Calculation Of Correlation Functions Research Articles

PyTransport: A Python package for the calculation of inflationary correlation functions

PyTransport constitutes a straightforward code written in C++ together with Python scripts which automatically edit, compile and run the C++ code as a Python module. It has been written for Unix-like systems (OS X and Linux). Primarily the module employs the transport approach to inflationary cosmology to calculate the tree-level power-spectrum and bispectrum of user specified models of multi-field inflation, accounting for all sub and super-horizon effects. The transport method we utilise means only coupled differential equations need to be solved, and the implementation presented here combines the speed of C++ with the functionality and convenience of Python. This document details the code and illustrates how to use it with a worked example. It has been updated to be a companion to the second version of the code, PyTransport 2.0, which includes functionality to deal with models of inflation with a curved field space metric.

A one-dimensional theory for Higgs branch operators

We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d mathcal{N}=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d mathcal{N}=4 theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d mathcal{N}=2 subalgebra of the mathcal{N}=4 algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on S3 that contain real mass and Fayet-Iliopolous parameters. We also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.

The Effect of Temperature on Nucleation of Condensed Water Phase on the Surface of a β-AgI Crystal. 1. Structure

The Monte Carlo method has been employed to study the effect of temperature on the structure and the mechanism of retaining condensed water phase nuclei on the surface of the basal face of a silver iodide crystal. Comparative calculations of spatial correlation functions and computer images of vapors being condensed at 260 and 320 K have indicated an increased stability of monomolecular water-film spots with respect to thermal fluctuations. The disturbances of the regular “honeycomb” structure have a collective character and occur according to the “domino principle”; i.e., the rupture of a hydrogen bond between neighboring molecules releases enhanced libration motions of the latter, which, in turn, provoke the rupture of bonds with other neighbors. In accordance with this scenario, the distortion of the hexagonal structure of the film under the action of thermal fluctuations develops with the formation of growing spots of destruction. The thermal fluctuations significantly affect the orientational molecular order and the degree of clustering on the surface. The positions of molecules relative to the ions of the surface crystallographic layer of a substrate weakly depend on temperature.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

Rotating superfluids and spinning charged operators in conformal field theory

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.

Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions

The Chebyshev expansion offers a numerically efficient and easy-implement algorithm for evaluating dynamic correlation functions using matrix product states (MPS). In this approach, each recursively generated Chebyshev vector is approximately represented by an MPS. However, the recurrence relations of Chebyshev polynomials are broken by the approximation, leading to an error which is accumulated with the increase of the order of expansion. Here we propose a reorthonormalization approach to remove this error introduced in the loss of orthogonality of the Chebyshev polynomials. Our approach, as illustrated by comparison with the exact results for the one-dimensional XY and Heisenberg models, improves significantly the accuracy in the calculation of dynamical correlation functions.

Power-counting during single-field slow-roll inflation

We elucidate the counting of the relevant small parameters in inflationary perturbation theory. Doing this allows for an explicit delineation of the domain of validity of the semi-classical approximation to gravity used in the calculation of inflationary correlation functions. We derive an expression for the dependence of correlation functions of inflationary perturbations on the slow-roll parameter ϵ = −Ḣ/H2, as well as on H\\ Mp, where H is the Hubble parameter during inflation. Our analysis is valid for single-field models in which the inflaton can traverse a Planck-sized range in field values and where all slow-roll parameters have approximately the same magnitude. As an application, we use our expression to seek the boundaries of the domain of validity of inflationary perturbation theory for regimes where this is potentially problematic: models with small speed of sound and models allowing eternal inflation.

Magnetic field effects on charge structure factors of gapped graphene structure

We present the behaviors of dynamical and static charge susceptibilities of undoped gapped graphene using the Green's function approach in the context of tight binding model Hamiltonian. Specially, the effects of magnetic field on the plasmon modes of gapped graphene structure are investigated via calculating correlation function of charge density operators. Our results show the increase of magnetic field leads to disappear high frequency plasmon mode for gapped case. We also show that low frequency plasmon mode has not affected by increase of magnetic field and chemical potential. Finally the temperature dependence of static charge structure factor of gapp graphene structure is studied. The effects of both magnetic field and gap parameter on the static structure factor are discusses in details.

Improving the theoretical prediction for the Bs - B̅s width difference: matrix elements of next-to-leading order ΔB = 2 operators

We present lattice QCD results for the matrix elements of R2 and other dimension-7, ΔB = 2 operators relevant for calculations of Δs, the Bs - B̅s width difference. We have computed correlation functions using 5 ensembles of the MILC Collaboration’s 2+1 + 1-flavour gauge field configurations, spanning 3 lattice spacings and light sea quarks masses down to the physical point. The HISQ action is used for the valence strange quarks, and the NRQCD action is used for the bottom quarks. Once our analysis is complete, the theoretical uncertainty in the Standard Model prediction for ΔΓs will be substantially reduced.

Calm Multi-Baryon Operators

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

Schwinger-Keldysh diagrammatics for primordial perturbations

We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use a quasi-single-field inflation model as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case (m<3H/2) that has been previously studied, and the heavier scalar case (m>3H/2) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large.

Structure of a Na+ cation hydration shell on heating in a planar nanopore

Resistance to heating above the boiling point of water of the molecular structure of a single-charged sodium cation hydration shell growing under the conditions of a model planar nanopore with a width of 5 A is studied by computer simulation. Monte Carlo calculations of spatial correlation functions are performed in a detailed model with regard to many-body interactions between the ion and water molecules. The system demonstrates an increased resistance to thermal fluctuations along the pore plane and a decreased one in the transverse direction. The heating is accompanied by an enhanced coating effect of molecules around the ion and a diminished effect of extruding the ion out of its own hydration shell. The orientational molecular order due to strong spatial anisotropy inside the nanopore is much more stable than the hydrogen bonds between the molecules.

