Classification of the automorphisms of the noncommutative torus among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones

TL;DR

This paper classifies automorphisms of the noncommutative torus based on quantum logical depth, distinguishing between chaotic, non-chaotic shallow, and non-chaotic complex types, to understand their complexity and behavior.

Contribution

It introduces a classification of noncommutative torus automorphisms using quantum logical depth, highlighting distinctions between chaotic and non-chaotic, shallow and complex automorphisms.

Findings

Automorphisms are classified into chaotic and non-chaotic categories.

Quantum logical depth effectively differentiates automorphism complexity.

The classification reveals structural insights into noncommutative torus automorphisms.

Abstract

Adopting the measure of quantum complexity, the quantum logical depth, previously introduced by the author the automorphisms of the noncommutative torus are classified among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones.