Search results for "Series expansion"
showing 10 items of 42 documents
(F, G) -summed form of the QED effective action
2021
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F}=\frac{1}{4}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, $\mathcal{G}=\frac{1}{4}{\stackrel{\texttildelow{}}{F}}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrar…
Resummation of anisotropic quartic oscillator. Crossover from anisotropic to isotropic large-order behavior
1996
We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small negative $g$ as a series expansion in the anisotropy parameter $\delta$. From this, the large-order behavior of the $g$-expansions accompanying each power of $\delta$ are obtained by means of a dispersion relation in $g$. These $g$-expansions are summed by a Borel transformation, yielding an approximation to the ground-state energy for the region near the isotropic limit. This approximation is found to be excellent in a rather wide region of $\delta$ aro…
Effects of damage on the response of Euler-Bernoulli beams traversed by a moving mass
2003
The perturbation induced by damage in the dynamic response of Euler-Bernoulli beams traversed by a moving mass is investigated. The structure is discretized into segments of constant bending stiffness, connected together by elastic hinges representing damaged sections. The beam-moving mass interaction force is modelled in the most accurate way by taking into account the effective structural mass distribution and the convective acceleration terms, often omitted in similar studies. The analytical response is obtained through a series expansion of the unknown deflection in a basis of the beam eigenfunctions. The results of experimental tests, performed on a small-scale model of a prototype bri…
Lattice Gauge Theory Sum Rule for the Shear Channel
2010
An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $\alpha_s^2(\omega)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtr…
Study of the derivative expansions for the nuclear structure functions
2008
We study the convergence of the series expansions sometimes used in the analysis of the nuclear effects in deep inelastic scattering (DIS) processes induced by leptons. The recent advances in statistics and quality of the data, in particular for neutrinos calls for a good control of the theoretical uncertainties of the models used in the analysis. Using realistic nuclear spectral functions which include nucleon correlations, we find that the convergence of the derivative expansions to the full results is poor except at very low values of x.
Three-body correlations in electromagnetic dissociation of Borromean nuclei: The 6He case
2005
20 pages, 2 tables, 9 figures, 1 appendix.-- PACS nrs.: 25.60.-t; 27.20.+n; 25.70.De; 25.75.Gz.-- Printed version published Sep 5, 2005.
Methods for Calculating Bending Moment and Shear Force in the Moving Mass Problem
2004
Two methods able to capture with different levels of accuracy the discontinuities in the bending moment and shear force laws in the dynamic analysis of continuous structures subject to a moving system modeled as a series of unsprung masses are presented. The two methods are based on the dynamic-correction method, which improves the conventional series expansion by means of a pseudostatic term, and on an eigenfunction series expansion of the continuous system response, which takes into account the effect of the moving masses on the structure, respectively.
R-summed form of adiabatic expansions in curved spacetime
2020
The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this (non-perturbative) property of the Schwinger-DeWitt series has a natural and equivalent counterpart in the adiabatic (Parker-Fulling) series expansion of the scalar modes in an homogeneous cosmological spacetime. The equivalence between both R-summed adiabatic expansions can be further extended when a background scalar field is also present.
Monte Carlo study of the bimodal three-state Potts glass
1992
Employing Monte Carlo simulations, we compute the spin-glass susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) of the three-state Potts glass model on a simple-cubic lattice for various temperatures and lattice sizes ranging from L=4 to 10. We use the discrete \ifmmode\pm\else\textpm\fi{}J distribution for the bonds. Comparing our results with a recent high-temperature series expansion, we find a systematic deviation at lower temperatures, which cannot be explained by finite-size effects in our data. The low-temperature behavior of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) is compatible with d = 3 being the lower critical dimension of this model.
High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices
1999
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings \(\). In these star-graph expansions up to order 22 in the inverse temperature \(\), the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling Kc and the critical exponent \(\) of the spin-glass susceptibility in a large region of …