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1.
周世琦 《中国物理》2007,16(4):1167-1175
A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.  相似文献   

2.
周世琦 《中国物理快报》2002,19(9):1322-1325
In this Letter,we truncate the functional expansion of the non-uniform first-order direct correlation function (DCF) around the bulk density at the lowest order.But the truncation is performed formally and exactly by making use of functional counterpart of the Lagrangian theorem of differential calculus.Consequently the expansion coefficient,i.e.the uniform second-order DCF,is replaced by its non-uniform counterpart whose density argument is an appropriate mixture of calculated density distribution and the bulk density with a mixing parameter determined by a hard-wall sum rule.The non-uniform second-order DCF is then approximated by the uniform second-order DCF with an appropriate weighted density as its density argument.The present formally exact truncated functional expansion predicts the density distribution in good agreement with simulation data for hard sphere and Lennard-Jones fluid exerted by an external field.  相似文献   

3.
The ornstein-zenike equation is solved with the Rogers-Young approximation for bulk hard sphere fluid and Lennard-Jones fluid for several state points.Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function.It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve.Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J.Chem.Phys,112(2000)8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid.The good agreement of theoretical predictions with the computer simulation data is obtained.The present numerical procedure incroporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more filexible for various interaction potential fluid.  相似文献   

4.
A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.  相似文献   

5.
周世琦 《中国物理快报》2003,20(12):2107-2109
Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first-order direct correlation function to a non-uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non-uniform first-order direct correlation function.  相似文献   

6.
Within the framework of the density functional theory for classical fluids, the equilibrium density profiles of charged hard sphere fluid confined in micro-cavity are studied by means of the modified fundamental measure theory. The dimension of micro-cavity, the charge of hard sphere and the applied electric field are found to have significant effects on the density profiles. In particular, it is shown that Coulomb interaction, excluded volume interaction and applied electric field play the central role in controlling the aggregated structure of the system.  相似文献   

7.
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0^(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ^3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.  相似文献   

8.
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.  相似文献   

9.
A new semianalytical method, which is a combination of the density functional theory with Rosenfeld density functional and the Ornstein-Zernike equation, is proposed for the calculation of the effective depletion potentials between a pair of big spheres immersed in a small hard sphere fluid. The calculated results are almost identical to the integral equation method with the Percus-Yevick approximation, and are also in agreement well with the Monte Garlo simulation results.  相似文献   

10.
11.
We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.  相似文献   

12.
YAN Jun 《理论物理通讯》2008,50(10):893-896
The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.  相似文献   

13.
Molecule geometry structures, frequencies, and energetic stabilities of ammonia borane (AB, NH3BH3 ) and metal amidoboranes (MAB, MNH2BH3), formed by substituting H atom in AB with one of main group metal atoms, have been investigated by density-functional theory and optimized at the B3LYP levels with 6-311G++ (3dr, 3pd) basic set. Their structural parameters and infrared spectrum characteristic peaks have been predicted, which should be the criterion of a successfully synthesized material. Several parameters such as binding energies, vibrational frequencies, and the energy gaps between the HOMO and the LUMO have been adopted to characterize and evaluate their structure stabilities. It is also found that the binding energies and HOMO-LUMO energy gaps of the MAB obviously change with the substitution of the atoms. MgAB has the lowest binding energy and is easier to decompose than any other substitutional structures under same conditions, while CaAB has the highest chemical activity.  相似文献   

14.
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.  相似文献   

15.
Functional Integrals and Excitation Energy in Three-Band Hubbard Model   总被引:1,自引:0,他引:1  
YAN Jun 《理论物理通讯》2008,49(3):567-570
The normal and anomalous Green's functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green's function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.  相似文献   

16.
The unified bound on the fundamental limit of quantum dynamics rate, as quietly recently obtained by Levitin and Toffoli [Phys. Rev. Lett. 103 (2009) 160502], is improved and refined. The improvement may be arbitrarily large in certain cases. In particular, this puts a limit on the operation rate of quantum gates allowed by quantum mechanics.  相似文献   

17.
In a Euclidean space functional integral treatment of the free energy of QCD, a chemical potential enters only through the functional determinant of the Dirac operator which for any flavor is /D+m-mu(f)gamma(0) (where mu(f) is the chemical potential for the given flavor). Any nonzero mu alters all of the eigenvalues of the Dirac operator relative to the mu=0 value, leading to a naive expectation that the determinant is altered and which thereby alters the free energy. Phenomenologically, this does not occur at T=0 for sufficiently small mu, in contradiction to this naive expectation. The problem of how to understand this phenomenological behavior in terms of functional integrals is solved for the case of an isospin chemical through the study of the spectrum of the operator gamma(0)(/D+m). The case of the baryon chemical potential is briefly discussed.  相似文献   

18.
Based on the revised geometric measure of entanglement (RGME) proposed by us [J. Phys. A: Math. Theor. 40 (2007) 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state (GSS) in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement (GME) and relative entropy of entanglement (RE). The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.  相似文献   

19.
The White Bear version of Fundamental Measure Theory (FMT-WB) has been tested in binary mixtures of hard spheres in the vicinity of the colloidal limit, where the size ratio of the two species is exceedingly large and the large sphere mole fraction is infinitely low. Contact values of large–large sphere radial distribution functions have been calculated and compared with molecular dynamics simulations and previously proposed theoretical formulas. In contrast to the failure of BMCSL (Boublik, Mansoori, Carnahan, Starling, Leland equation of state) predictions, FMT-WB gives good agreement with simulation for a range of species size ratios and mole fractions. The performance of BMCSL is qualitatively related to one of its model parameters, which could indicate the reliability of the BMCSL result. Our results confirm the accuracy of FMT-WB in the colloidal limit for the first time and suggest that BMCSL contact values must be applied carefully to account for chain connectivity when studying certain cases with classical Density Functional Theories.  相似文献   

20.
I discuss the modification of Einstein's Theory of General Relativity based on a periodic functional approach. In this new approach, a corrected periodic gravitational coupling constant arises and plays the role of periodic damping term acting on the theory. It is found that it is achievable to have an oscillating universe dominated by dark energy and expanding aceeleratedly in time.  相似文献   

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