Related papers: The functional $f(R)$ approximation
We summarize recent progress in understanding the role of higher-derivative terms in the asymptotic safety scenario of gravity. Extending previous computations based on the functional renormalization group approach by including a…
General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…
In this paper we use the asymptotic expansions of the binomial coefficients and the weights of the L1 approximation to obtain approximations of order $2-\alpha$ and second-order approximations of the Caputo derivative by modifying the…
The possibility of asymptotic safety scenario (asymptotic freedom) for quantum gravity has been pointed out in many contexts recently. From this point of view, we discuss some applications of cutoff identification to the black hole. If we…
We investigate perturbative aspects of gravity with a general F(R) Lagrangian, as well as nonperturbative dilatonic solutions. For the first part, we are interested in stability and the definition of asymptotic charges. The main result of…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the…
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function $\mathfrak{J}$ defined on dyadic cubes. We determine the exact upper order in terms of the critical…
The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt $f(R)$-type models of quantum gravity which display an interacting ultraviolet fixed point at…
The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by means of a reformulation of the original equilibrium theory in…
The asymptotic safety program assumes that quantum gravity becomes renormalizable through ultraviolet fixed points in metric-based couplings. We demonstrate that this approach {encounters fundamental symmetry violations} across multiple…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
Asymptotic approximations ($n \to \infty$) to the truncation errors $r_n = - \sum_{\nu=0}^{\infty} a_{\nu}$ of infinite series $\sum_{\nu=0}^{\infty} a_{\nu}$ for special functions are constructed by solving a system of linear equations.…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…