Related papers: Self-Similar Structures and Fractal Transforms in …
A scalar theory with a preferred reference frame is summarized. To test that theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has been developed. This associates a conceptual family of self-gravitating systems with…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…
Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify…
A quantum-field approach for describing many-particle Fermi systems at finite temperatures and with spontaneously broken symmetry has been proposed. A generalized model of self-consistent field (SCF), which allows one to describe the states…
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
The reader surely knows what particles physics is about: finding building blocks of nature that appear elementary at a given time and study their interactions - so why in the world this essay? The problem is how to arrive at a fundamental…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…