Mesoscopic Mechanics

TL;DR

This paper introduces Mesoscopic Mechanics, a new mathematical framework linked to quantum mechanics, to model emergent phenomena in planar electronic systems, and discusses its experimental relevance and connection to nonlinear field theories.

Contribution

It proposes a rigorous, space-independent mathematical model of emergent phenomena, extending the free electron model and connecting nonlinear Maxwell theory with quantum mechanics.

Findings

Provides a conceptual framework for emergent phenomena in electronic systems.

Links Mesoscopic Mechanics to nonlinear Maxwell Theory and observed phenomena.

Suggests experimental verification methods for the theory.

Abstract

This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are accomplished. First, a rigorous mathematical model is proposed of emergent character, which is conceptually bonded with Quantum Mechanics while apparently non-derivable from the many-body Schr\"{o}dinger equation. I call the resulting conceptual framework the Mesoscopic Mechanics (MeM). Its formulation is space-independent and comprises a nonlinear and holistic extension of the free electron model. Secondly, the question of relevancy of the proposed ``emergent mechanics" to the actually observed phenomena is discussed. In particular, I postulate a probabilistic interpretation, and indicate how the theory could be applied and verified by experiment. The Mesoscopic Mechanics proposed here has been deduced from the Nonlinear Maxwell Theory (NMT)--a classical in character nonlinear field theory. This latter theory has already been shown to provide a consistent phenomenological model of such phenomena as superconductivity, charge stripes, magnetic vortex lattice, and magnetic oscillations. The NMT, which arose from geometric considerations, has long been awaiting an explanation as to its ties with the fundamental principles. I believe the MeM provides at least a partial explanation to this effect.