Charge Density Correlation Function Research Articles

Topological susceptibility and η′ meson mass from Nf=2 lattice QCD at the physical point

In this paper we explore the computation of topological susceptibility and $\eta'$ meson mass in $N_f=2$ flavor QCD using lattice techniques with physical value of the pion mass as well as larger pion mass values. We observe that the physical point can be reached without a significant increase in the statistical noise. The mass of the $\eta'$ meson can be obtained from both fermionic two point functions and topological charge density correlation functions, giving compatible results. With the pion mass dependence of the $\eta'$ mass being flat we arrive at $M_{\eta'}= 772(18)\ \mathrm{MeV}$ without an explicit continuum limit. For the topological susceptibility we observe a linear dependence on $M_\pi^2$, however, with an additional constant stemming from lattice artifacts.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

Contact electrification and the work of adhesion

We present a general theory for the contribution from contact electrification to the work necessary to separate two solid bodies. The theory depends on the surface charge density correlation function which we deduce from Kelvin Force Microscopy (KFM) maps of the surface electrostatic potential. For silicon rubber (polydimethylsiloxane, PDMS) we discuss in detail the relative importance of the different contributions to the observed work of adhesion.

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).

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).

Universality class of the critical point in the restricted primitive model of ionic systems

A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated into disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.

Modulation of charge-density waves by superlattice structures

We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (non-random) pattern of repulsive (U>0) and free (U=0) sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wavevectors, k_F*, and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from q*=0 to \pi, but also due to sharp 2k_F*-4k_F* transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems.

Currents in a many-particle parabolic quantum dot under a strong magnetic field

Currents in a few-electron parabolic quantum dot placed into a perpendicular magnetic field are considered. We show that traditional ways of investigating the Wigner crystallization by studying the charge density correlation function can be supplemented by the examination of the density-current correlator. However, care must be exercised when constructing the correct projection of the multi-dimensional wave function space. The interplay between the magnetic field and Euler-liquid-like behavior of the electron liquid gives rise to persistent and local currents in quantum dots. We demonstrate these phenomena by collating a quasi-classical theory valid in high magnetic fields and an exact numerical solution of the many-body problem.

Friedel oscillation in charge profile around superconducting vortex core

We numerically perform microscopic calculations for charge distributions around a superconducting vortex core on the basis of the BdG formalism including the Poisson equation for the scalar potential. The numerical results reveal that the charge distribution shows the Friedel oscillation around a vortex core and the oscillation survives over the coherence length in small kFξ cases, i.e. the quantum limit. To clarify the origin of the oscillation we study the charge screening properties by calculating the charge density correlation function around a vortex core. The correlation function strongly depends on the position from the vortex center and remarkably oscillates around the vortex core. This result indicates that the Thomas–Fermi type screening is broken in the vortex core.

Dynamic charge-density correlation function in weakly charged polyampholyte globules.

We study solutions of statistically neutral polyampholyte chains containing a large fraction of neutral monomers. It is known that such solutions phase separate at very low concentrations, even if the quality of the solvent with respect to the neutral monomers is good. The precipitate is semidilute if the chains are weakly charged. This paper considers straight theta solvents and good solvents, and we calculate the dynamic charge density correlation function g(k,t) in the precipitate, using the quadratic approximation to the Martin-Siggia-Rose generating functional. It is convenient to express the results in terms of dimensionless space and time variables. Let xi be the blob size, and let tau be the characteristic time scale at the blob level. Define the dimensionless wave vector q=xik, and the dimensionless time s=t/tau. In the regime q<1, corresponding to length scales larger than the blob size, and 1<s<q(-4), corresponding to time scales in between the blob relaxation time and the relaxation time at scale q(-1), we find that the charge density fluctuations relax according to the power law g(q,s) approximately q(2)s(-1/2). This relaxation is qualitatively different from that of a neutral semidilute polymer solution. We expect our results to be valid for wave vectors q>0.1, where entanglements are unimportant.

