Unified Approach to Crossover Phenomena

TL;DR

This paper introduces a universal analytical method using algebraic self-similar renormalization to describe crossover phenomena in various physical systems, especially when limited asymptotic data is available.

Contribution

The paper presents a novel, general approach for analyzing crossover phenomena using algebraic self-similar renormalization, applicable with minimal asymptotic information.

Findings

Analytical solutions for several physical crossover problems.

Method effective with few asymptotic terms.

Applicable to complex problems lacking traditional techniques.

Abstract

A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions. The method can be employed for such difficult problems for which only a few terms of asymptotic expansions are available, and no other techniques are applicable. As an illustration, analytical solutions for several important physical problems are presented.