Static Self-energy Research Articles

Static Self-Energy and Effective Mass of the Homogeneous Electron Gas from Quantum Monte Carlo Calculations

Static Self-Energy and Effective Mass of the Homogeneous Electron Gas from Quantum Monte Carlo Calculations

Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods.

The performance of several methods for the calculation of vertical ionization potentials (IPs) or, more generally, electron-detachment energies based on unitary coupled-cluster (UCC) theory and the algebraic-diagrammatic construction (ADC) scheme is evaluated with respect to benchmark data computed at the level of equation-of-motion coupled-cluster theory, including single, double, and triple excitations (IP-EOM-CCSDT). Based on a statistical evaluation of about 200 electron-detached states of 41 molecules, the second-order methods IP-ADC(2) and IP-UCC2 show modest accuracies with IP-EOM-CCSDT as reference, exposing a mean signed error and a standard deviation of the error of -0.54 ± 0.50 and -0.49 ± 0.54eV, respectively, accompanied by a mean absolute error (MAE) of 0.61 and 0.58eV, respectively. The strict third-order IP-ADC method demonstrates an accuracy of 0.26 ± 0.35eV (MAE = 0.35eV), while the IP-UCC3 method is slightly more accurate with 0.24 ± 0.26eV (MAE = 0.29eV). Employing the static self-energy computed using the Dyson expansion method (DEM) improves the IP-ADC(3) performance to 0.27 ± 0.28eV, with the mean absolute error of this method being 0.32eV. However, employing the simpler improved fourth-order scheme Σ(4+) for the static self-energy provides almost identical results as the DEM. Based on the quality of the present benchmark results, it therefore appears not necessary to use the computationally more demanding DEM.

Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions

We compute the static self-energy of SU(3) gauge theory in four spacetime dimensions to order α20 in the strong coupling constant α. We employ lattice regularization to enable a numerical simulation within the framework of stochastic perturbation theory. We find perfect agreement with the factorial growth of high order coefficients predicted by the conjectured renormalon picture based on the operator product expansion.

O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schrodinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

Long time limit of equilibrium glassy dynamics and replica calculation

It is shown that the limit t − t ′ → ∞ of the equilibrium dynamic self-energy can be computed from the n → 1 limit of the static self-energy of an n-times replicated system with one step replica symmetry breaking structure. It is also shown that the Dyson equation of the replicated system leads in the n → 1 limit to the bifurcation equation for the glass ergodicity breaking parameter computed from dynamics. The equivalence of the replica formalism to the long time limit of the equilibrium relaxation dynamics is proved to all orders in perturbation for a scalar theory.

Elastic constants of nonionic anharmonic crystals

Taking into account the entire anharmonicity of the crystal an exact relation between the long-wavelength limit of the static self-energy and the isothermal elastic constants is established. The result can be reformulated as a sum rule for the displacement correlation function. The diagram technique is also employed to discuss the equation for the elastic constants in the pseudoharmonic approximation as well as to derive the integral equations for the quasiparticle parameters.

On Infinities in Generalized Meson-Field Theory

The results of an extension of Podolsky's generalized electrodynamics, corresponding to Proca's extension of Maxwellian electrodynamics, are presented. In this extension the Lagrangian is permitted to depend upon the field coordinates themselves, which is a major step in going from electrodynamics to meson-field theory.The static interaction and static self-energy, derived by exact classical and quantum methods, as well as the dynamic interaction and dynamic self-energy, obtained by a quantum-mechanical perturbation method, are given. The complete interaction and self-energy are free from singularities and infinities. This is in contrast with the results of ordinary relativistic meson-field theory. It thus appears that these defects may be removed from meson theory, just as in electrodynamics, by going to a generalized field theory in which the Lagrangian contains the second derivatives of the field coordinates.