A simple model for Coulombic systems. Thermodynamics, correlation functions and criticality

A simple Landau–Ginzburg Hamiltonian is proposed to study an example of critical behavior in ionic systems. We focus on the role of asymmetry between ions which is common in real systems. The free energy calculated via a functional integration contains a divergence due to the Coulombic self energy. The finite part is just the Debye–Huckel limiting law with the correction due to the asymmetry. The criticality in our model is associated with an attractive non-Coulombic interaction between ions whatever their sign. At the level of our model there is no criticality for the restricted primitive model. The correlation functions are calculated. Out of the criticality the charge–charge correlation function conforms to the Stillinger–Lovett conditions and the charge–density coupling vanishes in the long wavelength limit. At the criticality due to the asymmetry the effective density of free charge carriers has to be reduced to verify the second Stillinger–Lovett condition and the charge-density correlation function exhibits a long wavelength coupling.

Charge fluctuations in the slave fermion representation of the t - J model - evidence for phase separation from loop corrections

We investigate the charge density correlation function in the slave fermion representation of the two-dimensional t - J model using the self-consistent perturbation approach developed for that model by Li et al (1992 Phys. Rev. B 45 5428), which to lowest order in (t, J) gives a diagrammatic equivalent to the usual mean field theory. At the lowest order the equal-time correlation function (interpreted as the holon density correlation function) shows similar features to the results of recent high-temperature series calculations. However the loop corrections, representing scattering of holes by the antiferromagnetic spin fluctuations, lead to a divergent compressibility at low temperatures for low hole dopings and small J/t, which we interpret as indicating a tendency towards phase separation at a temperature .

Variational Monte-Carlo Studies of Hubbard Model. III. Intersite Correlation Effects

New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.

Microscopic theory of the long-wavelength modes of two-component plasmas and ionic liquids

Abstract The identity between the exact screening length obtained from the static charge density correlation function and the one which appears in the Einstein relation between the transport coefficients of electrical conductivity and mass diffusion is demonstrated from first principles. For the space-time correlation functions of the number densities we show that their long-wavelength behaviour is completely determined by the four hydrodynamical modes of the two-component system of neutral particles. For charged particle systems there are only three hydrodynamical modes while we have moreover to add the two charge relaxation modes in order to exhaust the long-wavelength limit of the first sum-rule. The strengths with which the various modes appear in the space-time correlation functions have been computed exactly in the limit of long wavelengths.

Plasmon-Phonon Interference in CdS

The Raman spectra of plasmons in In- and Ga-doped cadmium sulfide are shown to consist of very asymmetric peaks. A prominent interference shape is exhibited which is very similar to that manifested by anharmonic phonon interactions between two optical phonons, as in AlP${\mathrm{O}}_{4}$ and BaTi${\mathrm{O}}_{3}$. In the present case, the interaction between the heavily damped plasmon mode and one longitudinal optical phonon is due to the Coulomb interaction. The interference features of the Raman spectrum are related to the electronic (plasmon) and ionic (phonon) charge-density correlation functions, where the ionic charge is multiplied by a factor to include the nonionic (electronic) part of the light-phonon scattering amplitude. In other words, we treat the spectrum as due to interfering amplitudes for scattering into the plasmon state $〈\mathrm{PL}|$ via two channels: one direct, $〈\mathrm{PL}|\ensuremath{\alpha}|0〉$; and one via an intermediate LO-phonon state coupled by the Coulomb interaction, $〈\mathrm{PL}|\mathrm{Coul}.|\mathrm{LO}〉\ifmmode\times\else\texttimes\fi{}〈\mathrm{LO}|\ensuremath{\alpha}|0〉$. This calculation gives very good agreement with the observed line shape, and demonstrates the inadequacy of treating the spectrum in terms of the usual dielectric function. In the special case when the light-phonon scattering is purely ionic, however, our Green's-function calculation is shown to be equivalent to the dielectric-function formulation which includes both the plasmon and phonon contributions. A detailed comparison of our theory with the experimental spectrum yields an estimate of the relative contributions to the light-phonon scattering amplitude from electronic and ionic charges. For CdS, these contributions are found to be of the same order of magnitude, but opposite in sign.