Calculation Of Correlation Functions Research Articles

Collision-induced light scattering spectra of krypton layer confined between graphite slabs – MD simulation

We have used the molecular dynamics (MD) simulation method to obtain the collision-induced light scattering spectra of the thin krypton layer confined between two parallel graphite slabs. The simulations have been made under constant density, pressure and temperature condition. We have investigated four thin krypton layers of the thickness ranging from 13 to 24 Å. The 2-, 3- and 4-body correlation functions of collision-induced polarizability anisotropy were calculated. The spectra of colliding krypton atoms were simulated as cosine Fourier transform of the total polarizability anisotropy correlation function. The calculated correlation functions and their spectra show substantial dependence on the distance between graphite slabs. The collision-induced light scattering spectrum of krypton bulk sample was also simulated and compared with the krypton layer between graphite walls. The striking differences between these two systems are observed. We have further extended our analysis of krypton movement between graphite slabs by calculating the mean square displacement functions and diffusion coefficients. The decrease of the diffusion of krypton atoms with the increasing distance between graphite walls has been found. The structure of krypton layer has been also investigated by calculating the density profile and pressure tension across the rift. The distance between graphite slabs, for which the highest mobility of krypton's atoms occurred, has been found.

Electronic binding energy and thermal relaxation of Li and LiNa atomic alloying clusters.

We examined the effects of atomic hetero- and under-coordination on the relaxation of the interatomic bonding and electronic binding energy of Li and LiNa cluster alloying using a combination of the bond-order-length-strength correlation and density functional theory calculations. We found that bond nature alteration by heterocoordination, bond relaxation by thermal excitation and atomic coordination contribute intrinsically to the core-level energy shifts with resolution of the binding energy at the atomic sites of terrace edges, facets, and bulk of the LiNa alloy nanoclusters. Our strategies may simplify the complexity of core electron binding energies in analyzing the experimental data of the irregularly coordinating atoms.

DEFINITION OF AN INTERVAL OF COHERENT ACCUMULATION OF A PACK OF LONG RADIO IMPULSES AT DETECTION OF THE HIGH-SPEED PURPOSE BY A RADAR STATION WITH ACTIVE PHASED-ARRAY ANTENNA WITH SOLID-STATE DEVICES

Mathematical models of the signals used in radar stations of detection of the high-speed purposes on the big range, working in a decimeter range of wavelength and using solid-state transferring elements are considered. Calculation of correlation function for the pack of radio impulses reflected from the high-speed purpose is resulted. Possibility of application of algorithm of coherent accumulation of a pack of radio impulses of the big duration is considered and the estimation of time of coherent accumulation is made.

Collective field theory for quantum Hall states

We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.

Velocity of excitations in ordered, disordered, and critical antiferromagnets

We test three different approaches, based on quantum Monte Carlo simulations, for computing the velocity $c$ of triplet excitations in antiferromagnets. We consider the standard $S=1/2$ one- and two-dimensional Heisenberg models, as well as a bilayer Heisenberg model at its critical point. Computing correlation functions in imaginary time and using their long-time behavior, we extract the lowest excitation energy versus momentum using improved fitting procedures and a generalized moment method. The velocity is then obtained from the dispersion relation. We also exploit winding numbers to define a cubic space-time geometry, where the velocity is obtained as the ratio of the spatial and temporal lengths of the system when all winding number fluctuations are equal. The two methods give consistent results for both ordered and critical systems, but the winding-number estimator is more precise. For the Heisenberg chain, we accurately reproduce the exactly known velocity. For the two-dimensional Heisenberg model, our results are consistent with other recent calculations, but with an improved statistical precision; $c=1.65847(4)$. We also use the hydrodynamic relation $c^2=\rho_s/\chi_\perp(q\to 0)$ between $c$, the spin stiffness $\rho_s$, and the transversal susceptibility $\chi_\perp$, using the smallest non-zero momentum $q=2\pi/L$. This method also is well controlled in two dimensions, but the cubic criterion for winding numbers delivers better numerical precision. In one dimension the hydrodynamic relation is affected by logarithmic corrections which make accurate extrapolations difficult. As an application of the winding-number method, for the quantum-critical bilayer model our high-precision determination of the velocity enables us to quantitatively test, at an unprecedented level, field-theoretic predictions for low-temperature scaling forms where $c$ enters.

