Biot-Savart type magnetic field quantization via prime number theory, applications to symbolic dynamics

TL;DR

This paper introduces a prime number-based algorithm for estimating and quantizing magnetic fields in current-carrying rings, revealing new behaviors and applying to symbolic dynamics systems.

Contribution

It presents a novel prime number theory algorithm for magnetic field estimation and quantization, with applications to symbolic dynamics systems.

Findings

Magnetic field estimates agree well with Biot-Savart law calculations.

The algorithm produces quantized magnetic field values.

Reveals unique properties in waiting time distributions at quantized levels.

Abstract

In the present work we propose an algorithm based on the theory of prime numbers for the estimation of the magnetic field in a device of current carrying circular rings. Using the proposed algorithm, the magnetic field can be determined in a very good agreement with that resulting from an algorithm based on the Biot-Savart law. In addition, the prime-numbers-based algorithm gives quantized values of the magnetic field and reveals previously unknown behaviors such as special properties of the distribution of the waiting times at the quantized magnetic field values. Applications of the proposed prime-numbers-based algorithm to systems exhibiting symbolic dynamics is presented, proving its ability to provide a measure of the existence or not of dynamics in the system.