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Algorithm for computing time correlation functions in non-stationary complex dynamic systems

Chinese Physics B 2025年第3期34卷 77-83页

作者： Jiu Zhang Lifu Jin Bo Zheng Xiongfei Jiang Tingting Chen Cong Xu Yanqing Hu Department of Statistics and Data Science Southern University of Science and TechnologyShenzhen 518055China School of Economics and Management Wenzhou University of TechnologyWenzhou 325035China School of Physics and Astronomy Yunnan UniversityKunming 650091China College of Finance and Information Ningbo University of Finance and EconomicsNingbo 315175China School of Finance Zhejiang University of Finance and EconomicsHangzhou 310000China

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 *** proposed algorithm integrates two-point and multi-point time correlation functions into a unified ***,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.

关键词： complex dynamic systems non-stationary states time correlation functions

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Fourier transforms of time correlation functions using Hermite functions

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COMPUTER PHYSICS COMMUNICATIONS 2025年 308卷

作者： Li, Hui Wang, Shaojie Zhang, Youjun Dove, Martin T. Sichuan Univ Inst Atom & Mol Phys Chengdu 610065 Sichuan Peoples R China Queen Mary Univ London Sch Phys & Chem Sci Mile End Rd London E1 4NS England

We present an alternative to standard Fourier transform methods in order to obtain the power spectrum from a time correlation function. Our approach involves fitting the correlation function with a sum of Hermite functions, and recombining these to obtain the power spectrum directly. Although Fourier transform methods have been used for many decades, our approach avoids some ambiguities and uncertainties that face the user, and also allow for a more flexible form of the power spectrum to be obtained. We present a few examples to show the quality of the method.

关键词： Fourier transforms time correlation functions Hermite functions

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time correlation functions of Equilibrium and Nonequilibrium Langevin Dynamics: Derivations and Numerics Using Random Numbers

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SIAM REVIEW 2020年第4期62卷 901-935页

作者： Shang, Xiaocheng Kroger, Martin Swiss Fed Inst Technol Dept Mat Polymer Phys Leopold Ruzicka Weg 4 CH-8093 Zurich Switzerland Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England

We study the time correlation functions of coupled linear Langevin dynamics with and without inertial effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three dimensions in the presence of friction, additive noise, and an external field with both rotational and deformational components. This simple model plays pivotal roles in understanding more complicated processes. The analytical solution presented serves as a test of numerical integration schemes, and its derivation is presented in a fashion that allows it to be repeated directly in a classroom. While the results in the absence of fields (equilibrium) or confinement (free particle) are omnipresent in the literature, we write down, apparently for the first time, the full nonequilibriurn results that may correspond, e.g., to a Hookean dumbbell embedded in a macroscopically homogeneous shear or mixed flow field. We demonstrate how the inertial results reduce to their noninertial counterparts in the nontrivial limit of vanishing mass. While the results are derived using basic integrations over Dirac delta distributions, we also provide alternative approaches involving (i) Fourier transforms, which seem advantageous only if the measured quantities also reside in Fourier space, and (ii) a Fokker-Planck equation and the moments of the probability distribution. The results, verified by numerical experiments, provide additional means of measuring the performance of numerical methods for such systems. It should be emphasized that this article provides specific details regarding the derivations of the time correlation functions as well as the implementations of various numerical methods, so that it can serve as a standalone piece for lessons in the framework of Ito stochastic differential equations and calculus.

关键词： time correlation functions stochastic differential equations Brownian/Langevin dynamics harmonic oscillator nonequilibrium numerical integration

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JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS 2018年第2期127卷 305-315页

作者： Lundin, A. A. Zobov, V. E. Russian Acad Sci Semenov Inst Chem Phys Vorobevskoe Sh 26 Moscow 117977 Russia Russian Acad Sci Kirensky Inst Phys Fed Res Ctr Krasnoyarsk Sci CtrSiberian Branch Akademgorodok 50 Krasnoyarsk 660036 Russia

Based on the proposed theory, we have investigated the shape of the NMR absorption spectra for C-13 and Si-29 nuclei in diamond and silicon crystals attributable to the internuclear dipole-dipole interaction. In accordance with the available experimental data, we have considered both crystals with a 100% content of magnetoactive isotopes and crystals with a comparatively low dilution by nonmagnetic nuclei. The time correlation functions (the first of which is the Fourier transform of the NMR spectrum) arising in an infinite chain of coupled differential equations are shown to be mutually similar with a slight time delay. The proposed theory allows the spectrum to be calculated analytically. The results obtained agree satisfactorily with the experimental ones. It is noted that the mutual similarity of the time correlation functions is probably a corollary of the development of dynamical chaos in the system

关键词： Spectra time correlation functions crystals Fourier Transform carbon 13 swine erysipelas Differential equations nuclear magnetic resonance spectroscopy Si-29

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Quantum state diffusion and time correlation functions

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JOURNAL OF MODERN OPTICS 1996年第11期43卷 2289-2300页

作者： Brun, TA Gisin, N UNIV GENEVA APPL PHYS GRPCH-1211 GENEVA 4SWITZERLAND

In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum stale diffusion (QSD) gives a useful method of solving these problems by unravelling the master equation into stochastic trajectories;but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly;by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on the stochastic noise of the particular trajectory, and which agrees in the mean with the ensemble average definition of correlation functions.

