Calculation of spin-density matrix by diagrammatic perturbation theory

A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.     

Coupled-cluster approach in electronic structure theory of molecules

The coupled-cluster approach for the electronic-structure studies of molecular systems is formulated in non-degenerate and quasi-degenerate versions. It provides an efficient method how to construct and calculate simultaneously the diagrammatic perturbation terms of an arbitrary high order and a prescribed form of topology. This allows us to formulate simple procedures for the evaluation of infinite summations of perturbation diagrammatic terms. The theory is illustrated by numerical calculations for simple small molecular systems.     

Cluster expansions for correlated finite nuclei: The normalization integral

Cluster expansions of various kinds are studied with regard to the calculation of the normalization integral in ¹⁶O. The factor Aviles-Hartog-Tolhoek cluster expansion is shown to be very satisfactory at third order. A diagrammatic analysis of this cluster expansion is also included and numerically tested.     

Structure of 6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, <'6>He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.     

Structure and thermodynamics of polar interaction site fluids

We present results for the structure and thermodynamics of the dipolar hard dumbbell fluid obtained from a recently developed theory which is based on an extension of cluster perturbation theory (CPT) for atomic fluids to the interaction site formalism. The calculations are for the lowest order result in the theory which we denote as the optimized random phase approximation in the interaction site formalism (ISF-ORPA). This method does not include unallowed diagrammatic contributions to the structure and thermodynamics, in contrast to previous CPTs in the interaction site formalism. We compare the results to computer simulation data and find that the theory gives a realistic representation of the effect of the electrostatic interactions on the structure of the fluid.     

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.     

Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.     

Double perturbation calculations of spin-spin coupling constants using localized orbitals

The Fermi contact contribution to N.M.R. spin-spin coupling constants has been calculated to the fourth order by a double perturbation development starting from a fully localized determinant, according to the assumptions of the PCILO-CNDO method. The use of diagrammatic techniques greatly simplifies the evaluation. There is a cancellation of certain types of diagram. The coupling constant between bonded atoms appears in the second order through a contribution which only depends on the appropriate bond orbital. The next orders involve the other bonds and correlation effects. For nonbonded atoms, the first contribution appears in the fourth order and results from direct delocalization through space, involving only the bonds on the two atoms.

An analytical and numerical comparison with previous calculations is performed for H-H and C-H coupling constants on small organic molecules. The relative importance of the various processes is discussed for the J _HH vicinal coupling constants of ethylene.     

双时因果格林函数的费曼图解法

本文从解析性的讨论出发,应用朗道关系改进Дзялошинский的图解法,建立了双时因果格林函数的费曼图解法,它具有正确的零温权限,并可直接用来计算各种非平衡过程的动力学性质。     

Mayer sampling: calculation of cluster integrals using free-energy perturbation methods

Free-energy simulation methods are applied toward the calculation of cluster integrals that appear in diagrammatic methods of statistical mechanics. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of the integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. Virial coefficients, up to the sixth for the Lennard-Jones model and the fifth for the SPCE model of water, are calculated as a demonstration.     

类锂体系激发态1s2 nd(n=3,4,5)精细结构和项能的理论计算

使用全实加关联(fullcorepluscorrelation缩写为FCPC)和里兹(Ritz)变分方法计算了类锂体系(Z=11—20)激发态1s2nd(n=3,4,5)的非相对论能量和波函数;包括动能修正、电子电子接触项、轨道轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出,量子电动力学(quantumelectronicdynamics缩写为QED)修正由有效核电荷方法和类氢公式计算;给出了高电离类锂体系激发态的激发能、精细结构和项能(termenergy),并 关键词： 类锂体系 全实加关联 精细结构 激发能     

The spherical sector of the Calogero model as a reduced matrix model

We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.     

