For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
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 differenc...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
Motivated by experimental measurements,we investigate the p-Ωcorrelation functions and interactions on the basis of a quark model.By solving the inverse scattering problem with channel coupling,we renormalize the cou...Motivated by experimental measurements,we investigate the p-Ωcorrelation functions and interactions on the basis of a quark model.By solving the inverse scattering problem with channel coupling,we renormalize the coupling to other channels into an effective single-channel p-Ωpotentials.The effects of Coulomb interaction and spin-averaging are also discussed.According to our results,the depletion of the p-Ωcorrelation functions,which is attributed to the J^(P)=2^(+)bound state not observed in the ALICE Collaboration's measurements(Nature 588,232(2020)),can be explained by the contribution of the attractive J^(P)=1^(+)component in spin-averaging.So far,we have provided a consistent description of the p-Ωsystem from the perspective of the quark model,including the energy spectrum,scattering phase shifts,and correlation functions.The existence of the p-Ωbound state has been supported by all three aspects.Additionally,a sign of the p-Ωcorrelation function's subtle sub-unity part can be seen in experimental measurements,which warrants more precise verification in the future.展开更多
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 densi...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).展开更多
Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural...Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.展开更多
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 crosscorre...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.展开更多
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 ...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.展开更多
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 functi...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。展开更多
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
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 th...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.展开更多
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）. Us...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.展开更多
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 co...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.展开更多
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...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.展开更多
The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the sys...The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear, simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID control scheme.展开更多
The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wav...The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wave functions.Two plasma mediums,namely,the Debye plasma and quantum plasma environments are considered.The screened Coulomb potential(SCP)obtained from Debye-Hückel model is used to represent Debye plasma environments and the exponential cosine screened Coulomb potential(ECSCP)obtained from a modified Debye-Hückel model is used to represent quantum plasma environments.The resonance parameters(resonance positions and widths)are presented in terms of the screening parameters.展开更多
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. W...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.展开更多
The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simu...The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence(DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.展开更多
Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions v...Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.展开更多
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘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.
基金supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘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.
基金National Natural Science Foundation of China under Grant No.90403019
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11675080,11775118,12305087,11535005,and 11865019)supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYCX23_1675)+1 种基金the Doctoral Dissertation Topic Funding Program(Grant No.YXXT23-027)supported by the Start-up Funds of Nanjing Normal University(Grant No.184080H201B20)。
文摘Motivated by experimental measurements,we investigate the p-Ωcorrelation functions and interactions on the basis of a quark model.By solving the inverse scattering problem with channel coupling,we renormalize the coupling to other channels into an effective single-channel p-Ωpotentials.The effects of Coulomb interaction and spin-averaging are also discussed.According to our results,the depletion of the p-Ωcorrelation functions,which is attributed to the J^(P)=2^(+)bound state not observed in the ALICE Collaboration's measurements(Nature 588,232(2020)),can be explained by the contribution of the attractive J^(P)=1^(+)component in spin-averaging.So far,we have provided a consistent description of the p-Ωsystem from the perspective of the quark model,including the energy spectrum,scattering phase shifts,and correlation functions.The existence of the p-Ωbound state has been supported by all three aspects.Additionally,a sign of the p-Ωcorrelation function's subtle sub-unity part can be seen in experimental measurements,which warrants more precise verification in the future.
基金supported by the Ministry of Science and Technology of China(Grant Nos.2020SKA0110401,2020SKA0110402,and 2020SKA0110100)the National Key Research and Development Program of China(Grant Nos.2018YFA0404504,and 2018YFA0404601)+5 种基金the National Natural Science Foundation of China(Grant Nos.11890691,12205388,12220101003,12122301,12233001,and 12073088)the China Manned Space Project(Grant No.CMS-CSST-2021(A02,A03,A04,B01))the Major Key Project of PCLthe 111 project(Grant No.B20019)the Shanghai Natural Science Research Grant(Grant No.21ZR1430600)sponsorship from Yangyang Development Fund。
文摘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).
基金supported by the National Key R&D Program of China under Grant No.2021YFA1400500the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB33000000+1 种基金the National Natural Science Foundation of China under Grant No.12334003the Beijing Municipal Natural Science Foundation under Grant Nos.JQ22001 and QY23014。
文摘Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.
基金supported by the National Natural Science Foundation of China(NSFC)the Research Grants Council of Hong Kong(RGC)joint research scheme(Grant No.60218001)+1 种基金the NSFC project(Grant No.69931050)the National Key Laboratory of Communications(UESTC),and the Royal Society,UK.
文摘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.
基金Supported by the National Natural Science Foundation of China (11735003, 11975041, 11961141004)。
文摘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.
文摘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。
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
基金supported by National Science Foundation of USA(Grant No.DMS-1309359)National Natural Science Foundation of China(Grant No.11331001)
文摘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.
基金Supported by National Natural Science Foundation of China(11075027,11275037)
文摘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.
基金the financial support from the Jilin University,Max Planck Partner Group,and National Natural Science Foundation of China(Grant Nos.12075101,and 12047569).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374331 and 11534014)the National Key R&D Program of China(Grant No.2017YFA0304500)partially supported by CAS-TWAS President’s Fellowship for International PhD Students
文摘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.
文摘The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear, simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID control scheme.
基金Supported by the Natural Science Foundation of Heilongjiang Province(LH2024A025)。
文摘The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wave functions.Two plasma mediums,namely,the Debye plasma and quantum plasma environments are considered.The screened Coulomb potential(SCP)obtained from Debye-Hückel model is used to represent Debye plasma environments and the exponential cosine screened Coulomb potential(ECSCP)obtained from a modified Debye-Hückel model is used to represent quantum plasma environments.The resonance parameters(resonance positions and widths)are presented in terms of the screening parameters.
文摘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.
文摘The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence(DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.
基金supported by the National Natural Science Foundation of China(No.22273005 and No.22422301)the Innovation Program for Quantum Science and Technology(No.2023ZD0300200)+1 种基金the National Security Academic Foundation(No.U2330201)the Fundamental Research Funds for the Central Universities.
文摘Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.
