On One Controllability of the Schrödinger Equation as Coupled with the Atomic-Level Mannesmann Effect

• Main Author: Tomáš Perna
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Symmetry
• Subjects: controllability; Schrödinger equation; field equation; cyclic group; alternating group; tunnelling
• Online Access: https://www.mdpi.com/2073-8994/12/8/1301

In this paper we outline a certain way of understanding of macroscopically uncontrollable emergence of the so called Mannesmann effect by means of its induced controllable quantum-mechanical background. In other words, we factually present a modus operandi of how to avoid macroscopic models of specific atomic-level cavity origin based consequently on a classical fracture mechanics theory. Under such circumstances, the target solution of the controllable microscopic model cannot be determined, since it can obviously arise only as a macroscopic state of the structurally disturbed rolled metal semi-product during the Mannesmann process. We obtain this irrelevance of the target solution, using a very special kind of control of the famous Schrödinger equation employed as a fundamental model equation here. We show contextually that such control follows from some very elementary aspects of the group theory conditioning a physical meaning of the Schrödinger equation written in a controllable form. We specially emerge primary cyclic groups of symmetry of special solutions to the Schrödinger equation. Their imaginary part is given by a control satisfying the Klein-Gordon equation which can be driven (through a specific avoidance of the cyclic group Z4) into a connection with the characteristic series of primary cyclic groups and/or torsion groups respectively. We obtain a physically controllable special results representing a strange correspondence between a certain LET (Linear Energy Transfer) and “quantum-like” tunnelling interpreted for some “everyday” objects, particularly for the considered Mannesmann piercing process with a torsion known from metallurgy. The process violations are shown and further reflected via a standard finite element method (FEM) simulation.