Related papers: Self-consistent expansion and field-theoretic reno…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
We introduce a perturbation expansion for athermal systems that allows an exact determination of displacement fields away from the crystalline state as a response to disorder. We show that the displacement fields in energy minimized…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are…
We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow…
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…
In this paper, by utilizing the theory of matched asymptotic expansions, an efficient and accurate neural network method, named as "MAE-TransNet", is developed for solving singular perturbation problems in general dimensions, whose…
This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness we obtain a new version of Krein formula for resolvent…
Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to…
It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead…
In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for popularity of…
The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by…
In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…