Renormalization group approach to chaotic strings

TL;DR

This paper develops an analytical framework for understanding the invariant density and parameter-dependent observables of chaotic strings modeled by coupled Chebychev maps, linking their complex behavior to physical theories of vacuum fluctuations.

Contribution

It provides the first analytical results for the invariant density and coupling dependence of chaotic strings, revealing their self-similar and multi-scale structure.

Findings

Analytic expressions for invariant density of chaotic strings

Identification of self-similar parameter dependence

Good agreement between theory and numerical simulations

Abstract

Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic results for the invariant density of chaotic strings, as well as for the coupling parameter dependence of given observables of the chaotic string such as the vacuum expectation value. A highly nontrivial and selfsimilar parameter dependence is found, produced by perturbative and nonperturbative effects, for which we develop a mathematical description in terms of suitable scaling functions. Our analytic results are in good agreement with numerical simulations of the chaotic dynamics.