Quantum-phase-field: from de Broglie--Bohm double solution program to doublon networks

TL;DR

This paper explores phase-field equations within the de Broglie-Bohm framework, introducing doublon networks as finite space objects with potential implications for particle interactions and quantum oscillations.

Contribution

It develops a unified phase-field approach to model particles as nonlinear solutions and constructs doublon networks as elementary particle systems in higher dimensions.

Findings

Doublons are modeled as self-similar solutions of nonlinear phase-field equations.

A framework for particle interactions via charge and electromagnetic exchange is proposed.

Doublon networks form finite space objects with potential applications in quantum physics.

Abstract

We study different forms of linear and non-linear field equations, so-called `phase-field' equations, in relation to the de~Broglie-Bohm double solution program. This defines a framework in which elementary particles are described by localized non-linear wave solutions moving by the guidance of a pilot wave, defined by the solution of a Schr\"odinger type equation. First, we consider the phase-field order parameter as the phase for the linear pilot wave, second as the pilot wave itself and third as a moving soliton interpreted as a massive particle. In the last case, we introduce the equation for a superwave, the amplitude of which can be considered as a particle moving in accordance to the de~Broglie-Bohm theory. Lax pairs for the coupled problems are constructed in order to discover possible non-linear equations which can describe the moving particle and to propose a framework for investigating coupled solutions. Finally, doublons in 1+1 dimensions are constructed as self similar solutions of a non-linear phase-field equation forming a finite space-object. Vacuum quantum oscillations within the doublon determine the evolution of the coupled system. Applying a conservation constraint and using general symmetry considerations, the doublons are arranged as a network in 1+1+2 dimensions where nodes are interpreted as elementary particles. A canonical procedure is proposed to treat charge and electromagnetic exchange.