Related papers: At Which Order Should we Truncate Perturbative Ser…
We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the…
"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn…
Matrix model approach to multicolor induced QCD based on the quenched momentum prescription is presented. It is shown that this model exhibits the reduction of spatial degrees of freedom: the partition function is determined by the solution…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums…
We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. As a consequence, the kurtosis of a…
When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold.…
Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the…
The order relations of continuous cancellative t-subnorms are discussed. First, we present some necessary and sufficient conditions along with several interesting sufficient criteria for the comparability of continuous cancellative…
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…
We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and…
We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincar\'e-Lindstedt expansion. Each term of this series becomes divergent in the long time limit if…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…
It has been known for a long time that large-$N$ methods can give invaluable insights into non-perturbative phenomena such as confinement. Lattice techniques can be used to compute quantities at large $N$. In this contribution, I review…
We calculate Wilson loops of various sizes up to loop order $n=20$ for lattice sizes of $L^4 (L=4, 6, 8, 12)$ using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the…
The energy range and quality of strong-interaction data from recent years demand the study of higher orders in perturbative QCD, and of nonperturbative effects. I discuss a selection of recent progress in the theory of QCD at high energy,…
We formulate the first order corrections to processes involving the scattering or annihilation of quarks in a form in which the QCD and electroweak parts are exactly factorised. This allows for a straightforward physical interpretation of…
By studying an explicit analytical solution of the Coulomb problem on the lattice we demonstrate a breakdown of perturbative matching for the description of the Coulomb artifacts in lattice NRQCD, which leads to a large systematic error in…