Construct Correlation Functions Research Articles

Correlation functions from tensor network influence functionals: The case of the spin-boson model.

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Sustainability Analysis of the Water Environment Carrying Capacity of Harbin City Based on an Optimized Set Pair Analysis Posture-Deviation Coefficient Method Evaluation Model

To scientifically measure the water environment carrying capacity of Harbin City and its change trend, based on analysis of the implications of the sustainability of the urban water environment’s carrying capacity, an evaluation index system for the sustainability of the water environment carrying capacity of Harbin City was constructed. Most existing evaluation methods rely on static data to construct correlation functions between research objects and rank criteria, while the dynamic nature of the information is not considered enough. In this paper, we use hierarchical analysis (analytic hierarchy process, AHP) to determine the weights of each index of the system and then apply the projection tracing method (projection pursuit, PP) to optimize the determined weights. Combining the set pair analysis posture evaluation method and bias coefficients method to explore the dynamic balance mechanism between different index factor levels, a sustainability evaluation model for water environment carrying capacity integrating informational evolution is constructed. Finally, the applicability of the optimization model is tested by comparing the confidence criterion judging method. The model realizes quantitative evaluation of the carrying capacity of the urban water environment. It provides a new and effective means for accurate and reasonable determination of the coefficient of variance and the number of links and dynamic analysis of the water environment carrying capacity system and judgment of its sustainable development trend. The results show that the weight for water resource quality is 0.55, which is the subsystem with the greatest overall impact on the carrying capacity of the water environment in Harbin. The evaluation level of the set-to-potential eigenvalue for 2010–2017 is biased positive 2, and the rest of the years are quasi 2. The reduced value of the coefficient of oppositeness corresponding to the years 2010–2017 is more significant. The maximum value of the dynamic evolution of the load-carrying capacity level is nearly −0.35. From the vertical comparison of different levels, it is found that the water environment carrying capacity of Harbin City gradually recovered to the normal loadable level over time. This overall shows an improving trend.

Five-dimensional path integrals for six-dimensional conformal field theories

In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an SU(1, 3) spacetime symmetry in the presence of instantons. We explicitly show how SU(1, 3) is enhanced to SU(1, 3) × U(1) where the additional U(1) acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters.

Calculation and optimization of correlation function in distillation method of lattice quantum chromodynamcis

Lattice quantum chromodynamics (lattice QCD) is a theory based on quantum chromodynamics, which is widely used in strong interaction related calculations. As a research method that can give accurate and reliable theoretical results, with the improvement of computer ability, Lattice QCD is playing an increasingly important role in recent years. Distillation method is an important numerical method to calculate hadron correlation function in lattice QCD, and can improve the signal-to-noise ratio of calculated physical quantities. Distillation is a method to approximately compute full propagator via replace the laplacian operator with it's outerproduct of laplace eigenvectors. In this way, the construction of operators is independent of the inversion of propagator which is costful. The eigenvector system and perambulator can be used in different physical projects and we don't need to compute these data repeatedly. It's also convinent for computing disconnected part of correlation function. However, it also faces to the problem of large amount of data in constructing correlation function because the difficulty of compuation is proportional to the cubic of the number of eigenvectors, so it is necessary to further improve its computational efficiency. A program is developed in this work to construct correlation function of quark bilinear with distillation method, and solved the bottleneck of computing performance by using MPI(Message Passing Interface, https://www.open-mpi.org), OpenMP(Open Multi-Processing) and SIMD(Single Instruction Multiple Data) multi-level optimization technology. And this program distribute timeslices to different MPI processes because the computation of each timeslice is independent. In order to show the efficiency of our program some tests result are presented. After various tests of the program, it shows that our design can support large-scale computation. Under the strong scalability test, the parallel computing efficiency of 512 processes can still achieve about 70%. The ability of calculating correlation function is greatly improved. The correction of results also has been checked via compute pseudo-scalar correlators of charmonium. Three different <inline-formula><tex-math id="M1">\begin{document}$ 0^{-+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210030_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210030_M1.png"/></alternatives></inline-formula> operators were adopted for variational analysis and there effecitive mass plateau were compared with the effective mass obtained from the tradional method with point source. The results of distillation method are consistent with traditional method. After variational analysis, three state is obtained, which means the variational analysis take effects and the correlation functions obtained from distillation method is reasonable.

