Phase Correlation Functions Research Articles

Dynamical Mean Field Solution of the Bose-Hubbard Model

We present the effective action and self-consistency equations for the bosonic dynamical mean field approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations, we use a continuous-time MonteCarlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.

Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.

Universal characteristics of nonuniform quasi–two-dimensional cold atom systems

We study the nonuniform potential effect in a quasi--two-dimensional (2D) Bose gas system at a finite temperature by numerically solving the projected Gross-Pitaevskii equation. The gradual emergence of superfluidity is confirmed by calculating the moment of inertia as the temperature decreases. Reflecting the nonuniformity of the system, the long-distance decay of a phase-correlation function is characterized by a local effective exponent, $\ensuremath{\eta}(r)$, which depends on the local superfluid density. This ``local-density approximation'' is endorsed by the 2D Gaussian field theory with the nonuniform coupling constant. Indeed, the effective exponent turns out to be close to $1/4$ at the boundary of the phase-coherent region.

Finite-temperature transition in a quasi-2D Bose gas trapped in the harmonic potential

We study the finite-temperature transition of the quasi-2D Bose gas in an uniaxially-compressed harmonic trap by numerically solving the projected Gross-Pitaevskii equation. Gradual emergence of superfluidity is confirmed by calculating the moment of inertia when a temperature decreases. By investigating the long-distance behavior of a phase correlation function, superfluid density gradually increases reflecting the development of the phase correlation around the center of the system. From these results, we obtain the evidence for the emergence of superfluidity in this system directly.

Angle-of-arrival fluctuations for general-type beams

Starting with the recently introduced phase correlation function of a general-type beam, the angle-of-arrival fluctuations are derived and evaluated in atmospheric turbulence for lowest-order Gaussian, cos-Gaussian, cosh-Gaussian, annular, and flat-topped beams. Our motivation is to examine the improvement in the performance of optical atmospheric links when such beams are employed. For these beams, the dependence of the angle-of-arrival fluctuations on the propagation length, displacement and focusing parameters, source size, inner and outer scales of turbulence, and receiver radius is investigated. It is found that in the majority of the cases examined, the angle-of-arrival fluctuations remain small and hence are not expected to adversely affect the operation of free-space atmospheric links. It is observed that amongst the beams considered, the cos-Gaussian beam offers the least amount of angle-of-arrival fluctuations, while the worst behavior is exhibited by the cosh-Gaussian beam. This situation is reversed, however, if focused beams are used.

Structure functions in turbulence for incidence with arbitrary-field distribution

In a turbulent atmosphere, the log-amplitude, phase-correlation, and structure functions are formulated for light sources exhibiting arbitrary-field distribution. This is done by extending the formulations of the correlation and structure functions for the known general-type beam sources to cover any type of source having arbitrary-field distribution. To introduce the arbitrary field, the source is presented by an incidence that is a function of transverse source coordinates. The received field in the random medium is found by employing the Rytov method, which is a single-scattering solution obtained by the first-order approximation; thus our results are valid in weak turbulence. All the existing results can be correctly reproduced from our formulations when the corresponding source-field distributions are inserted into our presented correlation and structure-function expressions. Our results for the arbitrary-source field profiles can be utilized in finding the scintillation index and the angle-of-arrival fluctuations of any type of incidence in optical atmospheric links. Additionally, our formulations can find applications in reflection from rough surfaces and imaging in turbulence.

Variational study of the one dimensionalt–J model: a unified description of the ground state phase diagram

We find that the Gutzwiller projected Fermi sea wavefunction (GPWF) has the correct phasestructure to describe the kink nature of the doped holes in the ground state of the one dimensionalt–J model. We find the residual charge correlation beyond the GPWF is well described by anXXZ-type effective Hamiltonian. A Pfaffian-type variational wavefunction with onlyone parameter is proposed based on this observation and is found to reproducecorrectly the global phase diagram and correlation functions of the one dimensionalt–J model in both the Tomonaga–Luttinger regime and the Luther–Emery regime.

