Search results for "perturbation theory"
showing 10 items of 584 documents
Perturbative treatment of the electron-correlation contribution to the diagonal Born-Oppenheimer correction.
2007
A perturbative scheme for the treatment of electron-correlation effects on the diagonal Born-Oppenheimer correction (DBOC) is suggested. Utilizing the usual Moller-Plesset partitioning of the Hamiltonian formulas for first and second orders (termed as MP1 and MP2) are obtained by expanding the wave function in the corresponding coupled-cluster expressions for the DBOC[J. Gauss et al., J. Chem. Phys. 125, 144111 (2006)]. The obtained expressions are recast in terms of one- and two-particle density matrices in order to take advantage of existing analytic second-derivative implementations for many-body methods. Test calculations show that both MP1 and MP2 recover large fractions (on average 90…
Energy relaxation in a? 4 with long range interactions
1995
We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential ofϕ 4-type and “infinite” range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions of the fluctuations of the one-particle energiesE n(t) decays exponentially. The corresponding relaxation time τ is proportional toN and is given by τ(T, N) =Nτ0(T). The temperature dependent time scale τ0 can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode cou…
Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations.
2015
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for p…
Equation-of-motion coupled cluster perturbation theory revisited
2014
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]
On the convergence of perturbative coupled cluster triples expansions:Error cancellations in the CCSD(T) model and the importance of amplitude relaxa…
2015
Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate th…
Cosmological data analysis of f(R) gravity models
2009
A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies all the observational tests considered and we derive the allowed range of parameters. Current data s…
Self‐consistent intermediate Hamiltonians : A coupled cluster type formulation of the singles and doubles configuration interaction matrix dressing
1995
This paper presents a new self‐consistent dressing of a singles and doubles configuration interaction matrix which insures size‐consistency, separability into closed‐shell subsystems if localized molecular orbitals (MOs) are used, and which includes all fourth order corrections. This method yields, among several schemes, a reformulation of the coupled cluster method, including fully the cluster operators of single and double excitations, and partially those of the triples (Bartlett’s algorithm named CCSDT‐1a). Further improvement can be easily included by adding exclusion principle violating corrections. Since it leads to a matrix diagonalization, the method behaves correctly in case of nea…
Analytic form of the full two-loop five-gluon all-plus helicity amplitude
2019
We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude, and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms and rational functions.
Cosmological Perturbations in Renormalization Group Derived Cosmologies
2002
A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $\Lambda$ is presented. A gauge-invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, $G$, and $\Lambda$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $\Lambda$ vary according to renormalization group equations in the vicinity of a fixed point.
Hamiltonian lattice QCD at finite density: equation of state in the strong coupling limit
2001
The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. Our result is in qualitative agreement with continuum models and should be verifiabl…