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.     

Diagrammatic non-degenerate RSPT for evaluation of ground-state energy of simple open-shell molecular systems

The diagrammatic non-degenerate Rayleigh-Schrödinger perturbation theory and the coupled cluster approach are applied to the evaluation of the ground state energy of a simple open-shell molecular system described in the zeroth order approximation by a single determinant wavefunction. The corresponding hamiltonian is built up by the creation and annihilation operators introduced over an orthonormal set of restricted Hartree-Fock one-particle functions. The perturbation H₁ is composed of one- and two-particle terms, the one-particle term depending in an explicit way upon the type of restricted Hartree-Fock theory used. The efficiency of the elaborated theory is illustrated for the BeH molecule.     

Improved uncoupled Hartree-Fock perturbation theory

Various uncoupling schemes used in the first-order Hartree-Fock perturbation theory are compared. The analysis and extraction of the most important terms in the coupled Hartree-Fock perturbation scheme leads to a definition of the new functional for the determination of the first-order perturbed orbitals. This new functional represents an alternative uncoupling scheme for the first-order Hartree-Fock perturbation theory. Some special cases of real and pure imaginary perturbations and also the connections with previously proposed uncoupling schemes are discussed.

The uncoupling procedure proposed in this paper is illustrated by electric dipole polarizability calculations for some Be- and Ne-like atomic systems. The results obtained are almost as good as those calculated by using coupled Hartree-Fock perturbation theory.     

Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La_1/3Ca_2/3MnO₃ that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites.     

Renormalization beyond the framework of the perturbation theory

By the example of a scalar field model with ϕ⁴ interaction, the possibility of separating the finite parameters beyond the framework of standard (in the interaction representation) perturbation theory is discussed. A scheme of divergence separation for large momenta and their compensation by infinite initial parameters – mass and coupling constant – is examined. The one-particle sector of the diagonal component of the total Hamiltonian admits this procedure. In this case, the energy of the one-particle spectrum has a relativistic form.     

Spin-adaptation in many-body perturbation theory

In this paper we present a method of incorporating spin-adapted configurations in a Many-Body Perturbation Theory (MBPT) framework. It has been demonstrated how the use of doubly excited Serber-type spinadapted configurations leads in a straightforward way to a well-defined MBPT series which in effect involves an infinite summation of orbital-diagonal ladders for all possible spin allocations. The formalism implicitly defines a partition of the hamiltonian in which the diagonal matrix elements of the hamiltonian in the Serber-type configurations figure as the unperturbed part. This may thus be called a spin-adapted Epstein-Nesbet (E-N) type of partition. The formalism has been tested on a selection of 6π-electron conjugated systems where we have calculated their orbital pair-correlation energies, and compared the performance against E-N perturbation results and a variational calculation of the same quantities. The comparison reveals that, with canonical Hartree-Fock orbitals, the E-N partition tends to overestimate the pair-correction energy which the spinadapted formalism tends to compensate, but without involving much additional effort. The results for the localized H-F orbitals are rather less sensitive and no definitive conclusions could be discerned for them. The advantages of using the spin-adapted MBPT formalism have also been delineated.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Effective hamiltonian of the nuclear moments electronic shielding

An information is given allowing to use the second quantization and the effective operator methods in the ligand field theory. The operator was constructed accounting for the interaction of the multi-shell electronic configurations through a one-particle perturbation V≪R. The expression obtained is believed to be useful in microscopic calculations and phenomenological interpretation of spectroscopic experiments. As an illustration, the effective hamiltonian of the nuclear moments electronic shielding has been deduced. It was found, in particular, that the dipolar part of the hyperfine interaction contributes to the shift of the nuclear g-factor in the systems with the electronic spin S>0.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

An approach to the nonequilibrium theory of highly excited semiconductors

We present an investigation of the optical properties of semiconductors, which are excited by a strong laser pulse. On the basis of a nonequilibrium Green's function technique (Keldysh formalism) we study the system of electrons and holes, interacting among themselves and with the exciting pulse. A set of coupled equations for the one-particle Green's function and the transverse and longitudinal polarizability is derived, which is valid for arbitrary excitation conditions. For an initially prepared state, which is not too far from a quasiequilibrium state of the excited system, the theory is elaborated in detail, using a screened Hartree-Fock approximation scheme. Within this approximation earlier results of various theoretical approaches are found to be special cases of the equilibrium limit of the present theory.     