SU(N) quantum spin models: a variational wavefunction study

SU(N) quantum spin systems may be realized in a variety of physical systems includingultracold atoms in optical lattices. The study of such models also leadsto insights into possible novel quantum phases and phase transitions ofSU(2) spin models. Here we use Gutzwiller projected fermionic variationalwavefunctions to explore the phase diagram and correlation functions ofSU(N) quantum spin models in the self-conjugate representation. In one dimension, the ground state of theSU(4) spin chain with Heisenberg bilinear and biquadratic interactions is studied by examininginstabilities of the Gutzwiller projected free fermion ground state to various broken symmetries.The variational phase diagram so obtained agrees well with exact results. The spin–spinand dimer–dimer correlation functions of the Gutzwiller projected free fermion state withN flavours of fermions are in good agreement with exact and1/N calculations for thecritical points of SU(N) spin chains. In two dimensions, the phase diagram of the antiferromagnetic Heisenbergmodel on the square lattice is obtained by finding instabilities of the Gutzwiller projectedπ-flux state. In the absence of biquadratic interactions, the model exhibits long-range Néel order forN = 2 and 4, and spin Peierls (columnar dimer) order forN>4. Upon including biquadratic interactions in theSU(4) model (with a sign appropriate to a fermionic Hubbard model), the Néel order diminishes andeventually disappears, giving way to an extended valence bond crystal. In the case of theSU(6) model, the dimerized ground state melts at sufficiently large biquadratic interaction, yielding a projectedπ-flux spin liquid phase which in turn undergoes a transition into an extended valence bondcrystal at even larger biquadratic interaction. The spin correlations of the projectedπ-flux state atN = 4 are in goodagreement with 1/N calculations. We find that the state shows strongly enhanced dimer correlations,in qualitative agreement with recent theoretical predictions. We alsocompare our results with a recent quantum Monte Carlo study of theSU(4) Heisenberg model.

Reduction of effective dimensionality in lattice models of superconducting arrays and frustrated magnets

Some frustrated magnets and superconducting arrays possess unusual symmetries that cause the free energy or other physics of a D-dimensional quantum or classical problem to be that of a different problem in a reduced dimension d < D . Examples in two spatial dimensions include the square-lattice p + i p superconducting array, the Heisenberg antiferromagnet on the checkerboard lattice (studied by a combination of 1 / S expansion and numerical transfer matrix), and the ring-exchange superconducting array. Physical consequences are discussed both for “weak” dimensional reduction, which appears only in the ground state degeneracy, and “strong” dimensional reduction, which applies throughout the phase diagram. The “strong” dimensional reduction cases have the full lattice symmetry and do not decouple into independent chains, but their phase diagrams, self-dualities, and correlation functions indicate a reduced effective dimensionality. We find a general phase diagram for quantum-dimensional reduction models in two quantum dimensions with N-fold anisotropy, and obtain the Kosterlitz–Thouless-like phase transition as a deconfinement of dipoles of 3D solitons.

Bandgap mapping for III-V quantum well by electron spectroscopy imaging

The concept of 'bandgap mapping' was proposed originally to map the inhomogeneity of band energy in III-V semiconductors with a spatial resolution of a few nanometres in a scanning transmission electron microscope with the focus beam mode. In this paper, several techniques were developed to demonstrate the possibility to map the distribution of bandgap energies for GaN/AlN quantum-well structures using electron spectroscopy imaging (ESI). The phase correlation function was used to register different energy-loss images among ESI series with an accuracy of 1 pixel. The energy dispersion of ESI series was improved by a fast Fourier transform interpolation method. An iterative multivariable least square algorithm was derived to refine the fitting of the single scattering distribution to an analytic form of the density of states function a(E - E(g))(0.5). The inhomogeneity of the band energy of the quantum well can be revealed from the band-energy map. A threshold filter method is applied to estimate the average value and SD of the bandgap energy from barrier and well regions in the energy map. The average bandgap energy of AlN and GaN is determined to be 5.62 +/- 0.35 and 3.87 +/- 0.36 eV, respectively. The effect of delocalization on the accuracy of band-energy determination is discussed. The 2sigma(E(g)) accuracy of this analysis is comparable to half of the energy resolution of the ESI experiment.

Correlation and structure functions of Hermite-sinusoidal-Gaussian laser beams in a turbulent atmosphere.

To study the performance of atmospheric optical links by using Hermite-sinusoidal-Gaussian laset beam sources, we derive the log-amplitude and the phase correlation and structure functions of such beams in a turbulent atmosphere. Our formulations correctly reduce to the known higher-order mode correlation and structure functions, which in turn reduce to the fundamental-mode (TEM00-mode) results. Several special cases of our formulation are presented, among which the case involving Hermite-cosh-Gaussian dependence is especially noted, since this case is of interest to us owing to the nature of cosh dependence exhibiting the concentration of the energy in the outer lobes of the beam.

Calculations of free energies in liquid and solid phases: fundamental measure density-functional approach.

In this paper, a theoretical description of the free energies and correlation functions of hard-sphere (HS) liquid and solid phases is developed using fundamental measure density-functional theory. Within the framework of Weeks-Chandler-Andersen perturbation theory, free energies of liquid and solid phases with many interaction potentials can be obtained from these characteristics of the HS system within a single theoretical description. An application to the Lennard-Jones system yields liquid-solid coexistence results in good agreement with the ones from simulations.

A new method for the determination of the wave aberration function for high-resolution TEM.: 2. Measurement of the antisymmetric aberrations

A new method is presented for the determination of the antisymmetric coefficients of the wave aberration function from a tableau of tilted illumination images. The approach is based on measurements of the apparent defocus and two-fold astigmatism using a phase correlation function and phase contrast index calculated from a short focus series acquired at each tilt. This method is shown to be suitable for a wide range of specimens and is sufficiently accurate for exit plane wave restoration at 0.1 nm resolution. Experimental examples of this approach are provided and the method is compared to results obtained from measurements of conventional power spectra.

