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Jaichan Hwang - One of the best experts on this subject based on the ideXlab platform.

  • cosmological post newtonian approximation compared with Perturbation Theory
    The Astrophysical Journal, 2012
    Co-Authors: Hyerim Noh, Jaichan Hwang
    Abstract:

    We compare the cosmological first-order post-Newtonian (1PN) approximation with the relativistic cosmological linear Perturbation Theory in a zero-pressure medium with the cosmological constant. We compare equations and solutions in several different gauge conditions available in both methods. In the PN method we have Perturbation equations for density, velocity, and gravitational potential independently of the gauge condition to 1PN order. However, correspondences with these 1PN equations are available only in certain gauge conditions in the Perturbation Theory. Equations of perturbed velocity and the perturbed gravitational potential in the zero-shear gauge exactly coincide with the Newtonian equations, which remain valid even to 1PN order (the same is true for perturbed velocity identified in the comoving gauge), and equations of perturbed density in the zero-shear gauge and the uniform-expansion gauge coincide to 1PN order. We identify other correspondences available in different gauge conditions of the Perturbation Theory.

  • cosmological post newtonian approximation compared with Perturbation Theory
    arXiv: Cosmology and Nongalactic Astrophysics, 2012
    Co-Authors: Hyerim Noh, Jaichan Hwang
    Abstract:

    We compare the cosmological first-order post-Newtonian (1PN) approximation with the relativistic cosmological linear Perturbation Theory in a zero-pressure medium with the cosmological constant. We compare equations and solutions in several different gauge conditions available in both methods. In the PN method we have Perturbation equations for density, velocity and gravitational potential independently of the gauge condition to 1PN order. However, correspondences with these 1PN equations are available only in certain gauge conditions in the Perturbation Theory. Equations of perturbed velocity and the perturbed gravitational potential in the zero-shear gauge exactly coincide with the Newtonian equations which remain valid even to 1PN order (the same is true for perturbed velocity in the comoving gauge), and equations of perturbed density in the zero-shear gauge and the uniform-expansion gauge coincide to 1PN order. We identify other correspondences available in different gauge conditions of the Perturbation Theory.

Andreas M. Köster - One of the best experts on this subject based on the ideXlab platform.

  • time dependent auxiliary density Perturbation Theory
    Journal of Chemical Physics, 2010
    Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. Köster
    Abstract:

    The recently developed auxiliary density Perturbation Theory is extended to time-dependent Perturbations. As its static counterpart, it is based on auxiliary density functional Theory in which the Coulomb and exchange-correlation potentials are expressed through one auxiliary function density. As in the case of static Perturbations a noniterative alternative to the corresponding coupled perturbed Kohn–Sham method is formulated. The new methodology is validated by local and gradient corrected dynamical polarizability calculations. Comparison with experiment indicates that for low frequencies reliable dynamical polarizabilities are obtained. Our discussion also shows that the computational performance of time-dependent auxiliary density Perturbation Theory is similar to the previously described static approach. In order to demonstrate the potential of this new methodology, dynamic polarizabilities of C60, C180, and C240 are calculated.

  • auxiliary density Perturbation Theory
    Journal of Chemical Physics, 2008
    Co-Authors: Roberto Floresmoreno, Andreas M. Köster
    Abstract:

    A new approach, named auxiliary density Perturbation Theory, for the calculation of second energy derivatives is presented. It is based on auxiliary density functional Theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn–Sham equations the perturbed density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary density Perturbation approach match quantitative with the ones from standard density functional Theory if augmented auxiliary function sets are used. The computational advantages of auxiliary density Perturbation Theory are discussed, too.

Jose Galvez T Ghersi - One of the best experts on this subject based on the ideXlab platform.

  • numerical renormalization group based approach to secular Perturbation Theory
    Physical Review E, 2021
    Co-Authors: Jose Galvez T Ghersi, Leo C Stein
    Abstract:

    Perturbation Theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive Perturbation Theory often fails on long timescales, leading to secularly growing solutions. These divergences have been treated with a variety of techniques, including the powerful dynamical renormalization group (DRG). Most of the existing DRG approaches rely on having analytic solutions up to some order in Perturbation Theory. However, sometimes the equations can only be solved numerically. We reformulate the DRG in the language of differential geometry, which allows us to apply it to numerical solutions of the background and Perturbation equations. This formulation also enables us to use the DRG in systems with background parameter flows and, therefore, extend our results to any order in Perturbation Theory. As an example, we apply this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. We numerically construct DRG solutions which are valid on secular timescales, long after naive Perturbation Theory has broken down.

Jacques K Desmarais - One of the best experts on this subject based on the ideXlab platform.

  • Perturbation Theory treatment of spin orbit coupling part i double Perturbation Theory based on a single reference initial approximation
    Journal of Chemical Theory and Computation, 2021
    Co-Authors: Jacques K Desmarais, Alessandro Erba, Jeanpierre Flament, Bernard Kirtman
    Abstract:

    We develop a Perturbation Theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree-Fock (SR UHF) solution, we carry out a double Perturbation expansion in terms of spin-orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two. Illustrative calculations on the halogen series of neutral and singly positive diatomic molecules show that the Perturbation expansion is well-converged by taking into account only the leading (nonvanishing) term at each order of the electron fluctuation potential. Our Perturbation Theory approach provides a computationally attractive alternative to a two-component self-consistent field treatment of SOC. In addition, it includes coupling with the fluctuation potential through third order and can be extended (in principle) to multireference calculations, when necessary for both closed- and open-shell cases, using quasi-degenerate Perturbation Theory.

D R Bowler - One of the best experts on this subject based on the ideXlab platform.

  • notes on density matrix Perturbation Theory
    Journal of Chemical Physics, 2020
    Co-Authors: Lionel A Truflandier, Rivo M Dianzinga, D R Bowler
    Abstract:

    Density matrix Perturbation Theory (DMPT) is known as a promising alternative to the Rayleigh–Schrodinger Perturbation Theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method.

  • notes on density matrix Perturbation Theory
    arXiv: Chemical Physics, 2020
    Co-Authors: Lionel A Truflandier, Rivo M Dianzinga, D R Bowler
    Abstract:

    Density matrix Perturbation Theory (DMPT) is known as a promising alternative to the Rayleigh-Schrodinger Perturbation Theory, in which the sum-over-state (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys.127, 054103 (2007)] is reformulated via the Sylvester equation, and the recursive DMPT of A.M.N. Niklasson and M. Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from [J. Chem. Phys. 144, 091102 (2016)]. Comparison of the computational performances shows that the aformentioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method