Aqueous solvation of an amide molecule from first principles molecular simulations: Structure, hydrogen bond dynamics and spectral signature

Density functional theory (DFT) based Car–Parrinello molecular dynamics (CPMD) simulations were carried out to investigate the structure and dynamics of aqueous solvation shell of a single formamide (FA) molecule. Vibrational frequency through wavelet analysis and correlation function calculations have been performed to understand the spectral signature of water molecules in the first solvation shell and dynamics of solute–solvent hydrogen bonds, respectively. Structural aspects have been analyzed by calculating various pair correlation functions. FA takes part in more than two hydrogen bonds with water via carbonyl oxygen. Due to the presence of carbonyl group, the solvation through amine group hydrogen atoms is asymmetrical; each hydrogen participates in roughly one hydrogen bond. Carbonyl–water hydrogen bonds are stronger than the water–water hydrogen bonds; amine–water hydrogen bonds are much weaker than other two types of hydrogen bonds.

Real time correlation functions and the functional renormalization group

We put forward a functional renormalisation group approach for the direct computation of real time correlation functions, also applicable at finite temperature and density. We construct a general class of regulators that preserve the space-time symmetries, and allows the computation of correlation functions at complex frequencies. This includes both imaginary time and real time, and allows in particular the use of the plethora of imaginary time results for the computation of real time correlation functions. We also discuss real time computation on the Keldysh contour with general spatial momentum regulators. Both set-ups give access to the general momentum and frequency dependence of correlation functions.

Short-time dynamics of 2-thiouracil in the light absorbing S2(ππ(∗)) state.

Ultrahigh quantum yields of intersystem crossing to the lowest triplet state T1 are observed for 2-thiouracils (2TU), which is in contrast to the natural uracils that predominantly exhibit ultrafast internal conversion to the ground state upon excitation to the singlet excited state. The intersystem crossing mechanism of 2TU has recently been investigated using second-order perturbation methods with a high-level complete-active space self-consistent field. Three competitive nonadiabatic pathways to the lowest triplet state T1 from the initially populated singlet excited state S2 were proposed. We investigate the initial decay dynamics of 2TU from the light absorbing excited states using resonance Raman spectroscopy, time-dependent wave-packet theory in the simple model, and complete-active space self-consistent field (CASSCF) and time dependent-Becke's three-parameter exchange and correlation functional with the Lee-Yang-Parr correlation functional (TD-B3LYP) calculations. The obtained short-time structural dynamics in easy-to-visualize internal coordinates were compared with the CASSCF(16,11) predicted key nonadiabatic decay routes. Our results indicate that the predominant decay pathway initiated at the Franck-Condon region is toward the S2/S1 conical intersection point and S2T3 intersystem crossing point, but not toward the S2T2 intersystem crossing point.

Coupledππ,KK¯scattering inP-wave and theρresonance from lattice QCD

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_\pi = 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $\pi\pi$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $\pi\pi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $\rho$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.

Novel Cortical Thickness Pattern for Accurate Detection of Alzheimer's Disease.

