Current Correlation Function Research Articles

Supersymmetric Adler functions and holography

We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.

Hydrodynamics in adaptive resolution particle simulations: Multiparticle collision dynamics

A new adaptive resolution technique for particle-based multi-level simulations of fluids is presented. In the approach, the representation of fluid and solvent particles is changed on the fly between an atomistic and a coarse-grained description. The present approach is based on a hybrid coupling of the multiparticle collision dynamics (MPC) method and molecular dynamics (MD), thereby coupling stochastic and deterministic particle-based methods. Hydrodynamics is examined by calculating velocity and current correlation functions for various mixed and coupled systems. We demonstrate that hydrodynamic properties of the mixed fluid are conserved by a suitable coupling of the two particle methods, and that the simulation results agree well with theoretical expectations.

Breakdown of electron-pairs in the presence of an electric field of a superconducting ring

The quantum dynamics of quasi-one-dimensional ring with varying electron filling factors is investigated in the presence of an external electric field. The system is modeled within a Hubbard Hamiltonian with attractive Coulomb correlation, which results in a superconducting ground state when away from half-filling. The electric field is induced by applying time-dependent Aharonov–Bohm flux in the perpendicular direction. To explore the non-equilibrium phenomena arising from the field, we adopt exact diagonalization and the Crank–Nicolson numerical method. With an increase in electric field strength, the electron pairs, a signature of the superconducting phase, start breaking and the system enters into a metallic phase. However, the strength of the electric field for this quantum phase transition depends on the electronic correlation. This phenomenon has been confirmed by flux-quantization of time-dependent current and pair correlation functions.

Chiral Fermion and boundary state formulation: Resonant point-contact tunneling

We study a model of resonant point-contact tunneling of a single Luttinger-liquid lead, using the boundary state formulation. The model is described by a single chiral Fermion in one-dimensional space with one point contact interaction at the origin. It is the simplest model of this type. By folding the infinite line, we map the model onto a nonchiral model on the half infinite line and transcribe the point-contact tunneling interaction into a boundary interaction. The tunneling interaction yields a nonlocal effective action at the boundary. We explicitly construct the boundary state and evaluate the current correlation functions. The contact interaction is shown to act on the lower frequency modes more strongly.

Mapping the current–current correlation function near a quantum critical point

The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.

An Advanced Physics of Superfluidity and Superconductivity

This paper presents an advanced Physics of superfluidity and superconductivity. We know from Quantum Mechanics that there are two types of particles, bosons and fermions. Single states can be occupied by any number of bosons while for fermions a single state can be occupied at most by one fermion. The charged boson system is found to exhibit superfluidity: the gauge-invariant Lagrangian, coupling between the bosons and the electromagnetic gauge field. It is observed that current conservation puts constraints on current correlation. Current correlation functions and electromagnetic responses are then determined for superfluids and metals. The response function in a metallic conductor is used in obtaining its several parameters which include conductivity, dielectric constant, polarization, magnetic moment density and magnetic susceptibility. The London equation is then deduced for superconductors.

Stokes-Einstein relation and excess entropy scaling law in liquid Copper

We report an ab initio study of structural and dynamic properties of liquid copper as a function of temperature. In particular, we have evaluated the temperature dependence of the self-diffusion coefficient from the velocity autocorrelation function as well the temperature dependence of the viscosity from the transverse current correlation function. We show that LDA based results are in close agreement with experimental data for both the self-diffusion coefficient and the viscosity over the temperature range investigated. Our findings are then used to test empirical approaches like the Stokes-Einstein relation and the excess entropy scaling law widely used in the literature. We show that the Stokes-Einstein relation is valid for the liquid phase and that the excess entropy scaling law proposed by Dzugutov is legitimate only if a self-consistent method for determining the packing fraction of the hard sphere reference liquid is used within the Carnahan-Starling approach to express the excess entropy.

Effects of interaction symmetry on delocalization and energy transport in one-dimensional disordered lattices.

We study effects of interaction symmetry in one-dimensional, momentum-conserving disordered lattices. It is found that asymmetric and symmetric interparticle interactions may result in significant difference: localized modes can be delocalized by very weak asymmetric interactions but survive much stronger symmetric interactions. Moreover, in the delocalization regime, asymmetric and symmetric interactions also have qualitatively different effects on transport: the former (the latter) may lead to a fast decaying (slow power-law decaying) heat current correlation function and in turn a convergent (divergent) heat conductivity. A method for detecting delocalization in systems at a nonzero temperature is proposed as well.

Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux

The phase diagram of a half-filled hard-core boson two-leg ladder in a flux is investigated by means of numerical simulations based on the density matrix renormalization group (DMRG) algorithm and bosonization. We calculate experimentally accessible observables such as the momentum distribution, as well as rung current, density wave, and bond-order wave correlation functions, allowing us to identify the Mott Meissner and Mott vortex states. We follow the transition from commensurate Meissner to incommensurate vortex state at increasing interchain hopping until the critical value [Piraud et al. Phys. Rev. B 91, 140406 (2015)] above which the Meissner state is stable at any flux. For flux close to $\ensuremath{\pi}$, and below the critical hopping, we observe the formation of a second incommensuration in the Mott vortex state that could be detectable in current experiments.

Novel Lissajous figure based location method for fiber-optic distributed disturbance sensor

A location method based on the Lissajous figure is proposed for fiber-optic distributed disturbance sensor based on Mach–Zehnder interferometer. The disturbance is located by the fiber-optic distributed disturbance sensor due to the time delay between the two signals from clockwise and counter-clockwise Mach–Zehnder interferometers. In the Lissajous figure of the two signals, a fitting ellipse with constant semi-major and azimuths is induced to evaluate the time delay. The relationship between the time delay and semi-minor of the ellipse is obtained by linear fitting. Then, the time delay can be calculated by the semi-minor of the fitting ellipse. In the experiment with 2km long fiber and 4MHz sampling frequency, the maximal location errors with Lissajous figure based method and current cross correlation function based method, without phase generation carrier technique, are 75m and 1.25km, respectively. It seems to be that our proposed Lissajous figure based method is a useful for improving fiber-optic distributed disturbance sensor.

Spin Dependent Thermoelectric Currents of Tunnel Junctions, Small Rings and Quantum Dots: Onsager Theory

Spin Currents in Tunnel Junctions for example induced by thermoelectric forces due to temperature and magnetization gradients etc. are analyzed. Using Onsager theory in particular for magnetic tunnel junctions, metallic rings and quantum dots yields directly, spin dependently all thermoelectric and thermomagnetic effects like Seebeck and Peltier ones and Josephson like Spin currents driven by the phase gradient of the magnetization. The results can be compared with recent experiments determining the Spin dependent Seebeck effect and other thermoelectric effects. The Onsager theory can be extended towards an electronic theory by expressing the Onsager coefficients by current correlation functions and then calculating these using Lagrange formalism, symmetry and scaling analysis. Note, Onsager theory can also be applied to spin currents in molecules and in magnetic ionic liquids.

Singlet axial-vector coupling constant of the nucleon in QCD without instantons

We have analyzed axial-vector current–current correlation functions between one-nucleon states to calculate the singlet axial-vector coupling constant of the nucleon. The octet–octet and the octet–singlet current correlators, investigated in this work, do not require any use of instanton effects. The QCD and hadronic parameters used for the evaluation of correlators have been varied by (10–20)%. The value of the singlet axial-vector coupling constant of the nucleon obtained from this analysis is consistent with its current determination from experiments and QCD theory.

Non-linear quantum noise effects in scale invariant junctions

We study non-equilibrium steady state transport in scale invariant quantum junctions with focus on the particle and heat fluctuations captured by the two-point current correlation functions. We show that the nonlinear behavior of the particle current affects both the particle and heat noise. The existence of domains of enhancement and reduction of the noise power with respect to the linear regime are observed. The impact of the statistics is explored. We demonstrate that the bosonic particle noise exceeds the fermionic one in the common domain of heat bath parameters. Multi-lead configurations are also investigated and the effect of probe terminals on the noise is discussed.

Transverse excitations in liquid Fe, Cu and Zn

Transverse acoustic (TA) excitation modes were observed in inelastic x-ray scattering spectra of liquid Fe, Cu and Zn. From the analysis of current correlation functions, we concluded that TA excitation modes can experimentally be detected through the quasi-TA branches in the longitudinal current correlation spectra in these liquid metals. The microscopic elastic constants are estimated and a characteristic difference from macroscopic polycrystalline value was found in Poisson's ratio of liquid Fe, which shows an extremely softer value of ∼0.38 compared with the macroscopic value of ∼0.275. The lifetime of the TA modes were determined to be ∼0.45 ps for liquid Fe and Cu and ∼0.55 ps for liquid Zn, reflecting different interatomic correlations between liquid transition metals and non-transition metals. The propagation length of the TA modes are ∼0.85 nm in all of liquid metals, corresponding to the size of icosahedral or similar size of cages formed instantaneously in these liquid metals.