The normal liquid 3He one-body momentum distribution at zero and finite temperature

The normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism. The lowest order constrained variational (LOCV) and the extended LOCV (ELOCV) method are used to calculate the correlation functions at zero and finite temperatures. The input inter-atomic potential is the familiar 6–12 Lennard-Jones interaction. The gap in n(k) at the Fermi surface is found to be about 0.41 comparing to 1.0 (0.72) for the noninteracting (dilute hard-sphere) Fermi gas model at zero temperature and it decreases by increasing the temperature. It is also demonstrated that the high-momentum tail of n(k) gets larger as we increase the temperature and finally, we find a good agreement between present calculated n(k) and those coming from more sophisticated approaches such as Diffusion and Green-function Monte Carlo techniques.     

Diagrammatic structure of the general coupled cluster equations

The general formula for the number of diagrammatic terms occurring in the T_n equation within a particular coupled cluster model is derived. Both the antisymmetrized and Goldstone diagrams are considered. In addition to the full coupled cluster equation approximate approaches are discussed, and for each the general formula for the number of terms is given. Analogous expressions are presented for the number of diagrammatic terms contributing to the elements of the transformed Hamiltonian [Hbar] = e^?T He^T .     

Hopf term in the action for vortices/skyrmions with odd filling of Landau levels

A term in the action that is of third order in the derivatives of the rotation matrix is calculated. A direct diagrammatic method in the limit of high magnetic fields is used. It is shown that the action contains the standard Hopf invariant with a coefficient corresponding to fermionic behavior of vortices/skyrmions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 178–183 (10 August 1997)     

Effect of magnetoelastic interaction on the thermodynamics of ferromagnets: Simulation by the method of spin-lattice dynamics

Thermodynamic properties of systems with coupled magnetic and lattice degrees of freedom are analyzed by the numerical spin-lattice dynamics (SLD) method. A scheme of numerical integration is developed for SLD equations in a thermostat, that follows the earlier formulated approaches and is modified to describe systems with realistic interatomic interactions. The method proposed allows one to calculate the spectral density of oscillations, heat capacity, magnetization, and thermal expansion coefficient within a single scheme. It is established that, due to short-range magnetic order, the interplay between magnetic and lattice degrees of freedom contributes to the thermodynamic properties of the system even in the paramagnetic state. It is shown that there exist two mechanisms how the spin-lattice interaction influences the thermodynamic properties: static and dynamic mechanisms; the first is determined by its contribution to the thermal expansion of the lattice, and the second, by the dynamic interaction between magnetic moments and crystal lattice vibrations.     

Dynamic density and spin responses of a superfluid Fermi gas in the BCS–BEC crossover: Path integral formulation and pair fluctuation theory

We present a standard field theoretical derivation of the dynamic density and spin linear response functions of a dilute superfluid Fermi gas in the BCS–BEC crossover in both three and two dimensions. The derivation of the response functions is based on the elegant functional path integral approach which allows us to calculate the density–density and spin–spin correlation functions by introducing the external sources for the density and the spin density. Since the generating functional cannot be evaluated exactly, we consider two gapless approximations which ensure a gapless collective mode (Goldstone mode) in the superfluid state: the BCS–Leggett mean-field theory and the Gaussian-pair-fluctuation (GPF) theory. In the mean-field theory, our results of the response functions agree with the known results from the random phase approximation. We further consider the pair fluctuation effects and establish a theoretical framework for the dynamic responses within the GPF theory. We show that the GPF response theory naturally recovers three kinds of famous diagrammatic contributions: the Self-Energy contribution, the Aslamazov–Lakin contribution, and the Maki–Thompson contribution. We also show that unlike the equilibrium state, in evaluating the response functions, the linear (first-order) terms in the external sources as well as the induced order parameter perturbations should be treated carefully. In the superfluid state, there is an additional order parameter contribution which ensures that in the static and long wavelength limit, the density response function recovers the result of the compressibility (compressibility sum rule). We expect that the f$f$-sum rule is manifested by the full number equation which includes the contribution from the Gaussian pair fluctuations. The dynamic density and spin response functions in the normal phase (above the superfluid critical temperature) are also derived within the Nozières–Schmitt–Rink (NSR) theory.     

Quantum field theory for discrepancies II: 1/N corrections using fermions

We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including the second-order in 1/N. For some discrepancies, we give the explicit expansion to first order.     

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards’ field theory

Edwards’ functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules, and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of binary homopolymer blends and diblock copolymer melts.