Brain network occupies an important position in representing abnormalities in Alzheimer's disease (AD) and mild cognitive impairment (MCI). Currently, most studies only focused on morphological features of regions of interest without exploring the interregional alterations. In order to investigate the potential discriminative power of a morphological network in AD diagnosis and to provide supportive evidence on the feasibility of an individual structural network study, we propose a novel approach of extracting the correlative features from magnetic resonance imaging, which consists of a two-step approach for constructing an individual thickness network with low computational complexity. Firstly, multi-distance combination is utilized for accurate evaluation of between-region dissimilarity; and then the dissimilarity is transformed to connectivity via calculation of correlation function. An evaluation of the proposed approach has been conducted with 189 normal controls, 198 MCI subjects, and 163 AD patients using machine learning techniques. Results show that the observed correlative feature suggests significant promotion in classification performance compared with cortical thickness, with accuracy of 89.88% and area of 0.9588 under receiver operating characteristic curve. We further improved the performance by integrating both thickness and apolipoprotein E ɛ4 allele information with correlative features. New achieved accuracies are 92.11% and 79.37% in separating AD from normal controls and AD converters from non-converters, respectively. Differences between using diverse distance measurements and various correlation transformation functions are also discussed to explore an optimal way for network establishment.

Imaginary time density-density correlations for two-dimensional electron gases at high density.

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

Galaxy and mass assembly (GAMA): projected galaxy clustering

We measure the projected 2-point correlation function of galaxies in the 180 deg$^2$ equatorial regions of the GAMA II survey, for four different redshift slices between z = 0.0 and z=0.5. To do this we further develop the Cole (2011) method of producing suitable random catalogues for the calculation of correlation functions. We find that more r-band luminous, more massive and redder galaxies are more clustered. We also find that red galaxies have stronger clustering on scales less than ~3 $h^{-1}$ Mpc. We compare to two different versions of the GALFORM galaxy formation model, Lacey et al (in prep.) and Gonzalez-Perez et al. (2014), and find that the models reproduce the trend of stronger clustering for more massive galaxies. However, the models under predict the clustering of blue galaxies, can incorrectly predict the correlation function on small scales and under predict the clustering in our sample of galaxies with ~3$L_r$ . We suggest possible avenues to explore to improve these cluster- ing predictions. The measurements presented in this paper can be used to test other galaxy formation models, and we make the measurements available online to facilitate this.

Constrained correlation functions from the Millennium Simulation

Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation functions. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields. Aims. In this work, we aim to obtain corresponding constraints in the case of higher-dimensional random fields and test them in a more realistic context. Methods. We develop numerical methods to compute the constraints on correlation functions which are also applicable for two- and three-dimensional fields. In order to test the accuracy of the numerically obtained constraints, we compare them to the analytical results for the one-dimensional case. Finally, we compute correlation functions from the halo catalog of the Millennium Simulation, check whether they obey the constraints, and examine the performance of the transformation used in the construction of the quasi-Gaussian likelihood. Results. We find that our numerical methods of computing the constraints are robust and that the correlation functions measured from the Millennium Simulation obey them. Despite the fact that the measured correlation functions lie well inside the allowed region of parameter space, i.e. far away from the boundaries of the allowed volume defined by the constraints, we find strong indications that the quasi-Gaussian likelihood yields a substantially more accurate description than the Gaussian one.

Superfluidity of heated Fermi systems in the static fluctuation approximation

Superfluidity properties of heated finite Fermi systems are studied in the static fluctuation approximation, which is an original method. This method relies on a single and controlled approximation, which permits taking correctly into account quasiparticle correlations and thereby going beyond the independent-quasiparticle model. A closed self-consistent set of equations for calculating correlation functions at finite temperature is obtained for a finite Fermi system described by the Bardeen–Cooper–Schrieffer Hamiltonian. An equation for the energy gap is found with allowance for fluctuation effects. It is shown that the phase transition to the supefluid state is smeared upon the inclusion of fluctuations.

Stochastic path-integral formalism for continuous quantum measurement

We generalize and extend the stochastic path integral formalism and action principle for continuous quantum measurement introduced in [A. Chantasri, J. Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the optimal dynamics, such as the most-likely paths, are obtained by extremizing the action of the path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behaviour of continuous quantum measurement, with examples given for the qubit case. For qubit measurement with zero qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most-likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.