Canonical perturbation theory in statistical mechanics

Hamiltonian formalism is used to develop a perturbation theory for the calculation of the mean values of arbitrary dynamic quantities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 7, pp. 87–93, July, 1986.     

On the stationary perturbation theory in quantum mechanics

A simple method is proposed for solving the Shcrödinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small. Under the additional assumption that it is small (in accordance with a well-defined criterion of smallness) the obtained results yield directly the results of Schrödinger's perturbation theory. The developed approach contains in compact form various formulations of perturbation theory. The calculations use neither the complex technique of projection operators nor the complicated formalism of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 33–36, November, 1980.     

等离子体重整化准线性理论中的渐近传播函数与色散关系

本文引入了系统中六维相空间的表象理论。利用这一理论分析了Misguich-Balescu所给出的单位子渐近传播算子和Dupree的平均格林函数之间的关系,发现在平稳过程中两者是一致的。从而解决了MB所给出非线性色散关系中共振函数的发散困难。指出产生发散困难的原因在于M-B在子动力学中引入的涨落产生算子的概念对多重时间尺度的摄动理论是不适用的。 关键词：     

Time-dependent perturbation theory with a classical limit

We construct a quantum mechanical perturbation theory which uses the multiple time scale technique. Working with the time translation operator, we use a variant on the method of Bender and Bettencourt. Our perturbation theory smoothly crosses over to the classical result as Planck's -->0. It is seen that this technique has a nonperturbative element built into it.     

Subdynamics and perturbation theory in wave-functions space

A formulation of perturbation theory is provided following the Brussels school formalism in wave-functions space. The text is also an introduction to the Brussels school theory of irreversibility.     

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.Supported by the NSF under Grant No. CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.     

Radiative perturbation theory for polarized radiances: 1. Theory

Radiative perturbation theory has proven to be a useful tool in radiative transfer calculations, especially in situations where repeated solution of the radiative transfer equation is required. So far however, its use has been restricted to non-polarized situations, including such applications as surface fluxes, UV indices, and the inversion of satellite radiance observations. Here, we extend the structure of radiative perturbation theory to incorporate the full Stokes formalism of polarization, to obtain the relevant equations for the first order term. This formalism will be applied to fluxes in a follow-up paper, and eventually to satellite observations.     

A Local (Perturbative) Construction of Observables in Gauge Theories: The Example of QED

Interacting fields can be constructed as formal power series in the framework of causal perturbation theory. The local field algebra is obtained without performing the adiabatic limit; the (usually bad) infrared behavior plays no role. To construct the observables in gauge theories we use the Kugo–Ojima formalism; we define the BRST-transformation as a graded derivation on the algebra of interacting fields and use the implementation of by the Kugo–Ojima operator Q _int. Since our treatment is local, the operator Q _int differs from the corresponding operator Q of the free theory. We prove that the Hilbert space structure present in the free case is stable under perturbations. All assumptions are shown to be satisfied in QED. Received: 5 August 1998 / Accepted: 20 November 1998     

Lie transform perturbation theory for Hamiltonian systems

A review of the theory of Lie transform perturbation theory for Hamiltonian systems is presented. The operator theory of Dewar for continuous families of canonical transformations is discussed. It is then used to derive the perturbation method of Deprit. Two examples of the use of this method are provided. In addition, the more efficient perturbation method of Dragt and Finn is discussed.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.