Chiral bosonic phases on the Haldane honeycomb lattice

Recent experiments in ultracold atoms and photonic analogs have reported the implementation of artificial gauge fields in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate the Haldane honeycomb lattice tight-binding model, for bosons with local interactions at the average filling of one boson per site. We analyze the ground state phase diagram and uncover three distinct phases: a uniform superfluid (SF), a chiral superfluid (CSF) and a plaquette Mott insulator with local current loops (PMI). Nearest-neighbor and next-nearest neighbor currents distinguish CSF from SF, and the phase transition between them is first order. We apply bosonic dynamical mean field theory and exact diagonalization to obtain the phase diagram, complementing numerics with calculations of excitation spectra in strong and weak coupling perturbation theory. The characteristic density fluctuations, current correlation functions, and excitation spectra are measurable in ultracold atom experiments.

Current–current correlation function in 3D massive Dirac theory with chemical potential

The response of fermionic system to external gauge fields is defined by current–current correlation function Πμν(q, q0). Transport properties of different physical quantities are determined by zero energy–momentum limit of it. As it is known close to half-filling the physics of graphene is described by (2+1)-dimensional Dirac theory. In this paper, we calculate current–current correlation function in Dirac theory in a presence of chemical potential η and gap m.

Heat-current correlation loss induced by finite-size effects in a one-dimensional nonlinear lattice.

The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.

Electromagnetic probes in heavy-ion collisions

Due to their penetrating nature, electromagnetic probes, i.e., lepton-antilepton pairs (dileptons) and photons are unique tools to gain insight into the nature of the hot and dense medium of strongly-interacting particles created in relativistic heavy-ion collisions, including hints to the nature of the restoration of chiral symmetry of QCD. Of particular interest are the spectral properties of the electromagnetic current-correlation function of these particles within the dense and/or hot medium. The related theoretical investigations of the in-medium properties of the involved particles in both the partonic and hadronic part of the QCD phase diagram underline the importance of a proper understanding of the properties of various hadron resonances in the medium.

Fermion pairing and the scalar boson of the 2D conformal anomaly

We analyze the phenomenon of fermion pairing into an effective boson associated with anomalies and the anomalous commutators of currents, bilinear in the fermion fields. In two spacetime dimensions the chiral bosonization of the Schwinger model is determined by the chiral current anomaly of massless Dirac fermions. A similar bosonized description applies to the 2D conformal trace anomaly of the fermion stress-energy tensor. For both the chiral and conformal anomalies, correlation functions involving anomalous currents, j 5 or T μν of massless fermions exhibit a massless boson 1/k 2 pole, and the associated spectral functions obey a UV finite sum rule, becoming δ-functions in the massless limit. In both cases the corresponding effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a new bosonic field, which becomes a bona fide propagating quantum field in its own right. In both cases this is expressed in Fock space by the anomalous Schwinger commutators of currents becoming the canonical commutation relations of the corresponding boson. The boson has a Fock space operator realization as a coherent superposition of massless fermion pairs, which saturates the intermediate state sums in quantum correlation functions of fermion currents. The Casimir energy of fermions on a finite spatial interval [0, L] can also be described as a coherent scalar condensation of pairs, and the one-loop correlation function of any number n of fermion stress-energy tensors 〈TT . . . T 〉 may be expressed as a combinatoric sum of n!/2 linear tree diagrams of the scalar boson.

Understanding the atomic-level Green-Kubo stress correlation function for a liquid through phonons in a model crystal

In order to gain insight into the connection between the vibrational dynamics and the atomic-level Green-Kubo stress correlation function in liquids, we consider this connection in a model crystal instead. Of course, vibrational dynamics in liquids and crystals are quite different and it is not expected that the results obtained on a model crystal should be valid for liquids. However, these considerations provide a benchmark to which the results of the previous molecular dynamics simulations can be compared. Thus, assuming that vibrations are plane waves, we derive analytical expressions for the atomic-level stress correlation functions in the classical limit and analyze them. These results provide, in particular, a recipe for analysis of the atomic-level stress correlation functions in Fourier space and extraction of the wave-vector and frequency-dependent information. We also evaluate the energies of the atomic-level stresses. The energies obtained are significantly smaller than the energies previously determined in molecular dynamics simulations of several model liquids. This result suggests that the average energies of the atomic-level stresses in liquids and glasses are largely determined by the structural disorder. We discuss this result in the context of equipartition of the atomic-level stress energies. Analysis of the previously published data suggests that it is possible to speak about configurational and vibrational contributions to the average energies of the atomic-level stresses in a glass state. However, this separation in a liquid state is problematic. We also introduce and briefly consider the atomic-level transverse current correlation function. Finally, we address the broadening of the peaks in the pair distribution function with increase of distance. We find that the peaks' broadening (by $\ensuremath{\approx}40%$) occurs due to the transverse vibrational modes, while contribution from the longitudinal modes does not change with distance.