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.

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.

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.

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.

Double differential cross sections for ionization of H by 75 keV proton impact:Assessing the role of correlated wave functions

The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.

Algebraic equation of motion approach for solving the Anderson model

Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.

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).

Self-diffusion Coefficient Model Based on Activation Energy and Free Volume

A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chapman-Enskog model. At the same time a new method for calculating activation energy was devised and applied to the new model. In addition, the free volume was defined by implementing the generic van der Waals equation of state, the radial distribution function of which was obtained by using the Morsali- Goharshadi empirical formula. Under the same conditions, the new model was better than the original free volume model.

Fractional Fourier Domain Filter for Image Restoration

The FOURIER transform is one of the most frequently used tools in signal analysis. A generalization of the Fourier transform-the fractional Fourier transform-has become a powerful tool for time-varying signal analysis. The mean square error(MSE) is used as design criteria to estimate signal. Wiener filter, which can be implement in O(NlogN) time, is suited for time-invariant degradation models. For time-variant and non-stationary processes, however, the linear estimate requires O(N 2 ). Filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering while requiring O(NlogN) implementation time. The blurred images that have several degradation models with different SNR are restored in the experiments. The results show that the method presented in this paper is valid and that the effect of restoration is improved as SNR is increased.

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.

Physical Properties of Ⅲ-Antiminodes—a First Principles Study

A comprehensive first principles study of III-Antimonide binary compounds is hardly found in literature. We report a broad study of structural and electronic properties of boron antimonide （BSb）, aluminium antimonide （AlSb）, gallium antimonide （GaSb） and indium antimonide （InSb） in zineblende phase based on density functional theory （DFT）. Our calculations are based on Full-PotentiM Lineaxized Augmented Plane wave plus local orbitals （FP- L（APWq-lo）） method. Different forms of exchange-correlation energy functional and corresponding potential are employed for structural and electronic properties. Our computed results for lattice parameters, bulk moduli, their pressure derivatives, and cohesive energy are consistent with the available experimental data. Boron antimonide is found to be the hardest compound of this group. For band structure calculations, in addition to LDA and GGA, we used GGA-EV, an approximation employed by Engel and Vosko. The band gap results with GGA-EV are of significant improvement over the earlier work.

Alternatives of Strategic Environmental Assessment for Road Traffic Development Planning——Case of Changchun City,China

On analyzing the achievement of the goal in the modem urban road traffic development planning, the alternative of Strategic Environmental Assessment for urban traffic planning should include the basic scheme, the extended scheme and the environmental protection scheme. This study from different perspectives designed the alternatives for Changchun＇s county-level road and urban road system planning, and used the method of System Dynamics to simulate, optimize and analyze those alternatives. Thereafter, some methods including the correlation function method were used to comprehensively assess and rank those alternatives for recommending two best alternatives with the consideration to the indicators, such as the total emission amount of CO, the total emission amount of nitrogen oxides, the noise value, the road construction cost, the fossil oil consumption and the traffic capacity. The result showed that the study would provide substantial supports for decision-makers to make more scientific decisions and promote the sustainable urban traffic in Changchun City.

Signal processing method for shear wave velocity measurement

Soil shear wave velocity （SWV） is an important parameter in geotechnical engineering. To measure the soil SWV, three methods are generally used in China, including the single-hole method, cross-hole method and the surface-wave technique. An optimized approach based on a correlation function for single-hole SWV measurement is presented in this paper. In this approach, inherent inconsistencies of the artificial methods such as negative velocities, and too-large and too-small velocities, are eliminated from the single-hole method, and the efficiency of data processing is improved. In addition, verification using the cross-hole method of upper measuring points shows that the proposed optimized approach yields high precision in signal processing.

Ghost images reconstructed from fractional-order moments with thermal light

We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.

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）.

Calculation of Scale of Fluctuation and Variance Reduction Function

The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and weighted curve fitting method were presented to make the calculation more simple and accurate. The vertical scales of fluctuation of typical layers of Tianjin Port were calculated based on a number of engineering geotechnical investigation data, which can be guidance to other projects in this area. Meanwhile, the influences of sample interval and type of soil index on the scale of fluctuation were analyzed, according to which, the principle of determining the scale of fluctuation when the sample interval changes was defined. It can be obtained that the scale of fluctuation is the basic attribute reflecting spatial variability of soil, therefore, the scales of fluctuation calculated according to different soil indexes should be basically the same. The non-correlation distance method was improved, and the principle of determining the variance reduction function was also discussed.

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.

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.

Application test of matter element analysis in earthquake forecast

Calculation by means of the previous indices of the seismic activity can have the matter element analysis possess the forecast function. Readjusting repeatedly the grade limit value of every index can maximize the historical fitting ratio of the calculated and actual grade of the annual maximum magnitude, whose result is relatively ideal.

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.