A Lagrangian perturbation theory in the presence of massive neutrinos

We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to third order in perturbation theory. Once the neutrinos become non-relativistic, their density fluctuations are modeled as being proportional to the CDM density fluctuations, with a scale-dependent proportionality factor. This yields a gravitational back-reaction that introduces additional scales to the linear growth function, which is accounted for in the higher order LPT kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we ensure that our theory has a well behaved large scale behavior free of unwanted UV divergences, which are common when neutrino and CDM densities are not treated on an equal footing, and in resummation schemes that manifestly break Galilean invariance. We use our theory to construct correlation functions for both the underlying matter field, as well as for biased tracers using Convolution-LPT. Redshift-space distortions effects are modeled using the Gaussian Streaming Model. When comparing our analytical results to simulated data from the \ extsc{Quijote} simulation suite, we find good accuracy down to r=20 Mpc h−1 at redshift z=0.5, for the real space and redshift space monopole particle correlation functions with no free parameters. The same accuracy is reached for the redshift space quadrupole if we additionally consider an effective field theory parameter that shifts the pairwise velocity dispersion. For modeling the correlation functions of tracers we adopt a simple Lagrangian biasing scheme with only density and curvature operators, which we find sufficient to reach down to r=20 Mpc h−1 when comparing to simulated halos.

Thermodynamic bootstrap program for integrable QFT\u2019s: form factors and correlation functions at finite energy density

We study the form factors of local operators of integrable QFT’s between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov’s form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.

An Acquisition Algorithm with NCCFR for BOC Modulated Signals

With the development of satellite navigation technology, BOC (Binary Offset Carrier) signals are proposed and applied in navigation system. However, in the advantages of enhancing the utilized rating of the band resource, some new problems are also emerging in the acquisition processing. On the basis of analyzing the limitations of the existing methods in suppressing side peaks, a NCCFR (New Cross-Correlation Function Reconstruction) algorithm is proposed, in which different modulation coefficients are used to construct correlation function with a shifter phase. The simulation results show that the new algorithm can suppress first side peaks and restrain other side peaks.

On the foundations of partially quenched chiral perturbation theory

It has been widely assumed that partially quenched chiral perturbation theory is the correct low-energy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa--Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.

Scalar quantum field theory on fractals

We investigate scale invariant measures over multiple variables for scalar field theories by imitating Wiener’s construction of the measure on the space of functions of one variable. We assign random fields values on the vertices of simple geometric shapes (triangles, squares, tetrahedra) which are subdivided into a finite number of similar shapes. We find several Gaussian measures with anomalous scaling associated with these field variables. A non-Gaussian fixed point arises from the Ising model on a fractal. In the continuum limit, we construct correlation functions that vary as a power of the distance. It is either a positive power (analogous to the Wiener process) or a negative power depending on the subdivision scheme used; however it is an irrational number for all the examples. This suggests that in the continuum limits it corresponds to quantum field theories (random fields) on spaces of fractional dimension.

New observables in topological instantonic field theories

Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type for the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on the linking of points. The new “arbitrary jump” observables may be used to construct correlation functions computing, e.g., the linking numbers of cycles, as we illustrate on Hopf fibration. We expect that such observables could be generalized in an interesting way to instantonic topological theories in all dimensions.

Modified Coulomb gas construction of quantum Hall states from nonunitary conformal field theories

Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties such as the Moore-Read Pfaffian for filling factor $\ensuremath{\nu}=5/2$. This wavefunction has been constructed by constructing correlation functions of a two-dimensional conformal field theory (CFT) involving a free boson and a Majorana fermion. By considering other CFTs many other clustered states have been proposed as candidate fractional quantum Hall states under appropriate circumstances. It is believed that the underlying CFT should be unitary if one wants to describe an incompressible, i.e., gapped liquid state. We show that by changing the way one derives the wavefunction from its parent CFT it is possible to obtain an incompressible candidate state when starting from a nonunitary parent. The construction mimics a global change in parameters in the phase space of the electron system. We explicit our construction in the case of the so-called Gaffnian state (a state for filling factor 2/5) and also for the Haldane-Rezayi state (a spin-singlet state at filling 1/2). We note that there are obstructions along this path in the case of the permanent spin-singlet state of Read and Rezayi which can be characterized as a robust gapless state.

Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors

Modeling experiments with qualitative and quantitative factors is an important issue in computer modeling. We propose a framework for building Gaussian process models that incorporate both types of factors. The key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors. An iterative estimation procedure is developed for the proposed models. Modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions. The proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center.

On the [formula omitted] super Liouville four-point functions

We construct the four-point correlation functions containing the top component of the supermultiplet in the Neveu–Schwarz sector of the N = 1 SUSY Liouville field theory. The construction is based on the recursive representation for the NS conformal blocks. We test our results in the case where one of the fields is degenerate with a singular vector on the level 3/2. In this case, the correlation function satisfies a third-order ordinary differential equation, which we derive. We numerically verify the crossing symmetry relations for the constructed correlation functions in the nondegenerate case.

On Polymer Expansion for Gibbsian States of Nonequilibrium Systems of Interacting Brownian Oscillators

The convergence of polymer cluster expansions for correlation functions of general Gibbs oscillator-type systems and related nonequilibrium systems of Brownian oscillators is established. The initial states for the latter are Gibbsian. It is proved that the sequence of the constructed correlation functions of the nonequilibrium system is a generalized solution of a diffusion BBGKY-type hierarchy.

An explicit example of HQET at one-loop order of perturbation theory

As an explicit example of HQET, we construct correlation functions containing a heavy-light axial current, both in the static approximation and in full QCD. This enables us to investigate the size of finite mass effects. As we use the lattice regularisation, we can also check the mass dependence of discretisation errors.

Breakup density in spectator fragmentation

Proton–proton correlations and correlations of protons, deuterons and tritons with α particles from spectator decays following 197 Au + 197 Au collisions at 1000 MeV per nucleon have been measured with two highly efficient detector hodoscopes. The constructed correlation functions, interpreted within the approximation of a simultaneous volume decay, indicate a moderate expansion and low breakup densities, similar to assumptions made in statistical multifragmentation models.

CORRELATION FUNCTIONS OF CMB ANISOTROPY AND POLARIZATION

We give a full analysis of the auto- and cross-correlations between the Stokes parameters of the cosmic microwave background. In particular, we derive the windowing function for an antenna with Gaussian response in polarization experiment, and construct correlation function estimators corrected for instrumental noise. They are applied to calculate the signal to noise ratios for future anisotropy and polarization measurements. While the small-angular-scale anisotropy-polarization correlation would be likely detected by the MAP satellite, the detection of electric and magnetic polarization would require higher experimental sensitivity. For large-angular-scale measurements such as the being planned SPOrt/ISS, the expected signal to noise ratio for polarization is greater than one only for reionized models with high reionization redshifts, and the ratio is less for anisotropy-polarization correlation. Correlation and covariance matrices for likelihood analyses of ground-based and satellite data are also given.

Correlation Functions of CMB Anisotropy and Polarization

While the temperature anisotropy of the cosmic microwave background is proved to be a promising tool for probing the early Universe, the CMB polarization is another important clue for extracting more cosmic information. We give a full analysis of the auto- and cross-correlations between the CMB Stokes parameters. In particular, we derive the windowing function for an antenna with Gaussian response in polarization experiment, and construct correlation function estimators corrected for instrumental noise. They are applied to calculate the signal to noise ratios for future MAP and Planck anisotropy and polarization measurements.

Bosonization of Massive Fermions

We study the Euclidean sine-Gordon field theory on the plane with β > 16π/3 and an interaction density confined to a finite square. For β= 4 π we construct correlation functions for the field : sin φ \colon; and show that they are equal to the pseudoscalar ―ψΓψ correlation functions for a free fermion theory with mass term confined to the finite square.

Asymmetric orbifolds: Path integral and operator formulations

We discuss some of the details involved in asymmetric orbifold construction. In particular, the path-integral formalism is developed and shown to be consistent with operator interpretation. Conditions of one-loop modular invariance are discussed in detail. We also describe how one can construct correlation functions involving twisted states.