Co-existence of states in quantum systems

TL;DR

This paper develops a mathematical framework for understanding the co-existence of multiple states in quantum systems, classifying nine distinct types, which may shed light on phenomena like phase transitions and symmetry breaking.

Contribution

It introduces a novel mathematical classification of state co-existence in quantum systems, expanding theoretical understanding of quantum phase phenomena.

Findings

Nine types of state co-existence classified

Mathematical framework for quantum states developed

Insights into phase transitions and symmetry breaking

Abstract

Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear more naturally in quantum-microscopic systems than in macroscopic systems. In this paper a mathematical theory describing co-existence of states in quantum systems is presented, and the co-existence is classified into 9 types.