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_\pi^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $\pi\pi \rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $\chi$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $\pi\pi$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $\chi$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $\pi N$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $\chi$EFT calculation includes $N$ and $\Delta$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

Correlation functions of net-proton multiplicity distributions in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider from a multiphase transport model

Fluctuations of conserved quantities are believed to be sensitive observables to probe the signature of the QCD phase transition and critical point. It was argued recently that measuring the genuine correlation functions (CFs) could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions.With the AMPT (a multiphase transport) model, the centrality and energy dependence of various orders of CFs of net protons in Au + Au collisions at $\sqrt{s_\mathrm{NN}}$=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV are investigated. The model results show that the number of antiprotons is important and should be taken into account in the calculation of CFs at high energy and/or in peripheral collisions. It is also found that the contribution of antiprotons is more important for higher order correlations than for lower ones. The CFs of antiprotons and mixed correlations play roles comparable to those of protons at high energies. Finally, we make comparisons between the model calculation and experimental data measured in the STAR experiment at the BNL Relativistic Heavy Ion Collider.

Gravitational dual of the Rényi displacement operator

We give a recipe for computing correlation functions of the displacement operator localized on a spherical or planar higher dimensional twist defect using AdS/CFT. Such twist operators are typically used to construct the $n$'th Renyi entropies of spatial entanglement in CFTs and are holographically dual to black holes with hyperbolic horizons. The displacement operator then tells us how the Renyi entropies change under small shape deformations of the entangling surface. We explicitly construct the bulk to boundary propagator for the displacement operator insertion as a linearized metric fluctuation of the hyperbolic black hole and use this to extract the coefficient of the displacement operator two point function $C_D$ in any dimension. The $n \rightarrow 1$ limit of the twist displacement operator gives the same bulk response as the insertion of a null energy operator in vacuum, which is consistent with recent results on the shape dependence of entanglement entropy and modular energy.

Study of the AdS$_2$/CFT$_1$ correspondence with the contribution from the Weyl anomaly

In this paper we will consider the Almheiri-Polchinski model of the AdS$_2$ back reaction coupled with Liouville field, which is necessary for quantum consistency. In this model, the Liouville field is determined classically by a bulk conformal transformation. The boundary time is also reparametrized by this transformation. It is shown that the on-shell action on the boundary for the gravity sector is given by a bulk integral containing the Liouville field. This integral stems from Weyl anomaly and is SL(2,R) invariant. A prescription is given for computing correlation functions of the operators dual to massless scalars. The generating function of the correlation functions of these operators is given by a sum of matter action and the bulk integral containing the Liouville field. The latter integral leads to extra contributions to $n(\geq 6)$ point functions.

Eigenvalue dynamics for multimatrix models

By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the $SU(2)$ sector of ${\cal N}=4$ super Yang-Mills theory, that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the BPS operators of the $SU(2)$ sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.

Adaptive synchronization in hidden broadband systems

Subject of Research. The paper deals with the method of adaptive synchronization in receiving devices of broadband communication systems of the hidden message exchange increasing the efficiency of computational capability usage of a receiving device. The research topicality is caused by the need in more effective usage of computing resources for accepting modules of broadband digital communication and radiolocation. Method. The proposed solution is an extension of sequential synchronization method being applied nowadays. The method consists of two synchronization stages: preliminary – hard, and subsequent – precise one. The entity of the proposed solution lies in computation of correlative function only in the area (window) near the expected central peak. The window movement along the accepted character sequence enables to find the actual peak position and to make synchronization. Decreasing of computing expenses is reached due to reduction of processed information volume. The method adaptivity is reached by exact retraining of synchronization during all communication session. The proposed solution is urgent for mobile systems of communication and radiolocation in condition of signal interference. Main Results. Simulation of synchronization system is carried out in the environment of Simulink (MATLAB). The signal created on the basis of a complex-valued matrix with the size equal to 3×4 with the special form of autocorrelation function is used as an example for synchronization. Model researches showed that the developed method enables to realize synchronization of transceiving system, without quitting the mode of the hidden (subnoise) message passing. It is shown that application of the developed method of the adaptive synchronization, gives the possibility to reduce significantly computational capability of a receiving device, necessary for synchronization. The number of operations in case of correlation function computation was decreased in 28 times as compared to a computation method in time over all range of counting and in 5 times concerning an algorithm of correlation function computation with the use of fast Fourier transform. Practical Relevance. Research results can find application in the design of receiving modules of broadband digital communication and radiolocation.

Investigating efficient methods for computing four-quark correlation functions

We discuss and compare the efficiency of various methods, combinations of point-to-all propagators, stochastic timeslice-to-all propagators, the one-end trick and sequential propagators, to compute two-point correlation functions of two-quark and four-quark interpolating operators of different structure including quark–antiquark type, mesonic molecule type, diquark–antidiquark type and two-meson type. Although we illustrate our methods in the context of the a0(980), they can be applied for other multi-quark systems, where similar diagrams appear. Thus our results could provide helpful guidelines on the choice of methods for correlation function computation for future lattice QCD studies of meson–meson scattering and possibly existing tetraquark states.

Relaxation dynamics of two coherently coupled one-dimensional bosonic gases

In this work we consider the non-equilibrium dynamics of two tunnel coupled bosonic gases which are created from the coherent splitting of a one-dimensional gas. The consequences of the tunneling both in the non-stationary regime as well as at large time are investigated and compared with equilibrium results. In particular, within a semiclassical approximation, we compute correlation functions for the relative phase which are experimentally measurable and we observe a transient regime displaying oscillations as a function of the distance. The steady regime is very well approximated by a thermal state with a temperature independent of the tunneling strength.