Search results for "Tree"
showing 10 items of 1841 documents
Experimental and theoretical study of thenf-level lifetimes of potassium
2008
The theoretical and experimental values of the 5f ,6 f ,7 f, and 8f radiative lifetimes of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole nf5/2-nd5/2, nf5/2-nd3/2, and nf7/2-nd5/2 transitions with n =5–8 in K arecalculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the 5f ,6 f ,7 f, and 8f states in neutral K and their uncertainties. The contributions from the nf5/2-ng7/2, nf7/2-ng7/2, and nf7/2-ng9/2 transitions to the lifetimes o…
Nucleon-to-Delta transition form factors in chiral effective field theory using the complex-mass scheme
2018
We calculate the form factors of the electromagnetic nucleon-to-$\Delta$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.
Feynman graph polynomials
2010
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
A programming guide for tensor networks with global SU(2) symmetry
2020
Abstract This paper is a manual with tips and tricks for programming tensor network algorithms with global S U ( 2 ) symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of codes, such as useful data structures to store the tensors, practical ways of manipulating them, and adapting typical functions for symmetric tensors. Here we do not restrict ourselves to any specific tensor network method, but keep always in mind that the implementation should scale well for simulations of higher-dimensional systems using, e.g., Projected Entangled Pair States, where tensors with many indices may show up. To this end, the structur…
Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level
2011
In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…
Tree-Loop Duality Relation beyond simple poles
2013
We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
Empirical determination of Einstein A-coefficient ratios of bright [Fe II] lines
2014
The Einstein spontaneous rates (A-coefficients) of Fe+ lines have been computed by several authors with results that differ from each other by up to 40%. Consequently, models for line emissivities suffer from uncertainties that in turn affect the determination of the physical conditions at the base of line excitation. We provide an empirical determination of the A-coefficient ratios of bright [Fe II] lines that would represent both a valid benchmark for theoretical computations and a reference for the physical interpretation of the observed lines. With the ESO-Very Large Telescope X-shooter instrument between 3000 Å and 24700 Å, we obtained a spectrum of the bright Herbig-Haro object HH 1. …
Spin projected unrestricted Hartree-Fock ground states for harmonic quantum dots
2008
We report results for the ground state energies and wave functions obtained by projecting spatially unrestricted Hartree Fock states to eigenstates of the total spin and the angular momentum for harmonic quantum dots with $N\leq 12$ interacting electrons including a magnetic field states with the correct spatial and spin symmetries have lower energies than those obtained by the unrestricted method. The chemical potential as a function of a perpendicular magnetic field is obtained. Signature of an intrinsic spin blockade effect is found.
Benchmarking global SU(2) symmetry in two-dimensional tensor network algorithms
2020
We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite projected entangled pair states and infinite projected entangled simplex states methods. Our implementation of $SU(2)$ symmetry follows the formalism based on fusion trees from Schmoll et al. [Ann. Phys. 419, 168232 (2020)]. In order to assess the utility of implementing $SU(2)$ symmetry, the algorithms are benchmarked for three models with different local spin: the spin-1 bilinear-biquadratic model on the square lattice, and the kagome Heisenberg antiferromagnets (KHAFs) for spi…
Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry
2017
International audience; We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.