Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Boundary Correlation Functions of the gl(1|1) Supersymmetric Vertex Model

The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.

Improving constraint onΩ_(m)from SDSS using marked correlation functions

Large-scale structure(LSS)surveys will increasingly provide stringent constraints on our cosmological models.Recently,the density-marked correlation function(MCF)has been introduced,offering an easily computable density-correlation statistic.Simulations have demonstrated that MCFs offer additional,independent constraints on cosmological models beyond the standard two-point correlation(2PCF).In this study,we apply MCFs for the first time to SDSS CMASS data,aiming to investigate the statistical information regarding clustering and anisotropy properties in the Universe and assess the performance of various weighting schemes in MCFs,and finally obtain constraints onΩ_(m).Upon analyzing the CMASS data,we observe that,by combining different weights(α=[-0.2,0,0.2,0.6]),the MCFs provide a tight and independent constraint on the cosmological parameterΩ_(m),yieldingΩ_(m)=0.293±0.006 at the 1σlevel,which represents a significant reduction in the statistical error by a factor of 3.4 compared to that from 2PCF.Our constraint is consistent with recent findings from the small-scale clustering of BOSS galaxies(Zhai et al.Astronphys.J.948,99(2023))within the 1σlevel.However,we also find that our estimate is lower than the Planck measurements by about 2.6σ,indicating the potential presence of new physics beyond the standard cosmological model if all the systematics are fully corrected.The method outlined in this study can be extended to other surveys and datasets,allowing for the constraint of other cosmological parameters.Additionally,it serves as a valuable tool for forthcoming emulator analysis on the Chinese Space Station Telescope(CSST).

Strangeness S=-2 baryon-baryon interactions and femtoscopic correlation functions in covariant chiral effective field theory

We study the baryon-baryon interactions with strangeness S=-2 and corresponding momentum correlation functions in leading order covariant chiral effective field theory.The relevant low energy constants are determined by fitting to the latest HAL QCD simulations,taking into account all the coupled channels.Extrapolating the so-obtained strong interactions to the physical point and considering both quantum statistical effects and the Coulomb interaction,we calculate the ΛΛ and Ξ^(-)p correlation functions with a spherical Gaussian source and compare them with recent experimental data.We find a good agreement between our predictions and the experimental measurements by using the source radius determined in proton-proton correlations,which demonstrates the consistency between theory,experiment,and lattice QCD simulations.Moreover,we predict the Σ^(+)Σ^(+),Σ^(+)Λ,and Σ^(+)Σ^(-) interactions and corresponding momentum correlation functions.We further investigate the influence of the source shape and size of the hadron pair on the correlation functions studied and show that the current data are not very sensitive to the source shape.Future experimental measurements of the predicted momentum correlation functions will provide a non-trivial test of not only SU(3) flavor symmetry and its breaking but also the baryon-baryon interactions derived in covariant chiral effective field theory.

Genus two correlation functions in CFTs with TT deformation

Since the definition of TT deformation in the curved Riemann surface is obstructive in the literature,we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription.We construct the correlation functions of conformal field theories(CFTs)on genus two Riemann surfaces with the TT deformation in terms of the perturbative CFT approach.Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry,we systematically obtain the first-order TT correction to the genus two correlation functions in the TT deformed CFTs,e.g.,partition function and one/higher-point correlation functions.

New theoretical bounds on the aperiodic correlation functions of binary sequences

In order to reduce or eliminate the multiple access interference in code division multiple access (CDMA) systems, we need to design a set of spreading sequences with good autocorrelation functions (ACF) and crosscorrelation functions (CCF). The importance of the spreading codes to CDMA systems cannot be overemphasized, for the type of the code used, its length, and its chip rate set bounds on the capability of the system that can be changed only by changing the code. Several new lower bounds which are stronger than the well-known Sarwate bounds, Welch bounds and Levenshtein bounds for binary sequence set with respect to the spreading sequence length, family size, maximum aperiodic autocorrelation sidelobe and maximum aperiodic crosscorrelation value are established.

Correlation Functions of an Autonomous Stochastic System with Nonlinear Time Delays

The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.

