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Journal ArticleDOI

Stability of the thermal hartree-fock approximation

01 Jan 1963-Annals of Physics (Academic Press)-Vol. 21, Iss: 1, pp 99-121
TL;DR: In this paper, it is shown that isothermals with positive slope can occur in the Hartree-Fock equation of state only if an unstable solution has been used.
About: This article is published in Annals of Physics.The article was published on 1963-01-01. It has received 79 citations till now. The article focuses on the topics: Hartree–Fock method & Instability.
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Book ChapterDOI
TL;DR: In this article, the effect of spatial and other external confinements on the ground and excited state energy levels of many electron atoms, ions and exotic systems is discussed, and the spectral line shifts under strongly coupled plasma have been compared with data available from laser plasma experiments.
Abstract: The effect of spatial and other external confinements on the ground and excited state energy levels of many electron atoms, ions and exotic systems is discussed. Special emphasis is given to analyzing and estimating the changes in the spectral properties of plasma embedded systems in which, apart from changes in the free particle potential due to atom plasma interaction, spatial confinement enters through the introduction of boundary conditions. Effects of weak as well as strong plasma on the dipole polarizabilities, ionization potentials, singly and doubly excited state energy levels, oscillator strengths and transition probabilities have been discussed using simple plasma models but adopting rigorous quantum chemical methods. The spectral line shifts under strongly coupled plasma have been compared with data available from laser plasma experiments. Specific attention has been given to extremely accurate estimates of the energies of different three-body systems under plasma environments. The importance of the use of finite boundary conditions originating from spatial confinement of the plasma has been demonstrated and the effect of electron correlation in estimating various confined atomic properties is shown. Attempt has been made to interpret the changes in the spectral properties of atoms trapped in cavities inside liquid helium environments, by comparing the results estimated on the basis of current quantum chemical methodologies with the data available from laser induced fluorescence experiments.

120 citations

Journal ArticleDOI
TL;DR: In this paper, the density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures.
Abstract: The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

77 citations

Journal ArticleDOI
TL;DR: In this paper, a new model was developed to explain the ionization potential data, successfully reproducing the results that previous models could not, and the model was applied to dense plasmas, found in stellar interiors.
Abstract: Dense plasmas, found in stellar interiors, are composed of atoms with decreased ionization potentials compared with isolated atoms. Researchers have developed a new model to explain the ionization potential data, successfully reproducing the results that previous models could not.

70 citations

Journal ArticleDOI
TL;DR: This work presents a time-dependent formulation of coupled cluster theory that allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal cluster cumulant theory of Mukherjee and co-workers.
Abstract: We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal cluster cumulant theory of Mukherjee and co-workers [ Chem. Phys. Lett. 1992, 192, 55−61; Phys. Rev. E 1993, 48, 3373−3389; Chem. Phys. Lett. 2001, 335, 281−288; Chem. Phys. Lett. 2002, 352, 63−69; Int. J. Mod. Phys. B 2003, 17, 5367−5377]. Our derivation of the finite-temperature theory highlights connections to perturbation theory and to zero-temperature coupled cluster theory. We show explicitly how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory and how response properties can be efficiently computed using a variational Lagrangian. We discuss the implementation for realistic systems and showcase the potential utility of the method with calculations of the exchange correlation ener...

68 citations

Journal ArticleDOI
TL;DR: It is demonstrated that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions, and benchmark calculations for a four-electron system are provided.
Abstract: The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

64 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a series of papers dealing with many-particle systems from a unified, nonperturbative point of view is presented, which includes derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers.
Abstract: This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.

1,283 citations

Journal ArticleDOI
TL;DR: In this paper, a method for generating conserving approximations was developed based on a consideration of the equations of motion obeyed by the propagator G, defined in the presence of a nonlocal external scalar field U.
Abstract: ln describing transport phenomena, it is vital to build the conservation laws of number, energy, momentum, and angular momentum into the structure of the approximation used to determine the thermodynamic many-particle Green's functions. A method for generating conserving approximations was developed. This method is based on a consideration, at finite temperature, of the equations of motion obeyed by the one-particle propagator G, defined in the presence of a nonlocal external scalar field U. Approximations for G(U) are obtained by replacing the G/ sub 2/(U) which appears in these equations by various functionals of G(U). lf the approximation for G/sub 2/(U) satisfies certain simple symmetry conditions, then the G(U) thus defined obeys all the conservation laws. Furthermore, the two- particle correlation function, generated as ( delta G/ delta U) - /sub U=O/ plus or minus L, in terms of which all linear transport can be described, will obey all the conservation laws as well as several essential sum rules, such as the longitudinal f-sum rule. Examples of conserving approximations are described. The Hartree approximation, G/sub 2/(U) = G(U)G(U), generates the random-phase approximation for L. The Hartree-Fock approximation for G(U) leads to a natural generalization of the random-phase approximation in which hole-particlemore » ladder diagrams are summed. Another conserving approximation for G(U) is obtained by expanding the self-energy to first order in the many-particle scattenring matrix T(U). This T is obtained by summing ladder diagrams in which the sides of the ladder are composed of G(U)'s. The resulting L equation, which involves coefficients proportional to T/sup 2, is analogous to the linearized version of the usual Boltzmann equation. Finally, in order to obtain a description of collisions in a plasma, the selfenergy is expanded to first order in a dynamically shielded potential, V/sub 3/(U). This potential is obtained by summing bubbles composed of two G(U)'s. The resulting L equation is similar in structure to a Boltzmann equation in which the collision cross section is proportional to V/sub 3/sup 2/.(auth)« less

1,185 citations

Journal ArticleDOI
TL;DR: In this article, the moment of inertia of an axially symmetric system is derived within the framework of the Hartree-Fock theory, and the expression for a determinant is generalized to include the type of wave functions used in the theory of superconductivity.

711 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that it is always possible to choose an independent particle wave function which makes all collective modes stable in the random phase approximation of the Green's function.

456 citations

Journal ArticleDOI
TL;DR: In this article, the possibility of a many particle system undergoing a classical gas-liquid phase transition, is shown to be reflected in the structure of the two-particle Green's function in the random phase approximation.

25 citations