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51.
Sandro Faetti Leone Fronzoni Paolo Grigolini Riccardo Mannella 《Journal of statistical physics》1988,52(3-4):951-978
It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation
1 and an unperturbed part
0. The standard Fokker-Planck structure is recovered at the second order in
1, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in
1 the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in
1, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in
1 vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in
1 vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation. 相似文献
52.
A comparative study for the fitting of X‐ray photoelectron spectra (XPS) using different model functions is presented. Synthetically generated test spectra using Gaussian/Lorentzian convolution and a real measured spectrum are fitted with the three commonly used models: product, sum and Gaussian/Lorentzian convolution functions. In these limited tests, it was found that the sum function is superior to the product function, particularly for low‐noise spectra. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
53.
用密度泛含方法研究了LaC5n(n=-1,0,+1)分子簇的结构和稳定性及振动光谱,对这个六原子体系提出了三种可能构型,点群结构为C2v对称性.第一个构型为La接在弯曲的C5链上,第二个是La通过二个键与C5环相连第三个是La通过一个键与C5环相连;结果表明,第一个构型即当La接在弯曲的C5链上时能量最低.振动光谱分析指出,当n=-1时,第二个构型为局域极小值;当n=+1时,第一个和第二个构型为局域极小值;对n=0,局域极小值没有找到. 相似文献
54.
55.
We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T
1, the population relaxation rate, and 1/T
2, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T
21/2T
1, when fourth-order terms are included, in some instances 1/T
2<1/2T
1. 相似文献
56.
It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy. 相似文献
57.
Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable. 相似文献
58.
59.
R. Centoducatte E. P. Muniz F. E. Jorge M. T. Barreto 《Journal of Molecular Structure》2004,680(1-3):143-147
The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H2O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H2O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method. 相似文献
60.
A discrete variable representation (DVR) made from distributed Gaussians gn(x) = e, (n = ?∞, …, ∞) and its infinite grid limit is described. The infinite grid limit of the distributed Gaussian DVR (DGDVR) reduces to the sinc function DVR of Colbert and Miller in the limit c → 0. The numerical performance of both finite and infinite grid DGDVRs and the sinc function DVR is compared. If a small number of quadrature points are taken, the finite grid DGDVR performs much better than both infinite grid DGDVR and sinc function DVR. The infinite grid DVRs lose accuracy due to the truncation error. In contrast, the sinc function DVR is found to be superior to both finite and infinite grid DGDVRs if enough grid points are taken to eliminate the truncation error. In particular, the accuracy of DGDVRs does not get better than some limit when the distance between Gaussians d goes to zero with fixed c, whereas the accuracy of the sinc function DVR improves very quickly as d becomes smaller, and the results are exact in the limit d → 0. An analysis of the performance of distributed basis functions to represent a given function is presented in a recent publication. With this analysis, we explain why the sinc function DVR performs better than the infinite grid DGDVR. The analysis also traces the inability of Gaussians to yield exact results in the limit d → 0 to the incompleteness of this basis in this limit. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献