关键词： Shot noise Spectra trajectory Mechanical systems quanta time correlation functions Master equation ensemble average Fourier Transform correlation function

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Accurate estimation of transport coefficients using time correlation functions without fitting any analytic forms in equilibrium simulations

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POLYMER 2024年 290卷

作者： Liu, Xin Guo, Xuhong Liao, Qi East China Univ Sci & Technol State Key Lab Chem Engn Shanghai 200237 Peoples R China Chinese Acad Sci Inst Chem Beijing 100190 Peoples R China

Transport coefficients, such as the diffusion coefficient and shear viscosity, are important material properties that are calculated in computer simulations. In this study, the criterion for the accurate estimation of viscosity, as an example of transport coefficients, is determined by using the Green-Kubo formula without fitting any analytic forms for the stress decay function. The related algorithm is given by the estimation of the viscosities of polyethylene oxide solutions by using a molecular dynamics simulation for testing. The algorithm can be used in the simulations of complex systems with a long tail of correlations typically found in macromolecular and biological simulation systems.

关键词： Transport coefficients Viscosity Molecular dynamics simulation time correlation functions Green-kubo formula

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EQUILIBRIUM time correlation-functions IN THE LOW-DENSITY LIMIT

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JOURNAL OF STATISTICAL PHYSICS 1980年第2期22卷 237-257页

作者： VANBEIJEREN, H LANFORD, OE LEBOWITZ, JL SPOHN, H RUTGERS STATE UNIV DEPT MATHNEW BRUNSWICKNJ 08903 UNIV CALIF BERKELEY DEPT MATHBERKELEYCA 94720 UNIV MUNICH FACHBEREICH PHYSD-8000 MUNICH 22FED REP GER

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation (proved to be valid for all times). In the latter case the fluid (not including the tagged particle) is to zeroth order in thermal equilibrium and to first order its distribution is governed by a combination of the Rayleigh-Boltzmann equation and the linearized Boltzmann equation (proved to be valid for short times).

关键词： Boltzmann-Grad limit linearized Boltzmann equation low-density limit time correlation functions

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KINETIC-THEORY OF time correlation-functions FOR A DENSE ONE-COMPONENT PLASMA IN A MAGNETIC-FIELD

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JOURNAL OF STATISTICAL PHYSICS 1988年第5-6期53卷 1237-1260页

作者： SCHOOLDERMAN, AJ SUTTORP, LG 1.Instituut voor Theoretische Fysica Universiteit van Amsterdam Amsterdam The Netherlands

The time-dependent correlations of a one-component plasma in a uniform magnetic field are studied with the help of kinetic theory. The time correlation functions of the particle density, the momentum density, and the kinetic energy density are evaluated for large time intervals. In the collision-dominated regime the results agree with those found from linearized magnetohydrodynamics.

关键词： Kinetic theory time correlation functions one-component plasma magnetic field

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ON THE CALCULATION OF EQUILIBRIUM time correlation-functions IN HARD-SPHERE FLUIDS

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JOURNAL OF STATISTICAL PHYSICS 1989年第1-2期54卷 273-313页

作者： DESCHEPPER, IM COHEN, EGD KAMGARPARSI, B 1.The Rockefeller University 10021 New York New York

We discuss in detail techniques that have been used to determine single-particle equilibrium time correlation functions in a hard-sphere fluid on the basis of kinetic theory. The accuracy of various procedures is asse... 详细信息

关键词： time correlation functions kinetic theory hard spheres Boltzmann equation Enskog equation BGK solution method

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Energy and capacity time correlation functions for investigation of vibrational energy relaxation

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CHEMICAL PHYSICS 2004年第1-3期300卷 197-208页

作者： Schwarzer, D Vikhrenko, DV Vikhrenko, VS Max Planck Inst Biophys Chem Spect & Photochem Ki D-37077 Gottingen Germany Belarussian State Technol Univ Minsk 220050 BELARUS

Vibrational energy relaxation of a diatomic solute in a liquid solvent is investigated by means of the generalized Langevin equation. The vibrational energy, velocity and capacity time correlation functions (TCFs) are considered. It is shown that the detailed structure of the energy TCF contains an initial fast (subpicosecond) decay segment that is followed by weak oscillations on the background of an exponential relaxation curve. The direct method for evaluating the relaxation rate constant from equilibrium molecular dynamics simulations of a flexible solute is proposed and implemented. The closed form expressions for the memory function and for the relaxation rate constant in terms of quantities accessible from the simulations are derived. The simulation results for rigid and flexible solutes are compared and analyzed. (C) 2004 Elsevier B.V. All rights reserved.

关键词： vibrational energy relaxation energy fluctuations generalized Langevin equation linear response time correlation functions molecular dynamics

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