Effect of an In-Plane Magnetic Field on the Interlayer Phase Coherence in the Extreme-2D Organic Superconductor κ-(BEDT-TTF)2Cu(NCS)2

Using a high-sensitivity cavity perturbation technique (40 to 180 GHz), we have probed the angle dependent interlayer magneto-electrodynamic response within the vortex state of the extreme two-dimensional organic superconductor κ- (BEDT-TTF) 2 Cu(NCS) 2. A previously reported Josephson plasma resonance [M. Mola et al., Phys. Rev.B62, 5965 (2000)] exhibits a dramatic re-entrant behavior for fields very close (&lt; 1°) to alignment with the layers. In this same narrow angle range, a new resonant mode develops which appears to be associated with the non-equilibrium critical state. Fits to the angle dependence of the Josephson plasma resonance provide microscopic information concerning the superconducting phase correlation function within the vortex state. We also show that the effect of an in-plane magnetic field on the temperature dependence of the interlayer phase coherence is quite different from what we have previously observed for perpendicular magnetic fields.

Josephson plasma resonance in κ-(BEDT-TTF) 2Cu(NCS) 2 for close to in-plane magnetic fields

We report detailed angle dependent Josephson plasma resonance measurements within the decoupled vortex liquid phase of the extreme two-dimensional organic superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2 . The plasma resonance initially shows an approximately 1/cosθ dependence, followed by a sharp re-entrance for fields close to alignment with the layers (0 = 0°). This re-entrance may be attributed to an in-plane field dependence which may be directly related to the superconducting phase correlation function within the vortex state.

Low-temperature thermodynamic study of the diluted planar rotator model using a self-consistent harmonic approximation

The self-consistent harmonic approximation is used to study a dilute planar rotator model in two dimensions. The Kosterlitz–Thouless transition temperature is obtained as a function of p, where p is the concentration of links. The phase transition in the system is deduced from a deviation of the power law describing the decay of the phase correlation function and from a jump in the helicity modulus. Better results are obtained when vortex corrections are included.

Phase diagram and correlation function of a spin-Peierls system in the ground state: Effects of the quantum lattice fluctuations

Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.

A new method for the determination of the wave aberration function for high resolution TEM: 1. Measurement of the symmetric aberrations

A new method for the accurate determination of the symmetric coefficients of the wave aberration function has been developed. The relative defoci and displacements of images in a focus series are determined from an analysis of the phase correlation function between pairs of images, allowing the restoration of an image wave even when focus and specimen drift are present. Subsequently, the absolute coefficients of both defocus and 2-fold astigmatism are determined with a phase contrast index function. Overall this method allows a very accurate automated aberration determination even for largely crystalline samples with little amorphous contamination. Using experimental images of the complex oxide Nb 16W 18O 94 we have demonstrated the new method and critically compared it with existing diffractogram based aberration determinations. A series of protocols for practical implementation is also given together with a detailed analysis of the accuracy achieved. Finally a focal series restoration of Nb 16W 18O 94 with symmetric aberrations determined automatically using this method is presented.

Spatial Correlation of a HF Wave Field in the Case of Oblique Reflection from the Ionosphere

We consider the spatial statistical characteristics of an HF signal and the interdependence of the correlation functions of the field amplitude and phase in the case of oblique reflection from the ionosphere. The amplitude and phase parameters are expressed either in terms of the parameter β of ionospheric turbidity, which can be determined most easily, or only in terms of the correlation coefficient of amplitudes at different points. We obtain the expressions for the amplitude and phase correlation functions, which describe well the experimental data.

Linear simulation models for real-space interpretation of small-angle scattering experiments of random two-phase systems

A procedure is presented for modelling and interpreting small-angle scattering experiments of random isotropic two-phase media. There are applications in structure research. Based on the curvature behaviour of the small-angle scattering correlation function γ(r), the distribution laws of random distances between the interfaces of the phases are analysed. Furthermore, the function of occupancy Z(r) Z(r), defined by Porod (see Porod G 1951, 1952 Z. Kolloid 124 83–114, 125 51–122), is simulated. This includes the connection with the volume fraction c of the microparticles. Both functions are studied by use of a linear finite symmetrical one-dimensional model. A Mathematica program allows the numerical simulation of these functions for a large class of phase correlation functions (indicator functions). In this way, a scattering experiment can be interpreted in the light of chord length distribution. Explanations of this strategy for two types of discrete inhomogeneity are included: discussion of γ″(r) γ″(r) of a single hollow sphere and the analysis of an experimental γ(r) γ(r) function of an amorphous AlDy(6 at.%)Ni(10 at.%) alloy.