Correlation Functions, Universal Ratios and Goldstone Mode Singularities in n-Vector Models

Correlation functions in the O(n)models below the critical temperature are considered.Based on Monte Carlo(MC)data,we confirm the fact stated earlier by Engels and Vogt,that the transverse two-plane correlation function of the O(4)model for lattice sizes about L=120 and small external fields h is very well described by a Gaussian approximation.However,we show that fits of not lower quality are provided by certain non-Gaussian approximation.We have also tested larger lattice sizes,up to L=512.The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit at k→0 and h=+0,i.e.,G_(⊥)(k)≈ak−λ_(⊥)and G_(||)(k)≈bk−λk,respectively.Here a and b are the amplitudes,k=|k|is the magnitude of the wave vector k.The exponentsλ_(⊥),λk and the ratio bM^(2)/a^(2),where M is the spontaneous magnetization,are universal according to the GFD(grouping of Feynman diagrams)approach.Here we find that the universality follows also from the standard(Gaussian)theory,yielding bM^(2)/a^(2)=(n−1)/16.Our MC estimates of this ratio are 0.06±0.01 for n=2,0.17±0.01 for n=4 and 0.498±0.010 for n=10.According to these and our earlier MC results,the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory.This is expected from the GFD theory.We have found appropriate analytic approximations for G_(⊥)(k)and G_(||)(k),well fitting the simulation data for small k.We have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately。

Correlation functions of gauged linear σ-model

This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator （HIJING）. Using a three-dimension fast Fourier transform （FFT）, we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter a = 1 - 2/γ, where γ, is the dimensionless interaction strength. We also discuss the Tan＇s adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in terms of the fractional statistical parameter.

Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Weighted Multi-sensor Data Level Fusion Method of Vibration Signal Based on Correlation Function

As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.

CSHINE for studies of HBT correlation in heavy ion reactions

The compact spectrometer for heavy ion experiment(CSHINE)is under construction for the study of isospin chronology via the Hanbury Brown–Twiss(HBT)particle correlation function and the nuclear equation of state of asymmetrical nuclear matter.The CSHINE consists of silicon strip detector(SSD)telescopes and large-area parallel-plate avalanche counters,which measure the light charged particles and fission fragments,respectively.In phase I,two SSD telescopes were used to observe 30 MeV/u 40Ar?197Au reactions.The results presented here demonstrate that hydrogen and helium were observed with high isotopic resolution,and the HBT correlation functions of light charged particles could be constructed from the obtained data.

Influence of Noise on Time Evolution of Intensity Correlation Function

Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.

Criterion for Blind Signals Separation Based on Correlation Function

Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.

Temporal variation of noise correlation function(NCF) in Beijing and surroundings:Its relation with climate events and implications

Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.

Study on Correlation Characteristics of Static and Dynamic Explosion Temperature Fields

The warheads such as missiles and artillery shells have a certain speed of motion during the explosion.Therefore,it is more practical to study the explosion damage of ammunition under motion.The different speeds of the projectiles have a certain influence on the temperature field generated by the explosion.In this paper,AUTODYN is used to simulate the process of projectile dynamic explosion.In the experiment,the TNT spherical bare charges with the TNT equivalent of 9.53kg and the projectile attack speed of 0,421,675,1020m/s were simulated in the infinite air domain.The temperature field temperature peaks and temperature decay laws at different charge rates and the multi-function regression fitting method were used to quantitatively study the functional relationship between the temperature and peak temperature correlation calculations of static and dynamic explosion temperature fields.The results show that the temperature distribution of the dynamic explosion temperature field is affected by the velocity of the charge,and the temperature distribution of the temperature field is different with the change of the charge velocity.Through the analysis and fitting of the simulation data,the temperature calculation formula of the static and dynamic explosion temperature field is obtained,which can better establish the relationship between the temperature peak of the static and dynamic explosion temperature field and various influencing factors,and use this function.Relational calculations can yield better results and meet the accuracy requirements of actual tests.

Three vertex degree correlations of fixed act-size collaboration networks

A rate equation approach was presented for the exact computation of the three vertex degree correlations of the fixed act-size collaboration networks.Measurements of the three vertex degree correlations were based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k,with an appropriate boundary condition.The rate equation proposed can be generalized in more sophisticated growing network models,and also extended to deal with related correlation measurements.Finally,in order to check the theoretical prediction,a numerical example was solved to demonstrate the performance of the degree correlation function.

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.