

A theory is presented that relates the luminescence signal of a semiconductor to the current-density correlation function. It allows the calculation of the luminescence spectrum for nonthermal carrier distributions by means of solving the Bethe-Salpeter equation for the polarization. The present method passes important consistency checks and overcomes some limitations and shortcomings of previous approaches. A detailed comparison is made with previous results and numerical examples are presented to demonstrate the usefulness of the present method.

The effect of trapped flux upon the magnetic field dependence of the critical current of Josephson junctions

Measurements of the magnetic field dependence of the critical current I/sub c/(B) of Josephson junctions, involving high temperature superconductors, often give evidence that the supercurrents are spatially non-uniform. However, flux trapping can complicate the interpretation of I/sub c/(B) curves. A model has been developed for the behaviour of SNS type junctions in a trilayer geometry containing trapped flux. We have investigated, using this model, combined with simulations, how the features of the I/sub c/(B) curve change as the number of trapped fluxlines increases. For a uniform junction, flux-trapping distorts the I/sub c/(B) curve and suppresses the maximum critical current by 1//spl radic/N/sub f/ where N/sub f/ is the number of fluxlines. The effect of trapped flux on current density correlation functions derived using the Wiener-Khinchine theorem from I/sub c/(B) curves has also been investigated and is described. In addition we discuss the relevance of the model to planar geometries. >

Response functions and spectrum of collective excitations of fractional-quantum-Hall-effect systems.

We calculate the electromagnetic response functions of a Fractional Quantum Hall system within the framework of the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before. Our results are valid in a semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-\-by-\-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the $f$-sum rule.We obtain the spectrum of collective excitations of FQHE systems in the low-momentum limit. We find a rich spectrum of modes which includes a host of quasiparticle- quasihole bound states and, in general,two collective modes coalescing at the cyclotron frequency. The Hall conductance is obtained from the current-density correlation function, and it has the correct value already at the semiclassical level. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. Finally, we reconsider the anyon superfluid within our scheme and derive the spectrum of collective modes for interacting hard-core bosons and semions. In addition to the gapless phase mode, we find a set of gapped collective modes.

Theory of transport coefficients of simple fluids

The authors report exhaustive calculations of the density and temperature dependences of the time evolution of the velocity, transverse stress and energy current density correlation functions and the corresponding transport coefficients for Lennard-Jones fluids over wide ranges of densities and temperatures. The calculated results are compared with the recent molecular dynamics data. Overall, good agreement has been achieved.

Dynamic properties of supercooled Lennard-Jones liquids: a molecular-dynamics study

Results are presented of molecular-dynamics experiments in which the Lennard-Jones liquid is cooled isobarically into the metastable temperature region. At a reduced temperature T approximately=0.45 a specific-heat anomaly is observed. Results are given for the density and current-density correlation functions. The variation of viscosity and coefficient of self-diffusion with temperature can be fitted to a power-law behaviour with an exponent mu =1.8, in close agreement with predictions of recently proposed mode-coupling models.

Energy current density correlation function. II. Thermal conductivity

For pt.I see ibid., vol.1, p.6181 (1989). Expressions for the energy current density correlation function and the thermal conductivity have been derived using a continued-fraction representation of correlation function. A secant hyperbolic, a Gaussian and an exponential form of the memory function have been used. The parameters appearing in the memory function are determined from the zeroth-, second- and fourth-frequency sum rules of the energy current density correlation function. For the time dependence of the energy current density correlation function and the thermal conductivity, the results obtained for the Lennard-Jones fluids, have been compared with recent computer simulation data. Overall good agreement has been obtained over a wide range of densities and a wide range of temperatures.

Energy current density correlation function. I. Frequency sum rules

Expressions for zeroth-, second- and fourth-frequency sum rules of energy current density correlation function have been derived. These exact expressions involve static correlation functions of up to five particles. Because of the non-availability of any information about triplet and higher-particle correlation functions, the authors use a low-order decoupling approximation for these. The resulting expressions for the frequency sum rules, which now contain only a static pair correlation function and an inner-atomic potential, are suitable for applications. Numerical results for these frequency sum rules have been obtained for Lennard-Jones fluids over a wide range of densities and temperatures. The density and temperature dependence and the relative importance of higher-particle correlation contributions to the frequency sum rules have been discussed.

Generalized hydrodynamics for simple fluids

Abstract Linear response theory is used to derive generalized nonlocal macroscopic equations which descibe the free relaxation of a system initially constrained to be in a state not far from its unperturbed equilibrium state. When the complete set of macroscopic variables is the set of hydrodynamic variables, it is then demonstrated that the matrix of coefficients of these generalized equations can rigorously be used to relate the entire matrix of time-dependent conserved-variable correlation functions to the matrix of their equal-time correlation functions. By restricting the regime of interest to be the hydrodynamic regime, where the conserved variables vary much more slowly than the remaining dynamical variables of the system, the conservation laws are used to develop a procedure for obtaining the terms in the matrix of coefficients as an expansion in powers of the wavevector, k , with explicit molecular expressions worked out for the terms through order k4. The expressions are shown to involve limits of generalized current-density correlation functions containing no conserved parts which are therefore well behaved for small frequencies. The forms of the macroscopic equations and the correlation functios implied by this order approximation to the matrix of coefficients are discussed in detail. Reasons are given why a double generalization, which considers both the time dependence and k dependence of the terms in the matrix, is necessary beyond order k2 in simple fluids.

Generalized hydrodynamics for dilute gases: The application to light-scattering experiments

Abstract The application of generalized hydrodynamics to dilute gases is considered. A density expansion technique for treating k -nad ω-dependent current-density correlation functions is discussed and carried out for dilute gases. It is shown that to order k2, these correlatio functions can be reduced to single integral expressions involving only two or three Legendre components of the linearized Boltzmann collision operator. The expressions are evaluated analytically for a dilute gas of Maxwell molecules and exact numerical expressions for the generalized transport coefficients, consistent with the order of approximation considered, are obtained. From these expressions, the appropriate approximation to the density-density autocorrelation functions is determined and compared to forms obtained from the Navier-Stokes and the Burnett equations. The failure of the Burnett equations to predict cross-correlation functions which satisfy the appropriate symmetry properties is alos discussed. The detailed form for the light-scattering spectrum is presented and analyzed. It is shown that the spectrum does not consist of just three lorentzian lines. To the order of the first correction to the speed of sound, which exhibits a positive dispersion in this regime, a shift in the positions of the maxima of the Brillouin lines toward the Rayleigh line is shown to arise solely from the non-lorentzian shape of the Brillouin doublet and not from an overlap with the central line as has been reported previously, The results are presented in a form which can readily be compared to experiments done on gases. The interpretation of experiments on liquids is also discussed with an emphasis on how the importance of generalized hydrodynamic effects can be deduced from the data.