Molecular dynamics in a grand ensemble: Bergmann–Lebowitz model and adaptive resolution simulation

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz (P G Bergmann and J L Lebowitz 1955 Phys. Rev. 99 578). Despite its conceptual appeal, the model did not gain popularity in the field of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques that mimic open systems. We shall demonstrate that the model can serve as a tool in devising both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. In particular, we discuss the utility of the Bergmann–Lebowitz (BL) model for the calculation of equilibrium time correlation functions within the grand canonical adaptive resolution method (GC-AdResS) and report numerical results for the case of liquid water.

A density spike on astrophysical scales from an [formula omitted]-field waterfall transition

Hybrid inflation models are especially interesting as they lead to a spike in the density power spectrum on small scales, compared to the CMB, while also satisfying current bounds on tensor modes. Here we study hybrid inflation with N waterfall fields sharing a global SO(N) symmetry. The inclusion of many waterfall fields has the obvious advantage of avoiding topologically stable defects for N>3. We find that it also has another advantage: it is easier to engineer models that can simultaneously (i) be compatible with constraints on the primordial spectral index, which tends to otherwise disfavor hybrid models, and (ii) produce a spike on astrophysically large length scales. The latter may have significant consequences, possibly seeding the formation of astrophysically large black holes. We calculate correlation functions of the time-delay, a measure of density perturbations, produced by the waterfall fields, as a convergent power series in both 1/N and the field's correlation function Δ(x). We show that for large N, the two-point function is 〈δt(x)δt(0)〉∝Δ2(|x|)/N and the three-point function is 〈δt(x)δt(y)δt(0)〉∝Δ(|x−y|)Δ(|x|)Δ(|y|)/N2. In accordance with the central limit theorem, the density perturbations on the scale of the spike are Gaussian for large N and non-Gaussian for small N.

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

Two-dimensional conformal field theories with extended $\cal{W}$-symmetry algebras have dual descriptions in terms of weakly coupled higher spin gravity in AdS$_3\,$ at large central charge. Observables that can be computed and compared in the two descriptions include R\'enyi and entanglement entropies, and correlation functions of local operators. We develop techniques for computing these, in a manner that sheds light on when and why one can expect agreement between such quantities on each side of the duality. We set up the computation of excited state R\'enyi entropies in the bulk in terms of Chern-Simons connections, and show how this directly parallels the CFT computation of correlation functions. More generally, we consider the vacuum conformal block for general operators with $\Delta \sim c\,$. When two of the operators obey ${\Delta \over c} \ll 1\,$, we show by explicit computation that the vacuum conformal block is computed by a bulk Wilson line probing an asymptotically AdS$_3$ background with higher spin fields excited, the latter emerging as the effective bulk description of the excited state produced by the heavy operators. Among other things, this puts a previous proposal for computing higher spin entanglement entropy via Wilson lines on firmer footing, and clarifies its relation to CFT. We also study the corresponding computation in Toda theory and find that this provides yet another independent way to arrive at the same result.

Rényi entropies, the analytic bootstrap, and 3D quantum gravity at higher genus

We compute the contribution of the vacuum Virasoro representation to the genus-two partition function of an arbitrary CFT with central charge c > 1. This is the perturbative pure gravity partition function in three dimensions. We employ a sewing construction, in which the partition function is expressed as a sum of sphere four-point functions of Virasoro vacuum descendants. For this purpose, we develop techniques to efficiently compute correlation functions of holomorphic operators, which by crossing sym-metry are determined exactly by a finite number of OPE coefficients; this is an analytic implementation of the conformal bootstrap. Expanding the results in 1/c, corresponding to the semiclassical bulk gravity expansion, we find that — unlike at genus one — the result does not truncate at finite loop order. Our results also allow us to extend earlier work on multiple-interval Rényi entropies and on the partition function in the separating degeneration limit.

Pizzetti Formulae for Stiefel Manifolds and Applications

Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson-Zuber integral for the coset SO(4)/[SO(2)xSO(2)]. This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.